High-Energy Emission from Pulsars and their Systems

Astrophysics and Space Science Proceedings For further volumes: http://www.springer.com/series/7395 High-Energy Emis...

Author: Nanda Rea | Diego F. Torres

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Astrophysics and Space Science Proceedings

For further volumes: http://www.springer.com/series/7395

High-Energy Emission from Pulsars and their Systems Proceedings of the First Session of the Sant Cugat Forum on Astrophysics Editors

Nanda Rea Diego F. Torres

Editors Nanda Rea Institut de Ciències de l’Espai (IEEC-CSIC) Campus UAB Fac. de Ciències Torre C5, parell, 2a planta 08193 Barcelona Spain [email protected]

Diego F. Torres Institut de Ciències de l’Espai (IEEC-CSIC) Campus UAB Fac. de Ciències Torre C5, parell, 2a planta 08193 Barcelona Spain [email protected]

ISSN 1570-6591 e-ISSN 1570-6605 ISBN 978-3-642-17250-2 e-ISBN 978-3-642-17251-9 DOI 10.1007/978-3-642-17251-9 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011920988 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar S.L. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

This book is dedicated to the memory of Prof. Okkie de Jager

Preface

The Sant Cugat Forum on Astrophysics1 is a framework meant to host international meetings on violent and energetic phenomena in the Universe happening both at Galactic and extra-Galactic scales. Among the meetings hosted by the Forum, the most recognizable will be the Workshop sessions focusing on a specific aspect of astrophysics, like the one this book is about. These will typically be held every two years, with a typical size of 100 persons, hosting many plenary talks, and having a duration of about four days. The Forum has been established under the auspices of the Sant Cugat City Hall, the Institute for Space Sciences (ICE-CSIC), the Institut d’Estudis Espacials de Catalunya (IEEC), and the Institució Catalana de Recerca i Estudis Avançats (ICREA). The inaugural meeting of the Forum, which we are pleased to report on with this book, has been about the High-Energy Emission from Pulsars and their Systems. The aim of this meeting was to address, in a global context, the current knowledge and challenges on the high-energy emission from isolated and non-isolated neutron stars, as confronted with observations of both the Fermi satellite (and its main experiment: the Large Area Telescope) and the currently operating groundbased Cherenkov telescopes (like MAGIC, H.E.S.S., and VERITAS). Participants have also discussed the prospects for possible observations with planned instruments across the multi-wavelength spectrum (e.g. SKA, LOFAR, E-VLT, IXO, CTA) and how will they impact on our theoretical understanding of these systems. Following the Forum intentions, this book does not represent only the proceedings of such meeting, but also, a reflection on the state-of-the-art in the topic. The Forum enjoyed an inaugural act presided by the Sant Cugat Major, the Exmo. Sr. LLuis Recoder i Miralles, which was followed by a public talk by Prof. J. BellBurnell. This talk has been simultaneously translated from English to more than 500 attendees, among them, many local high-school students. The organizers warmly thank Prof. J. Bell-Burnell and Mr. Recoder i Miralles for their substantive support 1

Its website is http://www.ice.csic.es/research/forum . ix

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and commitment in giving the Forum such an stellar start. Also a first-timer, this meeting saw the presentation of the initial Sant Cugat Forum on Astrophysics Award given to the best presentation by a Young Scientist. It was given to Mr. Xue-Ning Bai, for his work on Modeling of gamma-ray Pulsar Light Curves from Force-Free Magnetosphere, which is included in this volume. Before putting this volume in the hands of its readers, hoping that it will contribute as a reference work of such an amazingly evolving field, it is then very appropriate, and a pleasure, to warmly thank Prof. J. Bell-Burnell, and the Scientific Organizing Committee (SOC), who have helped us shape the content and direction of the Workshop. The SOC was formed by Jonathan Arons (University of Berkeley, USA) Wlodek Bednarek (Lodz University, Poland) K. S. Cheng (Hong Kong University, China) Okkie de Jager (Potchefstroom, South Africa) Guillaume Dubus (LOAG, France) Alice Harding (NASA / GSFC, USA) Kouichi Hirotani (TIARA, Taiwan) Gianluca Israel (INAF, Italy) Simon Johnston (CSIRO, Australia) Sandro Mereghetti (IASF, Italy) Nanda Rea (IEEC-CSIC, Spain) Olaf Reimer (Innsbruck University, Austria) Diego F. Torres (ICREA / IEEC-CSIC, Spain). The meeting would have been impossible without the help of the local organization, which was formed by Anna Bertolin (IEEC) Andrea Caliandro (IEEC-CSIC) LLu´ıs Campins i Punter (Museu Monastir, Sant Cugat) Ana Castells (Casa de la Cultura, Sant Cugat) Aida Chavarr´ıa (Teatro Auditori, Sant Cugat) Marta de Castro (Oficina de Turismo, Sant Cugat) Elsa de Cea (IEEC-CSIC) Valent´ı Feixas i Sibila (Sant Cugat City Hall, Spain) Daniela Hadasch (IEEC-CSIC) Pilar Montes (IEEC) Delfi Nieto (IEEC) and especially, without the support of our sponsors: the Institució Catalana de Recerca i Estudis Avançats (ICREA), who presented us with its prestigious Conference Award for the organization of this meeting, the Institut d’Estudis Espacials de Catalunya (IEEC), the Institute for Space Sciences (ICE-CSIC), and the Agència de

Preface

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Gestió de Ajuts Universitaris i de Recerca (AGAUR). The Forum logo and artwork were created by Anna Pedescoll and Ignasi Sans, from the Sant Cugat City Hall Communication Department, to whom we are indebted.

Some ideas can never flourish without the far-reaching vision of those extraordinary persons that provide unfading support to projects that otherwise could only be qualified as chimeras. In this case, this person is Valent´ı Feixas i Sibila, Director of Cultural Affairs of the Sant Cugat City Hall.

Sant Cugat September 2010

Nanda Rea Diego F. Torres

Contents

Radio Pulsar Phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simon Johnston and Aris Karastergiou 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Observational Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Integrated profiles and polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Pulse width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Profile shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Linear polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Position angle swing and orthogonal modes . . . . . . . . . . . 3.5 Circular polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Rotating Vector Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Problems and Perils of the RVM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Radius-to-Frequency mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Velocity - spin axis alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Beam models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Rankin et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Lyne & Manchester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Karastergiou & Johnston . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Two Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 The radio loud magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Pulsars with notches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Future instruments and the Square Kilometre Array . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radio pulsar populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Duncan R. Lorimer 1 Selection effects in radio pulsar surveys . . . . . . . . . . . . . . . . . . . . . . . 1.1 Flux–distance relationship . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The radio sky background . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Propagation effects in the interstellar medium . . . . . . . . . .

1 1 2 4 5 5 6 7 7 8 10 11 12 12 12 13 14 14 14 15 16 17 18 21 21 22 22 22

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1.4 Finite size of the emission beam . . . . . . . . . . . . . . . . . . . . . 1.5 Pulse nulling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Intermittency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Correcting the biases in the observed sample . . . . . . . . . . . . . . . . . . 3 Recent results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Pulsar space distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Pulsar velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Pulsar luminosities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Magnetic alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Magnetic field decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Final thoughts and future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Rotating radio transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Millisecond pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Pulsars in the Magellanic Clouds . . . . . . . . . . . . . . . . . . . . 4.4 Globular cluster pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23 24 24 24 26 26 28 28 30 31 32 32 32 33 33 34

Pulsar Results with the Fermi Large Area Telescope . . . . . . . . . . . . . . . . . . . . Paul S. Ray and Pablo M. Saz Parkinson for the Fermi LAT Collaboration, the LAT Pulsar Timing Consortium, and the LAT Pulsar Search Consortium 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Gamma-ray Pulsars in the Year 2000 . . . . . . . . . . . . . . . . . 1.2 Fermi and AGILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The EGRET Pulsars in Exquisite Detail . . . . . . . . . . . . . . . . . . . . . . . 3 Young Pulsars Found Using Radio Ephemerides . . . . . . . . . . . . . . . 4 Millisecond Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Radio MSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Searches of LAT Unassociated Sources . . . . . . . . . . . . . . . 4.3 Globular Cluster MSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Blind Periodicity Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Pulsar Timing with the LAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Multiwavelength Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 The LAT Pulsar Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Future Expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Fermi view of the EGRET pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Gargano for the Fermi-LAT collaboration 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Analysis results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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37 37 38 39 42 42 43 44 45 46 48 49 52 54 55

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“Garden-variety” Gamma-ray Pulsars J0248+6021 & J2240+5832 . . . . . . David A. Smith for the Fermi LAT Collaboration 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Two Not-So-Typical Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 About those distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Understanding the Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Extension studies of galactic sources with Fermi . . . . . . . . . . . . . . . . . . . . . . . Francesco Giordano on behalf of the Fermi-LAT Collaboration 1 The simulated cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Galactic extended SNRs: the W51C, the W44 and the IC443 . . . . . 3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Advances in understanding double features in radio pulsar profiles . . . . . . Jarosław Dyks, Bronisław Rudak and Paul Demorest 1 The Double Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Emission from the Polar Cap and Slot Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alice K. Harding and Isabelle A. Grenier 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Polar cap and slot gap electrodynamics . . . . . . . . . . . . . . . . . . . . . . . 2.1 Polar cap pair cascades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The slot gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Geometry of high-energy radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Confronting the Fermi observations . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Population synthesis and light curve fitting . . . . . . . . . . . . 4.3 New insights from the increasing γ-ray MSP Population . 5 Learning from Nature - Future pulsar modeling . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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63 64 64 65 66 67

69 72 73 73

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79 80 81 82 84 85 86 87 94 96 97

Gamma-ray emission and pair creation of outer gap . . . . . . . . . . . . . . . . . . . . 99 K. S. Cheng 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 2 Two dimensional outergap model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 2.1 Gap structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 2.2 Curvature radiation spectrum . . . . . . . . . . . . . . . . . . . . . . . . 103 2.3 Properties of curvature spectra with gap parameters . . . . . 104 2.4 Fitting Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3 Pair creation mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.1 Photon-photon pair-creation process . . . . . . . . . . . . . . . . . . 108

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3.2 New gap closure mechanism . . . . . . . . . . . . . . . . . . . . . . . . 109 3.3 Predictions of new outer gap model . . . . . . . . . . . . . . . . . . 112 4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 What Pulsar High-Energy Emission Model Survives? . . . . . . . . . . . . . . . . . . 117 Kouichi Hirotani 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 2 Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 2.1 Poisson Equation for Electrostatic Potential . . . . . . . . . . . . 120 2.2 Particle Boltzmann Equations . . . . . . . . . . . . . . . . . . . . . . . 122 2.3 Radiative Transfer Equation . . . . . . . . . . . . . . . . . . . . . . . . . 123 2.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3 Self-consistent OG solution: the case of the Crab pulsar . . . . . . . . . 125 3.1 Gap geometry and acceleration electric field . . . . . . . . . . . 125 3.2 Photon mapping result and radiation spectrum . . . . . . . . . 125 4 Slot-gap model: the case of the Crab pulsar . . . . . . . . . . . . . . . . . . . . 126 4.1 Formation of a slot gap in the polar-cap region . . . . . . . . . 127 4.2 Lower-altitude slot-gap solution . . . . . . . . . . . . . . . . . . . . . 129 4.3 Higher-altitude slot-gap model . . . . . . . . . . . . . . . . . . . . . . 130 5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 Current Models of Pulsar Magnetospheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Anatoly Spitkovsky 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 2 Plasma supply and charge-separated models . . . . . . . . . . . . . . . . . . . 140 3 Force-free models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4 Implications of the magnetospheric solutions . . . . . . . . . . . . . . . . . . 149 4.1 Consequences for spin down . . . . . . . . . . . . . . . . . . . . . . . . 149 4.2 High energy emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.3 Reconnection and time-dependence . . . . . . . . . . . . . . . . . . 153 4.4 Current structure and origin . . . . . . . . . . . . . . . . . . . . . . . . . 154 4.5 Differential rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 Modeling of γ-ray Pulsar Light Curves from Force-Free Magnetosphere . . 159 Xue-Ning Bai & Anatoly Spitkovsky References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 A Tale of Two Current Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Jonathan Arons 1 Follow The Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 2 Follow the Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

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The high-energy emission from the pulsar striped wind . . . . . . . . . . . . . . . . . 181 Jérôme Pétri 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 2 The striped wind model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 3 Application to γ-ray pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 Gamma-rays from millisecond pulsars in Globular Clusters . . . . . . . . . . . . . 185 Włodek Bednarek 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 2 The stellar content of Globular Clusters . . . . . . . . . . . . . . . . . . . . . . . 186 3 Compact objects within Globular Clusters . . . . . . . . . . . . . . . . . . . . . 187 3.1 Millisecond pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 3.2 Cataclysmic Variables and LMXBs . . . . . . . . . . . . . . . . . . . 188 3.3 Intermediate mass black holes ? . . . . . . . . . . . . . . . . . . . . . 188 4 Non-thermal emission from Globular Clusters . . . . . . . . . . . . . . . . . 189 4.1 Low energy radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.2 Gamma-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 5 Models for gamma-ray emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 5.1 Interpretation of the observed GeV γ-ray emission . . . . . . 192 5.2 TeV γ-ray emission from MSP winds and shocks . . . . . . . 193 5.3 Constraints on the MSP population . . . . . . . . . . . . . . . . . . . 197 6 Gamma-rays from electrons injected from other sources ? . . . . . . . 200 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 Modelling the Growing Population of γ-ray Millisecond Pulsars . . . . . . . . . 207 C. Venter, A. K. Harding, and T. J. Johnson 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 2 Pulsar Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 4 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 A Joint Radio Gamma-ray Variability Study of the Crab Pulsar . . . . . . . . . 213 Glenn Jones and Ryan Shannon 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 2 Radio Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 2.1 Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 3 Gamma-Ray Radio Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

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AGILE observations of PSR B1509-58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 M. Pilia and A. Pellizzoni for the AGILE Team and Pulsar Working Group 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 2 AGILE Observations, Data Analysis and Results . . . . . . . . . . . . . . . 220 3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Understanding the fundamental parameters of millisecond pulsars . . . . . . 225 Benoit Pancrazi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 2 Observations and data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3 Discussion and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Pulsars as gravitational wave detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 George Hobbs 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 2 Using pulsars to search for GWs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 3 Current data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234 4 Potential sources of gravitational waves . . . . . . . . . . . . . . . . . . . . . . . 236 4.1 Single sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236 4.2 Burst sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238 4.3 Stochastic background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 5 Accessing pulsar data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 6 The future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 Magnetar outbursts: an observational review . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Nanda Rea & Paolo Esposito 1 Author’s preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 2 A bit of history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 3 General observational characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 250 4 Multiband view of magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 4.1 Radio emission of magnetars . . . . . . . . . . . . . . . . . . . . . . . . 251 4.2 Optical and infrared emission of magnetars . . . . . . . . . . . . 253 4.3 Soft X-ray emission of magnetars . . . . . . . . . . . . . . . . . . . . 253 4.4 Hard X-ray emission of magnetars . . . . . . . . . . . . . . . . . . . 254 5 Magnetars’ Outbursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 5.1 XTE J1810−197 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 5.2 1E 1547−5408 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 5.3 AX J1844−0258 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 5.4 1E 2259+586 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 5.5 1E 1048.1−5937 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 5.6 CXOU J1647−4552 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 5.7 4U 0142+614 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

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5.8 SGR 1806−20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 5.9 SGR 1627−41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 5.10 SGR 0501+4516 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 5.11 SGR 0418+5729 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 5.12 SGR 1833−0832 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Wide-band X-ray Studies of Magnetars with Suzaku . . . . . . . . . . . . . . . . . . . 275 T. Enoto, K. Makishima, N. Rea, Y. E. Nakagawa, K. Nakazawa, and T. Sakamoto 1 Suzaku Observations of Magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 2 Spectral Evolution of Magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Bursts and Flares from Highly Magnetic Pulsars . . . . . . . . . . . . . . . . . . . . . . . 279 GianLuca Israel and Simone Dall’Osso 1 MAGnetic NEutron sTARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 2 SGRs Giant Flares and their magnetic fields . . . . . . . . . . . . . . . . . . . 282 2.1 The Cavallo-Fabian-Rees Variability Limit . . . . . . . . . . . . 284 3 SGRs Intermediate Flares in the Swift era . . . . . . . . . . . . . . . . . . . . . 285 3.1 The March 2006 Burst Storm of SGR 1900+14 . . . . . . . . 287 3.2 Further Observations: the case of SGR 0501+4516 and 1E 1547.0-5408 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Activated Magnetospheres of Magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 Andrei M. Beloborodov 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 2 Electrodynamics of untwisting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 2.1 Evolution equation for axisymmetric twist . . . . . . . . . . . . . 301 2.2 j-bundle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 3 Transient magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 3.1 Magnetospheric activity or deep crustal heating? . . . . . . . 306 3.2 Individual objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 4 Pair creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 5 Plasma circulation in the magnetosphere . . . . . . . . . . . . . . . . . . . . . . 313 6 Magnetospheric emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

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Suzaku Detection of Hard X-ray Emission in SGR 0501+4516 Short Burst Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Yujin E. Nakagawa, Teruaki Enoto, Kazuo Makishima, Atsumasa Yoshida, Kazutaka Yamaoka, Takanori Sakamoto, Nanda Rea, Kevin Hurley, Suzaku SGR 0501+4516 Team and HETE-2 Team 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 2 Hard X-ray Emission in Burst Spectra . . . . . . . . . . . . . . . . . . . . . . . . 324 3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 The magnetar emission in the IR band: the role of magnetospheric currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Silvia Zane, Luciano Nobili and Roberto Turolla 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 2 Pair production in the inner magnetosphere . . . . . . . . . . . . . . . . . . . . 330 3 IR/Optical emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 Double features in mean pulsar profiles and the nature of their radio emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 George I. Melikidze and Janusz Gil 1 Frequency dependence of the bifurcation angle . . . . . . . . . . . . . . . . 337 2 Energy considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Can the magnetic field of long-period X-ray pulsars be supercritical ? . . . . 341 N.R. Ikhsanov and N.G. Beskrovnaya 1 Magnetar hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 2 Feedback hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 X-ray emission from isolated neutron stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 Sandro Mereghetti 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 2 Origin of the X-ray emission in isolated neutron stars . . . . . . . . . . . 347 3 The X-ray Dim Isolated Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . 348 4 Central Compact Objects in Supernova Remnants . . . . . . . . . . . . . . 351 5 The Magnetar candidates: Anomalous X-ray Pulsars and Soft Gamma-ray Repeaters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 6 Rotating Radio Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 7 Rotation-powered pulsars with high magnetic field . . . . . . . . . . . . . 357 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

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X-ray thermal radiation from hot polar cap in pulsars . . . . . . . . . . . . . . . . . . 365 Janusz Gil and George I. Melikidze 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 2 Surface magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 3 Drifting subpulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 Radio polarization of RRAT J1819-1458 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 A. Karastergiou 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 2 Polarization characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 3 Discussion and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 Multiwavelength Observations of Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . 373 Patrick Slane 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 2 Dynamical Evolution of PWNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 3 Spectral Evolution of PWNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 4 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 4.1 3C 58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 4.2 Vela X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 4.3 G327.1−1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 4.4 HESS J1640−465 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 Multi-wavelength Observations of Composite Supernova Remnants . . . . . . 393 Tea Temim 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 2 G54.1+0.3: Expansion into SN Ejecta . . . . . . . . . . . . . . . . . . . . . . . . 394 3 G327.1-1.1: Interaction with the Reverse Shock . . . . . . . . . . . . . . . . 395 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 Fermi-LAT Results on Pulsar Wind Nebulae after 1.5 year of Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 M.-H. Grondin & M. Lemoine-Goumard for the Fermi-LAT Collaboration and the Pulsar Timing Consortium 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 2 The Crab Nebula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 3 The Vela-X PWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 4 The PWN in MSH 15−52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 5 PSR J1907+0602 and its TeV PWN . . . . . . . . . . . . . . . . . . . . . . . . . . 404 6 The PWN HESS J1640-465 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

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A plausible pulsar wind nebula candidate powered by PSR J1023-5746 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 410

Pulsar Wind Nebulae: The GeV to TeV Connection . . . . . . . . . . . . . . . . . . . . 413 O. C. de Jager 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 2 The Crab Nebula in γ-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414 2.1 The acceleration limit for electrons in the Crab Nebula . . 414 2.2 The inverse Compton spectrum of the Crab Nebula towards the spectral tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 3 Accelerated PWN Spectra: Observations of the Cooling Effect . . . 417 4 A Single Spectral Component for the GeV to TeV Emission from the PWN of PSR B1509-58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419 5 Calorimetric GeV emission from PWN . . . . . . . . . . . . . . . . . . . . . . . 421 6 Discontinuous GeV and TeV Emission from Two-Component PWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 6.1 Two-Component Extended Emission from the Vela X PWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 6.2 Radio and X-Ray Torii of Vela X near the Termination Shock: Discontinuous Spectra . . . . . . . . . . . . . . . . . . . . . . . 422 7 HESS J1640–465: Another Two-Component Candidate? . . . . . . . . 424 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 Extended hard X-ray emission from Vela X . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Fabio Mattana, Régis Terrier, Diego Götz, Gabriele Ponti, Laurent Bouchet, Maurizio Falanga, Matthieu Renaud, Stephane Schanne 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 2 INTEGRAL identification of extended hard X-ray emission . . . . . . 432 3 Combined IBIS/ISGRI and Suzaku/XIS spectral analysis . . . . . . . . 434 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Cherenkov Telescopes Results on Pulsar Wind Nebulae and Pulsars . . . . . . 435 Emma de Oña Wilhelmi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 2 IACT Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 3 Observations of pulsars with IACTs . . . . . . . . . . . . . . . . . . . . . . . . . . 440 4 Observations of PWNe with Cherenkov telescopes . . . . . . . . . . . . . 441 4.1 Young/Composite Pulsar Wind Nebula . . . . . . . . . . . . . . . . 444 4.2 ”Relic” Pulsar Wind Nebula . . . . . . . . . . . . . . . . . . . . . . . . . 447 4.3 Other PWNe candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

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Lepton Acceleration in Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Matthew G. Baring 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 2 Lepton Acceleration at Relativistic Shocks . . . . . . . . . . . . . . . . . . . . 455 2.1 The Monte Carlo Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 2.2 Results for Relativistic Shock Acceleration . . . . . . . . . . . . 458 3 The Quasi-Perpendicular Pulsar Wind Termination Shock . . . . . . . 464 4 Connecting to PWN Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 MHD models of Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 Niccolò Bucciantini 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 2 Jet-Torus structure and Inner flow properties . . . . . . . . . . . . . . . . . . . 475 2.1 Time variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 2.2 Gamma rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 3 Evolution of PWNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 TeV Gamma Ray Survey on the Direction of Fermi-LAT Pulsars with the Tibet Air Shower Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 M. Amenomori, X. J. Bi, D. Chen, S. W. Cui, Danzengluobu, L. K. Ding, X. H. Ding, C. Fan, C. F. Feng, Zhaoyang Feng, Z. Y. Feng, X. Y. Gao, Q. X. Geng, Q. B. Gou, H. W. Guo, H. H. He, M. He, K. Hibino, N. Hotta, Haibing Hu, H. B. Hu, J. Huang, Q. Huang, H. Y. Jia, L. Jiang, F. Kajino, K. Kasahara, Y. Katayose, C. Kato, K. Kawata, Labaciren, G. M. Le, A. F. Li, H. C. Li, J. Y. Li, C. Liu, Y.-Q. Lou, H. Lu, X. R. Meng, K. Mizutani, J. Mu, K. Munakata, H. Nanjo, M. Nishizawa, M. Ohnishi, I. Ohta, S. Ozawa, T. Saito, T. Y. Saito, M. Sakata, T. K. Sako, M. Shibata, A. Shiomi, T. Shirai, H. Sugimoto, M. Takita, Y. H. Tan, N. Tateyama, S. Torii, H. Tsuchiya, S. Udo, B. Wang, H. Wang, Y. Wang, Y. G. Wang, H. R. Wu, L. Xue, Y. Yamamoto, C. T. Yan, X. C. Yang, S. Yasue, Z. H. Ye, G. C. Yu, A. F. Yuan, T. Yuda, H. M. Zhang, J. L. Zhang, N. J. Zhang, X. Y. Zhang, Y. Zhang, Yi Zhang, Ying Zhang, Zhaxisangzhu, and X. X. Zhou (The Tibet ASγ Collaboration) 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 2 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Fermi results on γ-ray binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Adam B. Hill, Richard Dubois, and Diego F Torres for the Fermi-LAT collaboration 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 2 LS I +61 303 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

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The original discovery, and further TeV observations: flux, spectrum, periodicity . . . . . . . . . . . . . . . . . . . . . . . . . . 498 2.2 TeV and X-ray simultaneous observations . . . . . . . . . . . . . 499 2.3 The Fermi results on LS I +61◦ 303 . . . . . . . . . . . . . . . . . . . 500 3 LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 3.1 The original discovery, and further TeV observations: flux, spectrum, periodicity . . . . . . . . . . . . . . . . . . . . . . . . . . 502 3.2 The Fermi results on LS 5039 . . . . . . . . . . . . . . . . . . . . . . . 503 4 Cygnus X-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 4.1 Historical observations at high energies . . . . . . . . . . . . . . . 503 4.2 The Fermi results on Cygnus X-3 . . . . . . . . . . . . . . . . . . . . 504 5 Cygnus X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 5.1 Reports of high energy and very high energy emission . . . 508 6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 Cherenkov Telescope results on gamma-ray binaries . . . . . . . . . . . . . . . . . . . 513 Juan Cortina 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 2 Detected in VHE: PSR B1259-63, LS 5039 and LS I+61◦303 . . . . 514 2.1 PSR B1259-63/SS2833 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 2.2 LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 2.3 LS I+61◦ 303 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517 3 Uncertain VHE binaries: Cyg X-1 and HESS J0632+057 . . . . . . . . 519 3.1 Cyg X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 3.2 HESS J0632+057 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521 4 Searches for other VHE binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 4.1 Cyg X-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 γ-ray binaries as non-accreting pulsar systems . . . . . . . . . . . . . . . . . . . . . . . . . 531 Diego F. Torres 1 Prologue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 2 Why is a non-accreting pulsar system a tenable alternative? . . . . . . 532 3 Caveats in the search for X-ray spectral lines . . . . . . . . . . . . . . . . . . 538 4 Caveats in the search for pulsations . . . . . . . . . . . . . . . . . . . . . . . . . . 540 5 Notes on the theoretical models based on pulsar systems . . . . . . . . 542 5.1 A perspective on the GeV cutoffs of LS I +61◦ 303 and LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 6 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 548

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Relativistic motion and beamed radiation in gamma-ray binaries . . . . . . . . 551 Benoˆıt Cerutti, Guillaume Dubus, and Gilles Henri 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 2 Observational backdrop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552 3 Doppler-boosted emission in LS 5039 and LS I +61 303 . . . . . . . . . 552 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 A leptonic One-Zone model of the X-Ray/VHE correlated emission in LS I +61 303 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 V. Zabalza, J.M. Paredes and V. Bosch-Ramon 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 2 Model description and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558 New Optical Results on γ-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 J. Casares, J.M. Corral-Santana, A. Herrero, J.C. Morales, T. Muñoz-Darias, I. Negueruela, J.M. Paredes, I. Ribas, M. Ribó, D. Steeghs, L. van Spaandonk and F. Vilardell 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559 2 Revised Orbital Solution in LS 5039 . . . . . . . . . . . . . . . . . . . . . . . . . 560 3 Probing Binarity in MWC 148 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 The International X-ray Observatory and other X-ray missions, expectations for pulsar physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 Yukikatsu Terada and Tadayasu Dotani 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 2 Future X-ray Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 2.1 Overview of X-ray Missions . . . . . . . . . . . . . . . . . . . . . . . . 565 2.2 The Small Satellite Missions in 2010s . . . . . . . . . . . . . . . . 566 2.3 The ASTRO-H Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 2.4 The International X-ray Observatory . . . . . . . . . . . . . . . . . 569 3 Pulsar Sciences with Future X-ray Missions . . . . . . . . . . . . . . . . . . . 570 3.1 General relativity under strong gravity . . . . . . . . . . . . . . . . 570 3.2 Equation of State in neutron stars . . . . . . . . . . . . . . . . . . . . 572 3.3 Plasma physics under a strong magnetic field . . . . . . . . . . 573 3.4 Emission mechanism from Magnetars . . . . . . . . . . . . . . . . 575 3.5 Diversity of Pulsar systems: white dwarf pulsars . . . . . . . . 577 4 Synergy with other wavelength observatories . . . . . . . . . . . . . . . . . . 580 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581

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X-ray Polarimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 Marco Feroci and Paolo Soffitta 1 Neutron Stars Science with X-ray Polarimetry . . . . . . . . . . . . . . . . . 585 2 Fundamental Parameters of X-ray Polarimetry . . . . . . . . . . . . . . . . 587 3 Classical Techniques and Observational Status . . . . . . . . . . . . . . . . 588 3.1 Bragg Polarimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588 3.2 Thompson/Compton Polarimeters . . . . . . . . . . . . . . . . . . . . 591 3.3 Observational results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 4 A jump in sensitivity: the focal plane photoelectric polarimeters for soft X-rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595 4.1 The Gas Pixel Detector (GPD) solution . . . . . . . . . . . . . . . 597 4.2 The Time Projection Chamber (TPC) polarimeter solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598 5 Observational Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 5.1 Gravity and Extreme Magnetism SMEX (GEMS) . . . . . . 600 5.2 New Hard X-ray Mission (NHXM) . . . . . . . . . . . . . . . . . . . 601 5.3 International X-ray Observatory (IXO) . . . . . . . . . . . . . . . . 604 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 New results on high energy cosmic ray electrons observed with Fermi LAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 Alexander Moiseev, on behalf of the Fermi LAT Collaboration 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 2 Detection of electrons by LAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612 3 Result and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 5 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 620 Positrons from pulsar winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 Pasquale Blasi and Elena Amato 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 2 A pulsar wind inside a supernova remnant . . . . . . . . . . . . . . . . . . . . . 626 3 A pulsar wind escaping the parent supernova remnant: bow shock nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 4 The positron flux from pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631 5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640

List of Contributors

Aliu Ester Barnard College / Columbia University Department of Physics and Astronomy Barnard College Columbia University New York NY 10027 USA [email protected] Arons Jonathan University of California Berkeley Astronomy Department 601 Campbell Hall Berkeley CA 94720-3411 [email protected] Bai Xue-Ning Princeton University Dept. of Astrophysical Sciences Peyton Hall Princeton University Princeton NJ 08544 USA [email protected] Baring Matthew Rice University Rice University Department of Physics and Astronomy - MS 108 P. O. Box 1892 Houston Texas 77251-1892 USA [email protected] Bates Samuel University of Manchester 7 Catterick Road Didsbury Manchester M20 6HN UNITED KINGDOM [email protected] Bednarek Wlodek Department of Astrophysics University of Lodz Department of Astrophysics University of Lodz ul. Pomorska 149 / 153 90-236 Lodz Poland [email protected] Bell-Burnell Jocelyn Oxford University Department of Physics Denys Wilkinson Building Keble Road Oxford OX1 3RH [email protected] Beloborodov Andrei Columbia University Physics Department 1013 Pupin Hall MC 5204 Box 04 538 W 120 St New York NY 10027 [email protected]

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Blasi Pasquale INAF / Aretri Astrophysical Observatory INAF / Osservatorio Astrofisico di Arcetri Largo E. Fermi 5 50125 Firenze Italy [email protected] Bronek Rudak Nicolaus Copernicus Astronomical Center Rabianska 8 87-100 Torun Poland [email protected]

Bucciantini Niccoló NORDITA / Albanova NORDITA Roslagstullsbacken 23 106 91 Stockholm [email protected] Burgay Marta INAF - Cagliari Observatory [email protected] Caliandro G. Andrea Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected]

Cañellas i Pagès, Albert Universitat de Barcelona Departament d’Astronomia i Meteorologia Facultat de Fsica 7a planta Universitat de Barcelona Mart i Franqus 1 08028 Barcelona Spain [email protected] Carramiñana Alberto INAOE Instituto Nacional de Astrofsica ptica y Electrnica Lus Enrique Erro 1 Tonantzintla Puebla 72840 Mxico [email protected] Casares Jorge IAC Instituto de Astrofisica de Canarias c / Via Lactea s / n 38200-La Laguna Tenerife [email protected] Celotti Anna Lisa SISSA Head of Astrophysics Sector via Beirut 2-4 34151 Trieste Italy [email protected] Cerutti Benoit Laboratoire d’Astrophysique de Grenoble Laboratoire d’Astrophysique Observatoire de Grenoble BP 53 F-38041 GRENOBLE Cdex 9 FRANCE [email protected] Cheng KS Department of Physics University of Hong Kong 530 Chong Yuet Ming Physics Bldg The University of Hong Kong Pokfulam Road Hong Kong [email protected] Coenen Thijs Universiteit van Amsterdam Plantage Kerklaan 16-II Amsterdam The Netherlands [email protected]


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Cortina Juan IFAE Institut de Fisica d’Altes Energies - IFAE Edifici Cn. UAB 08193 Bellaterra (Barcelona Spain). [email protected] de Cea Elsa Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected] de Jager Okkie North-West University Physics Department North-West University Potchefstroom South Africa 2520 [email protected]

de Oña Wilhelmi Emma Max-Planck-Institut fur KernPhysik Max-Planck-Institut fr Kernphysik Saupfercheckweg 1 69117 Heidelberg Germany [email protected] Dhillon Vik University of Sheffield Department of Physics and Astronomy University of Sheffield Sheffield S3 7RH [email protected] Dubois Richard SLAC MS 71 2575 Sandhill Road Menlo Park CA USA 94025 [email protected] Dumora Denis CEN Bordeaux-Gradignan / Universit Bordeaux 1 CENBG chemin du Solarium 33175 Gradignan Cedex [email protected] Dyks Jaroslaw Copernicus Astronomical Center ”Centrum Astronomiczne im. M. Kopernika Rabianska 8 87-100 Torun Poland” [email protected] Enoto Teruaki Tokyo University Department of Physics Graduate School of Science The University of Tokyo Hongo 7-3-1 Bunkyo-ku Tokyo 113-0033 Japan [email protected] Feroci Marco INAF / IASF ”INAF - ISTITUTO DI ASTROFISICA SPAZIALE E FISICA COSMICA Via Fosso del Cavaliere 100 00133 Rome ITALY” [email protected] Freire Paulo MPI Bonn Max-Planck-Institut fr Radioastronomie Auf dem Hgel 69 D-53121 Bonn Germany [email protected] Gargano Fabio INFN-Bari Via Orabona 4 70126 Bari Italy [email protected] Giavitto Gianluca IFAE Institut de Fsica d’Altes Energies Edifici Cn. Facultat Cincies UAB E-08193 Bellaterra Spain [email protected]

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Gil Janusz Institute of Astronomy University of Zielona Gora Institute of Astronomy University of Zielona Gora 65-265 Giordano Francesco Physics Department / INFN / Bari Via Amendola 173 I-70126 Bari - Italy [email protected] Grenier Isabelle AIM University Paris Diderot & CEA Saclay AIM Service d’Astrophysique CEA Saclay 91191 Gif sur Yvette France [email protected] Grondin Marie-Helene CENBG / CNRS-IN2P3 ”Centre d’Etudes Nucleaires de Bordeaux Gradignan Chemin du Solarium 33170 Gradignan France” [email protected] Hadasch Daniela Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected] Hermsen Wim SRON Netherlands Insitute for Space Research SRON Sorbonnelaan 2 3584 CA Utrecht [email protected] Hessels Jason ASTRON P.O. Box 2 990AA Dwingeloo The Netherlands” [email protected] Hirotani Kouichi TIARA TIARA 8F General bldg 2 Department of Physics National Tsing Hua University 101 Sec. 2 Kuang Fu Rd. Hsinchu Taiwan 300 [email protected] Hobbs George Australia Telescope National Facility CSIRO Australia Telescope National Facility PO Box 76 Epping NSW 1710 Australia [email protected] Ikhsanov Nazar NASA / Marshall Space Flight Center 320 Sparkman Drive Huntsville AL 35805 nazar [email protected] Israel GianLuca INAF - Roma Astronomical Observatory Via Frascati 33 Monte Porzio Catone (RM) I-00040 ITALY [email protected] Johnston Simon ATNF CSIRO ATNF CSIRO PO Box 76 Epping New South Wales 1710 Australia [email protected] Jones Glenn NRAO / Caltech Caltech MC 136-93 1200 E. California Blvd. Pasadena CA 91125 jones [email protected]


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Karastergiou Aris University of Oxford Oxford Astrophysics Denys Wilkinson Building Keble Road Oxford OX1 3RH UK [email protected] Kawata Kazumasa ICRR University of Tokyo Institute for Cosmic Ray Research University of Tokyo 5-1-5 Kashiwanoha Kashiwa Chiba 277-8582 Japan [email protected] Keane Evan University of Manchester Room 3.224 Alan Turing Building Jodrell Bank Centre for Astrophysics University of Manchester Manchester M13 9PL [email protected] Kirk John Max-Planck-Institut fuer Kernphysik Postfach 103980 69029 Heidelberg Germany [email protected] Klepser Stefan IFAE Spain Institut de Fsica d’Altes Energies Edifici Cn. Facultat Cincies UAB E-08193 Bellaterra Spain [email protected] Kondratiev Vladislav ASTRON ASTRON P.O. Box 2 7990 AA Dwingeloo The Netherlands [email protected] Kuiper Lucien SRON-The Netherlands Sorbonnelaan 2 3584-CA Utrecht The Netherlands [email protected] Lemoine-Goumard Marianne CENBG - CNRS-IN2P3 CENBG Chemin du Solarium BP120 33175 Gradignan Cedex France [email protected] Lorenz Eckart MPI Physics Munich Max Planck Inst. for Physics Foehringer Ring 6 D 80805 MUNICH [email protected] Lorimer Duncan West Virginia University Physics Department 210 Hodges Hall Morgantown WV 26501 [email protected] Mattana Fabio APC (CNRS-Universit Paris 7) Laboratoire APC Btiment Condorcet 10 rue Alice Domon et Lonie Duquet 75205 Paris Cedex 13 France [email protected] Melikidze George Institute of Astronomy University of Zielona Gora ”Institute of Astronomy Lubuska 2 65-265 Zielona Gora Poland” [email protected] Mereghetti Sandro IASF MILANO / INAF IASF via Bassini 15 20133 Milano Italy [email protected]

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Moiseev Alexander NASA / GSFC NASA / GSFC code 661 Greenbelt MD 20771 USA [email protected]

Moldón Javier Universitat de Barcelona Departament d’Astronomia i Meteorologia Facultat de Fsica Planta 7 Universitat de Barcelona Mart i Franqus 08028 Barcelona Spain [email protected] Nakagawa Yujin Institute of Physical and Chemical Research Makishima Cosmic Radiation Laboratory RIBF Bldg. 4F Higashi-Chiku (RIKEN) 2-1 Hirosawa Wako Saitama 351-0198 Japan [email protected] Nobili Luciano University of Padova ”Dip. di Fisica ””G.Galilei”” Via Marzolo 8 35131 Padova Italy” [email protected] Pancrazi Benoit CESR Toulouse 6 rue Duplex 87000 Limoges France [email protected] Paredes Josep Maria Universitat de Barcelona Departament d’Astronomia i Meteorologia Facultat de Fsica Planta 7 Universitat de Barcelona Mart i Franqus 08028 Barcelona Spain [email protected] Pellizzoni Alberto INAF-Osservatorio Astronomico di Cagliari INAF-Osservatorio Astronomico di Cagliari loc. Poggio dei Pini strada 54 I-09012 Capoterra (CA) ITALY [email protected] Pessah Martin Institute for Advanced Study Institute for Advanced Study School of Natural Sciences Bloomberg Hall 253 Princeton NJ 08540 [email protected] Pétri Jerome Observatoire Astronomique de Strasbourg Observatoire Astronomique de Strasbourg 11 rue de l’Universit 67000 Strasbourg [email protected] Pierbattista Marco AIM Sap CEA Saclay AIM Service d’Astrophysique CEA Saclay 91191 Gif / Yvette France [email protected] Pilia Maura Universit degli Studi dell’Insubria INAF c / o Dottorandi di Astrofisica via Valleggio 11 22100 Como ITALY [email protected] Ray Paul Naval Research Laboratory Code 7655.4 4555 Overlook Ave. SW Washington DC 20375-5352 USA [email protected]


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Ribó Marc Universitat de Barcelona Departament d’Astronomia i Meteorologia Facultat de Fsica 7a planta Universitat de Barcelona Mart i Franqus 1 08028 Barcelona Spain [email protected] Saz Parkinson Pablo Santa Cruz Institute for Particle Physics 715 Koshland Way Santa Cruz CA 95064 [email protected] Shannon Ryan Cornell University R.R. 1 S-58 C-9 Oliver BC V0H 1T0 Canada [email protected] Sheidaei Farzaneh North-West University Physics Department North-West University Potchefstroom South Africa 2520 [email protected] Slane Patrick Harvard-Smithsonian Center for Astrophysics 60 Garden Street Cambridge MA 02138 [email protected] Slowikowska Agnieszka Kepler Institute of Astronomy Institute of Astronomy Wieza Braniborska ul. Lubuska 2 65-265 Zielona Gora Poland [email protected] Smith David CNRS / IN2P3 / CENBG CENBG Chemin du Solarium - BP 20 F-33175 Gradignan Cedex [email protected] Soffitta Paolo IASF-Roma / INAF Via Fosso del Cavaliere 100 00133 Rome [email protected]

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Spitkovsky Anatoly Princeton University Department of Astrophysical Sciences. Princeton University. Peyton Hall Ivy Lane. Princeton NJ 08544 [email protected] Stappers Ben University of Manchester Jodrell Bank Centre for Astrophysics The University of Manchester Alan Turing Building Manchester M13 9PL United Kingdom [email protected] Stella Luigi INAF - Roma Astronomical Observatory Via Frascati 33 Monte Porzio Catone (RM) I-00040 ITALY [email protected] Tea Temim Harvard-Smithsonian Center for Astrophysics 60 Garden Street MS 21 Cambridge MA 02138 United States [email protected] Terada Yukikatsu Saitama University Saitama University Department of Science and Technology Physics 255 Simo Ohkubo Sakura-ku Saitama-city Japan 338-8570 [email protected] Terrier Regis APC CNRS / Universit Paris 7 Universit Paris Diderot-Paris 7 Laboratoire APC Btiment Condorcet Case 7020 75205 Paris Cedex 13 France [email protected] Tiengo Andrea INAF-IASF Milano INAF-IASF Milano via Bassini 15 I-20133 Milano Italy [email protected] Torres Diego F. Institut de Ciencies de L’Espai Institut de Ciencies de L’Espai (IEEC-CSIC) Campus UAB Fac. de Ciencies Torre C5 parell 2a planta 08193 Barcelona Spain [email protected] Trepl Ludwig AIU Jena Astrophysikalisches Institut und Universitaets-Sternwarte Schillergaesschen 2-3 07745 Jena [email protected] Treves Aldo Universit degli Studi dell’Insubria Via Valleggio 11 22100 Como Italy [email protected] Turolla Roberto Dept. of Physics University of Padova Department of Physics University of Padova Via Marzolo 8 35131 Padova Italy [email protected] van Leeuwen Joeri ASTRON ASTRON P.O. Box 2 7990 AA Dwingeloo The Netherlands [email protected]


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Venter Christo North-West University Potchefstroom Campus Unit for Space Physics North-West University Potchefstroom Campus Private Bag X6001 Potchefstroom 2520 South Africa [email protected]

Zabalza Víctor Universitat de Barcelona Dpt. Astronomia i Meteorologia Planta 7 Facultat de Fsica C / Marti i Franqus 1 08028 Barcelona [email protected] Zane Silvia MSSL University College London Mullard Space Science Laboratory University College of London Holmbury St Mary Dorking Surrey RH5 6NT UK [email protected] Zanin Roberta IFAE Institut de Fsica d’Altes Energies Edifici Cn. Facultat Cincies UAB E-08193 Bellaterra Spain [email protected] 3671949

Radio Pulsar Phenomenology Simon Johnston and Aris Karastergiou

Abstract Radio pulsars were discovered more than 40 years ago and continue to provide fertile scientific research programs. The vast majority of the nearly 2000 pulsars known are detected only at radio wavelengths. Current research at radio wavelengths includes surveys for pulsars, pulsar timing, pulsars as probes of Galactic structure, understanding the emission process and the study of phenomenlogy of pulsars generally. In this chapter we will concentrate on what can be learned from the integrated pulse profile i.e. the stable profile formed after integrating typically thousands of individual pulses. In particular we will show how to interpret the profiles, how to derive pulsar geometry by using the polarization information and comment on the various beam models developed over the years. We show how integrated profiles of the radio magnetars and pulsars with notches may help our understanding of the physics of the radio emission. Finally, we mention the future of pulsar research with telescopes such as the Square Kilometre Array.

1 Introduction The topic of radio pulsar phenomenology is an extremely large one, and one which cannot be encompassed in this short article. The following broad topics would fall under this remit: • Pulsar Timing • Propagation Effects • Pulsar Populations Simon Johnston ATNF, CSIRO, PO Box 76, Epping, NSW 1718, Australia. e-mail: [email protected] Aris Karastergiou Astrophysics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_1, © Springer-Verlag Berlin Heidelberg 2011

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Simon Johnston and Aris Karastergiou

• Single Pulses • Integrated Profiles

This chapter will concentrate mainly on the discussion of the integrated profiles of pulsars and the implications of the observations for beam models and will not consider the others in any great detail. However, we give a short outline of each of these other topics below along with references for the interested reader. For a general overview of radio pulsars from an observational perspective, readers are referred to the recent books by Lorimer & Kramer [1] and Lyne & Graham-Smith [2]. Pulsar Timing: After a pulsar has been discovered, a campaign of pulsar timing is required to determine its parameters including the spin period and its derivatives, the dispersion measure and associated derivables including surface magnetic field, spin down energy, radio luminosity and distance. If a pulsar is in a binary orbit, the orbital elements can be determined. Longer-scale timing programs on pulsars can lead to discovery of glitches, to uncovering timing noise and to aiding the discovery of pulsars at the highest energies (e.g. [3, 4]). High precision pulsar timing can yield stringent tests of gravity [5] and general relativity [6] through determination of post-Newtonian parameters and may allow detection of gravitational radiation in the future [7]. Propagation Effects: The radiation from pulsars traverses the magneto-ionic, turbulent plasma that we call the interstellar medium. Determining the dispersion and rotation measure of pulsars allows us to determine the density of free electrons in the Galaxy [8] and gives us an idea of the magnetic field configuration [9]. Observations of scintillation parameters [10, 11] and scatter broadening [12, 13] allow us to probe the turbulence in the medium [14, 15]. Pulsar population research aims to answer questions about the total number of pulsars in the Galaxy [16, 17], the evolution of pulsars from young highly energetic objects to the cessation of emission once the death line is crossed to possible resurrection via spin-up to millisecond pulsars, magnetic field evolution [18, 19], the beaming fraction [10, 21], the velocity distribution [28, 23] and the completeness of pulsar surveys [16]. Single pulses from pulsars have been studied since they first showed up on pen charts more than 40 years ago and is an area ripe in pulsar phenomenology. Manifestations of single pulses in total intensity are for example nulling pulsars [24, 25, 14], giant pulses [27, 28, 29], RRATS [30, 31] and drifting subpulses [32, 33, 34]. The polarization of single pulses yields a further treasure trove [35, 36] especially when studied over a wide frequency range [37, 38].

2 Observational Basics The period-period derivative diagram (P − P˙ diagram) is a useful starting point for understanding the various flavours of pulsars. Figure 1 is the modern version of the diagram with nearly 2000 pulsars currently known. Note that figure 1 shows the

Radio Pulsar Phenomenology

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lines of constant characteristic age, τc , magnetic field strength, B s , and the spin˙ These are given by down energy, E. τc (seconds) =

P 2 P˙

(1)

p B s(gauss) = 3.2 × 1019 P P˙ ˙ ˙ E(erg/s) = 4π I PP 2

3

(2) (3)

The pulsars on the P − P˙ diagram subdivide into four main regions. The majority of sources are the ‘normal’ pulsars with P ∼ 1 s, P˙ ∼ 10−15 and B s ∼ 1012 G. The pulsars near the top right of the diagram have long spin periods and high magnetic fields (B s > 1013 G). These are the anomalous X-ray pulsars, the soft gamma-ray repeaters, the magnetars and some of the RRATs. The pulsars near the bottom left of the diagram are the millisecond pulsars with P < 10 ms and B < 109 G. These have likely been spun-up and suffered magnetic field decay through accretion of material from their companion stars. In between the true millisecond pulsars and the bulk of the population are the mildly recycled pulsars and the double neutron star systems.

Fig. 1 The pulsar P − P˙ diagram. Yellow dots denote the position of known pulsars in the diagram. Dark blue lines are lines of constant magnetic field (Equation 2), green lines show constant characteristic age (Equation 1) and light blue denotes lines of constant E˙ (Equation 3).

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3 Integrated profiles and polarization Generally, the integration of thousands of single pulses from a given pulsar leads to a stable integrated profile. The stability of the integrated profile over many years enables high precision timing to be made and is one of the defining properties of radio pulsars. One surprising aspect is that the millisecond pulsars have integrated profiles which are largely indistinguishable from those of the normal pulsars even though their spin period are three orders of magnitude smaller and their magnetic field strengths four orders of magnitude smaller. Figure 2 shows, as an example of a typical pulsar, the integrated profile of PSR J0536–7543. There are a number of salient points to be taken from the figure which we outline in the subsections below.

Fig. 2 Integrated profile of PSR J0536–7543 at an observing frequency of 1.4 GHz with the Parkes radio telescope. The black trace shows the total intensity, red is the linear polarization and blue the circular polarization. The top panel show the position angle of the linear polarization.


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3.1 Pulse width Typically the width of the profiles of radio pulsars does not exceed 30◦ or some 10% of the pulse period. Although the observed pulse width depends on the often unknown geometry (see equation 6 below), it has been found by a number of authors [39, 40, 41, 42] that the pulse width is proportional to P−1/2 . This is expected if the edge of the active area of the polar cap is set by the last open field lines. This is an important result and implies (see equation 7) that the height at which a pulsar emits is largely independent of its period [42, 43] with typical values of 300 km at 1 GHz. A more recent study of this phenomenon [44] showed that the young, high E˙ pulsars did not always conform to this behaviour (see also [45]). Many of these pulsars have beams which are significantly wider than expected from a simple P−1/2 law. The interpretation that their emission heights are large, close to 1000 km or 10% of the light cylinder radius. There is also the special case of pulsars for which we see emission separated by close to 180◦ in phase which implies the pulsar is an orthogonal rotator and we see emission from both poles [46, 47]. In the case of PSR B1702–19, it appears as if there is some form of communication between the opposite poles because the pulse modulation is phase locked [48]. Recent results [49, 47] have also shown that emission might occur from the closed field lines in some pulsars with interpulses.

3.2 Profile shape Pulse profiles come in what seems to be a bewilderingly variety of shapes and the question of classification of pulse morphology has been addressed since the early days of pulsar research. In normal pulsars, the integrated profiles can be decomposed into a small number of Gaussian components [50, 51] even though the individual single pulses which go into making the integrated profile can be highly complex. We will discuss this further in section 8 below when we consider beam models in more detail.

Fig. 3 Integrated profile of PSR J2048–1616 at frequencies of (from left to right) 243, 320, 660, 1400 and 3100 MHz from data taken with the GMRT and Parkes [52].

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The shape of the profile varies with observing frequency as can be seen in for PSR J2048–1616 in figure 3. At low frequencies, the central component tends to dominate whereas at higher frequencies the outer components are brighter. Also the polarization fraction tends to be higher at lower frequencies, as does the overall pulse width.

3.3 Linear polarization The linear polarization from pulsars is typically 10-30% in older pulsars and in excess of 50% in younger pulsars. Note also from Figure 2 that the structure of the linearly polarized profile appears to follow that in total intensity and that the very edges of the profile are depolarized. This is also typical of many pulsars. 100

80

L [%]

60

40

20

0 29 10

30

10

31

10

32

10

33

10

34

10

10

35

36

10

10

37

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38

•

E [erg/s]

˙ taken from [44]. The dashed line shows a Fig. 4 Linear polarization fraction as a function of E, linear fit and the solid curve the fit of an arctan function illustrating the step in the degree of linear polarization.

It has been pointed out by several authors that degree of linear polarization is high for high E˙ pulsars [53, 54, 55, 44]. This correlation can clearly be seen in Figure 4. There is a transition from a low to a high degree of linear polarization which happens around E˙ ∼ 1034 −1035 erg s−1 . Virtually all pulsars with E˙ < 5 ×1033 erg s−1 have less than 50% linear polarization and for almost all pulsars with with


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E˙ > 2 × 1035 erg s−1 the percentage exceeds 50%. There appears to be a transition region in between where pulsars can both have low and high degrees of polarization, although the transition is remarkably sharp and there are well defined spaces in the figure which are almost empty.

3.4 Position angle swing and orthogonal modes As the radio emission is tied strongly to the magnetic field lines, the plane of polarization is determined by the angle of the magnetic field as it sweeps past the line of sight. The position angle of the linear polarization as a function of pulse longitude therefore contains geometric information as we shall see in the next section. The emission of pulsars is thought to be a combination of two orthogonally polarized modes (OPM, e.g. [56, 36]). This aspect of the emission can manifest itself in sharp ∼ 90◦ jumps in the position angle over a small pulse longitude range. These jumps are thought to be sudden transitions from the domination of one mode to the other. Jumps in the position angle swing therefore indicate that both modes are present in the emission. The mixing of both modes at a certain longitude will lead to depolarization. It is sometimes the case that orthogonal mode jumps are also accompanied by a change in the sign of the circular polarization [57]. Figure 7 shows an example of a pulsar with orthogonal mode jumps in its position angle swing accompanied by depolarization of the linear emission. However, it is not always the case that the jumps in position angle are exactly 90◦ as expected in the case of purely orthogonal mode superposition. One possible explanation is that the two modes suffer differing amounts of refraction in the magnetosphere [58]. A study of PSR 0329+54 showed the ordinary mode appeared to be affected by refraction and that the circular polarization is a natural by-product of elliptically polarized modes [59].

3.5 Circular polarization Pulsars generally have a reasonable degree of circular polarization in their pulse profiles. The handedness of circular polarization can change as a function of pulse longitude. Indeed, in a number of objects the handedness changes through the symmetrical centre of the pulse profile [60] which not only gives a clue as to the location of the magnetic axis but also has implications for the emission mechanism. This idea was questioned by [61] who in turn claimed evidence for a correlation between the handedness of circular polarization and the sense of swing of the position angle of the linear polarization. In the high E˙ pulsars with double profiles, it was found that the total power and the circular polarization usually dominates in the trailing component [62]. It remains unclear whether the circular polarization is intrinsic to the

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emission mechanism itself (i.e. the modes are naturally elliptically polarized [59]) or a result of the propagation through the magnetosphere [63].

4 Rotating Vector Model In the rotating vector model (RVM; [64]), the position angle (PA) as a function of pulse longitude, φ, can be expressed as ! sinα sin(φ − φ0 ) PA = PA0 + arctan (4) sinζ cosα − cosζ sinα cos(φ − φ0 ) Here, α is the angle between the rotation axis and the magnetic axis and ζ = α + β with β being the angle of closest approach of the line of sight to the magnetic axis. φ0 is the pulse longitude at which the PA is PA0 , which also corresponds to the PA of the rotation axis projected onto the plane of the sky. Figure 5 shows the geometry of the model. We note that RVM fitting does not depend on the total intensity profile, or the location of the profile symmetry points.

Fig. 5 Geometry of the polar cap model for pulsars showing the relevant angles, α, β and ζ as described in the text. Figure taken from [65].

Unfortunately, for most pulsars it is difficult to determine α and β with any degree of accuracy, partly because the longitude over which pulsars emit is rather small and partly because strong deviations from a simple swing of PA are often observed. This makes the determination of the various angles straightforward only in the ∼15 per cent of pulsars for which the RVM works - see the discussion in [66] for details. If the emission occurs at some height above the pulsar surface, the PA swing can be delayed with respect to the total intensity profile by relativistic effects such as aberration and retardation as initially discussed by [67]. The magnitude of the shift


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in longitude, δφ(PA) (in radians), is related to the emission height relative to the centre of the star, hem , via 8 π hem δφ(PA) = (5) Pc where P is the pulsar period and c the speed of light [67]. We note that, at least to first order, the PA swing is not altered by aberration and retardation effects other than the longitude delay [68, 69]. These effects therefore do not affect the measured values of α and β from equation 4. There is also a geometrical method which can be used to compute emission heights if the angles α and β are known. Under the assumption of a dipolar field and a circular emission zone, the half-opening angle of the emission cone, ρe can be expressed as cosρe = cosα cosζ + sinα sinζ cos(W/2) (6) where W is the measured pulse width in longitude [70]. If one assumes that the emission extends to the final open field line then the emission height can be derived through the expression given by [71]. r π hem ρo = 3 (7) 2Pc Here we use ρo to denote the half-opening angle of the cone at the last open field line (see figure 5, and note that unless the emission extends right to the edge of the cone then ρo > ρe . It is possible to compute relative emission heights of the radiation without the polarization information [72]. Imagine the emission which comes from a circularly symmetric region around the magnetic pole. Then, this conal emission arises higher in the magnetosphere than the pole emission, the entire circular structure will be shifted relative to the pole due to aberration and retardation effects and the profile will appear asymmetric. If a given profile contains well defined central and conal emission then the difference in separation between the leading and trailing conal components and the centre, δφ(CC), can be used to compute their relative emission heights, ∆hem . In this case [73] δφ(CC) =

4 π ∆hem Pc

(8)

This equation has been modified to take into account the viewing geometry which can affect the derived emission heights by ∼10 per cent in some cases [74]. It can be useful to compare the emission height with the radius of the light cylinder, rlc = Pc/2π. Generally it is found that the radio emission occurs in regions significantly below about 0.1 rlc . Substantial discussion of the merits and failings of all these methods can be found in recent papers [75, 76, 73, 74, 44].

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5 Problems and Perils of the RVM We have seen in Section 4 that it is possible to determine the geometrical parameters α and β through observations of the sweep of the position angle of linear polarization as a function of pulse longitude. In figure 2 we showed a fairly typical pulsar profile which appears to have smooth swing of position angle and thus amenable to determining geometry through equation 4.

Fig. 6 Left-hand panel: Contours of χ2 in the α-β plane after fitting the RVM equation to the position angle swing of PSR J0536–7543. It can be seen that although β can be constrained to lie between 0◦ and –4◦ , α cannot be constrained. Right-hand panel: Integrated profile of PSR J0536– 7543 showing the entire 360◦ of longitude. Two different RVM fits are shown (blue and green lines) both of which fit the observed position angle swing nicely but differ significantly outside the pulse window.

The top panel of figure 6 shows χ2 contours in the α-β plane after applying the RVM to the data in figure 2. The figure shows a typical ‘banana’ like shape. The implications of this are that α is very poorly constrained, whereas at least an upper bound on β can be obtained. Why is this the case? The main reason is the restricted longitude range over which radio emission is seen. The bottom panel of figure 6 shows the same pulsar as figure 2 but now with the full 360◦ of pulse rotation. Two RVM fits are shown; it can be seen that they fit the data well but clearly diverge outside the pulse window where there are no constraints. Exacerbating the problems of restricted longitude range and effects caused either by propagation through the pulsar magnetosphere or through the interstellar medium which can cause severe distortions of the RVM as seen in the two pulsars shown in figure 7. Clearly the position angle swing in these pulsars cannot be well described by the RVM even when an attempt is made to correct for orthogonal modes.


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Fig. 7 Integrated profiles for PSR J0452–1759 (left) and J1453–6413 (right). The position angle swing in PSR J0452–1759 shows evidence for 4 orthogonal mode jumps, whereas the behaviour of PSR J1453–6413 is not suitable for RVM fitting.

6 Radius-to-Frequency mapping The frequency dependence of radio emission from pulsars is a key aspect of the emission mechanism. In the radio part of the electromagnetic spectrum, pulsars are known to emit from low as 10 MHz [77] to at least 150 GHz [78]. Observations of a large sample of pulsars over a wide frequency range [79, 52] allows a generalization of the behaviour of integrated profiles with frequency: profiles get narrower, the polarization fraction declines and outer components become more prominent as the frequency increases. However, many counterexamples to these rules are also observed, and pulsars with complex profiles are especially prone to rule breaking. The so-called radius to frequency mapping (RFM) idea is that lower frequencies are emitted higher in the magnetosphere than higher frequencies which naturally results in wider observed profiles (see equation 7). This idea was originally formulated [80] in the early 1970s. It was observed that the components of double peaked pulsars move closer together as frequency increases and that this could be interpreted by assuming that the emission takes place at the local plasma frequency. The exact dependence on the emission height with frequency differed between physical models [81, 82]. A width-frequency law was postulated [83] which essentially shows that pulse widening only really occurs at frequencies below ∼1 GHz; above this value the pulse width is constant (see also figure 3). An important paper in this area came from a study of the single pulses in the Vela pulsar by Krishnamohan & Downs [84]. They showed that the properties of the single pulses in Vela could best be explained if the emission components originated from different heights in the magnetosphere at a particular frequency. In recent work, Gangadhara & Gupta [72] showed for PSR B0329+54 that the emission heights at a given frequency vary as a function of pulse longitude with high emission heights seen at the edges of profiles and low emission heights in the central parts of the profile. Furthermore, Mitra & Rankin [43] show that inner cones

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originate from lower in the magnetosphere than outer cones. The combination of these results are a key result which breaks the long-held assumption that emission from a given frequency arises at a uniform height above the pole.

7 Velocity - spin axis alignment The velocities of pulsars are significantly larger than those of their progenitor (highmass) stars (e.g. [28]). This implies that the birth process of pulsars also produces their high velocities and that the supernova or events soon thereafter must be asymmetrical. In the mid 1970s, the so-called rocket mechanism was proposed [85], whereby an offset of the magnetic dipole from the centre of the star causes the star to accelerate along its rotation axis. Observational tests of this model were largely inconclusive [86, 87, 88]. The debate started anew when both [89] and [90] proposed a model in which the same (off-centre) explosion processes that give pulsars their high velocity also produce their fast rotation. In these models, a single short duration impulse would ensure that the velocity and rotation axes were perpendicular whereas multiple, finite duration kicks would align the velocity and rotation axes. Observational evidence for a correlation came from X-ray observations of an equatorial torus and polar jets in a number of young pulsars [91, 92] whose axis of symmetry was consistent with the proper motion direction. The position angle of the axis of rotation of a pulsar can also be determined from polarization observations through two different techniques. In the first, one can determine both φ0 and PA0 directly from equation 4. However, as we have seen, in a large number of cases it is difficult to do unambiguously. In these cases, extra information can be brought to bear, for example a change in the handedness of circular polarization at φ0 [60], profile symmetry [93, 65] and the frequency evolution of the profiles [93, 65, 94]. Pulsar polarization was used to great effect by Johnston et al. [95] who showed strong observational evidence for a relationship between the direction of a pulsar’s motion and its rotation axis and concluded that the velocity vector and the rotation axis of pulsars are aligned at birth.

8 Beam models 8.1 Rankin et al. A hugely influential paper on the morphology and classification of pulsar profiles was published in the early 1980s by Rankin [93] and subsequently in a series of papers over the years [96, 71, 60, 42].


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Her classification scheme of pulsar profiles is best seen in Figure 8. Although the conal structure of pulsar beams had been postulated earlier [97, 98], Rankin proposed that an additional core component played a prominent role. She proposed that the core (central part) of the beam had a different emission process than the conal (outer) parts of the beam. At lower frequencies, core emission dominates, whereas at higher frequencies the conal emission tends to be more prominent. She also suggested that beams were elliptical rather than circular.

Fig. 8 Schematic diagram of the pulsar beam geometry taken from [93]. Different cuts of the line of sight through the beam then produce different pulse profiles as shown, Note also the cones are elliptical and the hatchings show the direction of the polarization vector.

8.2 Lyne & Manchester A seminal paper published in 1988, saw Lyne & Manchester [65] gather together all available data on the integrated pulse profiles. Although they recognised the core and cone structure outlined in [93], they suggested that rather than having two distinct emission processes, there was a gradual change in characteristics from the magnetic axis out to the last open field lines. Their model is sometimes referred to as the ‘patchy-beam model’ because they showed that the distribution of emission zones within the beam was random and patchy (see also [99]). An example of this patchiness was their classification of partial cones, those in which only the leading

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or trailing edge of the beam could be discerned. They further concluded that beams were largely circular and that alignment between the rotation axis and the magnetic axis occurred on a timescale of ∼ 107 yr (see also [10, 21]).

8.3 Karastergiou & Johnston Motivated by the recent results on the location of the radio emission in pulsar magnetospheres, Karastergiou & Johnston [100] developed a model which accounted for the large diversity found in the average profile shapes of pulsars. At the centre of their model lies the idea that radio emission at a particular frequency arises from wide range of altitudes above the surface of the star and that it is confined to a region close to the last open field lines. They showed that the radial height range over which emission occurs is responsible for the complex average pulse shapes rather than the transverse (longitudinal) range proposed in most other models. They claimed that there must be a change in the height range as a function of the pulsar spin down energy with highly energetic pulsars emitting only over a narrow range.

9 Two Case Studies 9.1 The radio loud magnetars An important sub-class of neutron stars are the magnetars which are neutron stars with long spin period (2-12 s) and very high magnetic fileds. Crucially, these stars are not powered by spin-down but rather by magnetic field decay. A growing number of magnetars are known, and three of them have been detected as radio pulsars – PSR J1809–1943 [101], PSR J1550–5418 [102] and PSR J1622–4950 [103]. The integrated profiles of these magnetars, somewhat surprisingly, show common features including [106, 105, 104] • • • • • •

variability in shape on short and long timescales variability in flux density almost complete linear polarization of the profile little variation with frequency emission with a flat spectral index a position angle swing which follows the RVM

The first two of these features (the variability) is very uncommon in other pulsars but yet is seen in all 3 of the magnetars. Furthermore the flat spectral index, which has yielded a detection of PSR J1809–1943 at frequencies up to 150 GHz [78] is also far removed from the relatively steep spectral index of most pulsars. Perhaps most surprisingly of all is the fact that the position angle swing follows the RVM. Why should this be the case, since it seems uncertain that magnetars have


15

Fig. 9 Integrated profiles of the magnetars PSR J1550–5418 at 1.4 GHz (left) and J1809–1943 at 8.4 GHz (right) showing the full pulse phase. Figures adapted from references [104] and [105].

regular dipole fields and that their super-strong magnetic fields are not conducive for radio emission in the first place? Although the RVM fits are not conclusive, it appears at least as if there is some evidence that all three of the radio-loud magnetars are close to being aligned rotators. If correct, this must also be an important clue as to their origin, as the probability of having an aligned rotator and small probability of intersecting the beam of an aligned rotator makes it very unlikely to occur by chance.

9.2 Pulsars with notches There are, at present, three pulsars which show “double notches” in their integrated profiles. These were first noted in PSR B1929+10 [107] and described in detail for PSR B0950+08 (as shown in figure 10) by McLaughlin & Rankin [108] who also pointed out that that these features were also present in the millisecond pulsar PSR J0437–4715 [109]. The notches have the appearance of an absorption feature in the profile [110] and in all three pulsars there are common features [111]. • The double notches have a W shape; the two notches have the same width and are relatively broad • The notches occur on the edges of the profile, far from the strongest component • The notches have a high degree of linear polarization • The position angle sweep is largely unaffected by the presence of the notches

It has been argued [111] that these features strongly support the idea that the radio emission from pulsars is maser-like (e.g. [112]). In particular, the seemingly wide-band radio coherency arises from inverse Compton scattering of a narrow band of frequencies by a broad energy distribution of electrons. The decrease in emission seen at the notch then arises either because the emitting region contains a gap or

16


Fig. 10 Integrated profile of PSR B0950+08 taken from [108]. The notches can be seen on the rising edge of the main component. The inset shows a blow-up of the region, showing the characteristic W shape of the notches.

their is an absorber high in the magnetosphere which blocks some of the radiation. The double nature of the notches arises naturally from the ‘hollow-cone’ type nature of the maser emission.

10 Summary Understanding the phenomenology of radio pulsars is both a quest to advance general knowledge by addressing a difficult open question in astrophysics, and a specific effort to improve timing models of pulsars to the extent that subtle effects such as gravitational radiation can be identified within pulsar timing residuals. The latter will become particularly interesting in the coming decade, as surveys will discover the populations of millisecond pulsars most suitable for gravitational wave detection through timing, and possibly the exotic pulsar binaries that will help address fundamental questions about gravity. The input of our understanding of pulsar phenomenology into pulsar timing models will be through a precise description of the effects intrinsic to the pulsar and, more specifically here, to the pulsar magnetosphere. We have given an overview in this short chapter of some of the current understanding which arises from a study of the integrated profiles of pulsars. We have seen that the RVM is a powerful tool to obtain the pulsar geometry, crucial for our


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understanding of both the radio and the high energy emission. In practice, however, obtaining constrained geometries remains difficult. We have briefly described some of the main beam models. Finally we looked at two classes of pulsars, the magnetars and the pulsars with notches and seen how detailed examination of their pulse profiles can yield insights into the physical mechanisms.

11 Future instruments and the Square Kilometre Array Progress in understanding the radio phenomenology will be made by advances in specific areas, through targetted surveys with new instruments. The first area involves solving the problem of pulsar polarization, and development of models that separate effects intrinsic to the pulsar from a variety of propagation induced effects. Recovering the intrinsic polarization relies on (i) better modelling of scattering through the interstellar medium (ii) understanding the impact on polarization of the emission height of the various components and (iii) understanding of orthogonal modes of polarization in the magnetosphere. Progress in this field will be achieved by polarimetry of many pulsars at the highest time resolutions, with the next generation of baseband recorders. Instruments like LOFAR [113], MeerKAT and ASKAP [114] will specifically target pulsars to address these questions across a very broad range of frequencies. Understanding the intrinsic polarization is key to understanding the geometric orientation of pulsars. Further to the above, the increased sensitivity across such a broad band of radio frequencies with instruments such as LOFAR, MeerKAT, the ATA and eVLA will be exploited by surveys of knon pulsars to examine the frequency dependence of emission components. Their number, width and intensity will be measured (together with the total pulse width) as a function of frequency over a continuous and unprecedented range. Where possible, this will be attempted through simultaneous or quasi-simultaneous observations, designed to address the question of radius-tofrequency mapping. The broadband total power and polarization measurements will provide 3D tomography of the magnetosphere, which will form the basis for interpretation of timing irregularities of magnetospheric origin. The great advantage of the Square Kilometre Array with respect to the above instruments will be its ability to obtain high signal to noise ratio measurements of individual pulses, illuminating the dynamic nature of the pulsar magnetosphere and permitting further refinements to the radio beam model. This is particularly important given the limited number of pulsars where individual pulses are observable today, particularly at frequencies above a few GHz. Studies of pulsar radio emission essentially require the highest possible sensitivity per time and frequency element, for which the Square Kilometre Array will be by far the best instrument planned [115, 116].

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Acknowledgements We would like to thank the organisers for inviting us to Barcelona and giving us the opening talk slot of the meeting! Thanks also to Patrick Weltevrede for the banana plot in Figure 6 and Mike Keith for comments on the document.

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Radio pulsar populations Duncan R. Lorimer

Abstract The goal of this article is to summarize the current state of play in the field of radio pulsar statistics. Simply put, from the observed sample of objects from a variety of surveys with different telescopes, we wish to infer the properties of the underlying sample and to connect these with other astrophysical populations (for example supernova remnants or X-ray binaries). The main problem we need to tackle is the fact that, like many areas of science, the observed populations are often heavily biased by a variety of selection effects. After a review of the main effects relevant to radio pulsars, I discuss techniques to correct for them and summarize some of the most recent results. Perhaps the main point I would like to make in this article is that current models to describe the population are far from complete and often suffer from strong covariances between input parameters. That said, there are a number of very interesting conclusions that can be made concerning the evolution of neutron stars based on current data. While the focus of this review will be on the population of isolated Galactic pulsars, I will also briefly comment on millisecond and binary pulsars as well as the pulsar content of globular clusters and the Magellanic Clouds.

1 Selection effects in radio pulsar surveys The current sample of radio pulsars is now close to 2000 and is continuously increasing thanks to a wide variety of large-scale and targeted searches being carried out at most of the major radio observatories. The approximate rate of discoveries at the current time is about 100 pulsars per calendar year, and we expect this trend to continue and accelerate over the next decade as more powerful facilities come online (both at radio and non-radio wavelengths). An excellent example of recent progress can be seen in the flurry of radio pulsar counterparts to Fermi gamma-ray sources as reported by Ray and Saz Parkinson elsewhere in these proceedings. It is Department of Physics, West Virginia University, Morgantown, WV 26506, USA, e-mail: Duncan. [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_2, © Springer-Verlag Berlin Heidelberg 2011

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Duncan R. Lorimer

important to note, however, that while this sample represents a great improvement over, say, the situation 20 years ago, it still likely only amounts to a few percent of the underlying population of pulsars whose properties we wish to constrain. The main observational selection effects that cause this are summarized below.

1.1 Flux–distance relationship Like all astronomical sources, observed pulsars of a given luminosity L are strongly selected by their apparent flux density, S . In a classical Euclidean model, for a pulsar a distance d from Earth which beams to a certain fraction f of 4π sr, the flux density S = L/(4πd2 f ). This is known as the inverse square law and is commonly assumed for astrophysical sources. Since all pulsar surveys have some limiting flux density, only those objects bright or close enough will be detectable. Note that in the absence of prior knowledge about beaming, geometrical factors are usually ignored and the resulting ‘pseudoluminosity’ is quoted at some standard observing frequency; e.g., at 1400 MHz, L1400 ≡ S 1400 d2 . Recently, the validity of the inverse square law has been called into question by Singleton et al. [1], and that perhaps the flux scales as 1/d instead. It is important to fully investigate this claim. As Singleton et al. point out, if confirmed, it would have dramatic implications for many of the conclusions presented here. In a search for radio transients in M31 with Westerbork, RubioHerrera [2] has investigated the implications of non-1/d2 scalings on his results and finds that many more transients should have be observable for a 1/d law, and that a 1/d2 law is consistent with the number of candidates seen. For now, we note that any flux–distance relationship will bias the sample towards bright and/or nearby objects.

1.2 The radio sky background A fundamental sensitivity limit on any radio observation is the system noise temperature, normally expressed in Kelvins as T sys . While every effort is made to minimize this at the telescope, synchrotron radiating electrons in the Galactic magnetic field contribute significantly with a ‘sky background’ component, T sky . At observing frequencies ν ∼ 0.4 GHz, T sky dominates T sys for observations along the Galactic plane. Fortunately, T sky ∝ ν−2.8 so this effect is significantly reduced when ν > 0.4 GHz.

1.3 Propagation effects in the interstellar medium Dispersion and scatter-broadening of the pulses in the interstellar medium hamper detection of short period and/or distant objects. The effects of scattering are shown in Fig. 1. Fortunately, like T sky , the scatter-broadening time τscatt has a strong fre-

Radio pulsar populations Pulsar

Emitted Pulse

23 Telescope

Detected Pulse

Fig. 1 Left: pulse scattering by irregularities in the interstellar medium shown here as an idealized ‘thin screen’ of material lying midway between the pulsar and the observer. Right: a simulation showing the fraction of pulsars undetectable due to scattering as a function of observing frequency.

quency dependence, scaling roughly as ν−4 . Fig. 1 shows that for survey frequencies below 1 GHz, scattering ‘hides’ a large fraction of the population. Additionally, scintillation, the diffractive and refractive modulation of apparent flux densities by turbulences in the interstellar medium [3] affect pulsar detection. For example, two northern sky surveys carried out 20 years apart with comparable sensitivity [4, 5] detected a number of pulsars above and below the nominal search thresholds of one experiment but not the other. Surveying the sky multiple times minimizes the effects of scintillation and enhances the detectability of intrinsically faint pulsars.

1.4 Finite size of the emission beam The fact that pulsars do not beam to 4π sr means that we see only a fraction f of the total active population. For a circular beam, Gunn & Ostriker [6] estimated f ∼ 1/6. A consensus on the precise shape of the emission beam has yet to be reached. Narayan & Vivekanand [7] argued that the beams are elongated in the meridional direction. Lyne & Manchester [14], on the other hand, favour a circular beam. Using the same database, Biggs [9] presented evidence in favour of meridional compression! All these studies do agree that the beam size is period dependent, with shorter period pulsars having larger beaming fractions. A very popular model assumed by current studies derives from the work of Tauris & Manchester [10] who found that f ≃ 0.09 log(P/s) − 1 2 + 0.03, where P is the period. A complete model for f needs to account for other factors, such as evolution of the inclination angle between the spin and magnetic axes and the beaming of millisecond pulsars.

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1.5 Pulse nulling The abrupt cessation of the pulsed emission for many pulse periods, was first identified by Backer [11]. Ritchings [12] subsequently presented evidence that the incidence of nulling became more frequent in older long-period pulsars, suggesting that it signified the onset of the final stages of the neutron star’s life as an active radio pulsar. Since most pulsar surveys have short (< few min) integration times, there is an obvious selection effect against nulling objects. Means of reducing the impact of this effect are to look for individual pulses in search data [13], survey the sky many times, or use longer integrations. Indeed, the longer dwell times (35-minute pointings) used in the Parkes multibeam survey have been particularly successful in this regard, discovering a number of nulling pulsars [14].

1.6 Intermittency Recently, a new class of “intermittent pulsars” has been found. These provide unique and new insights into neutron star physics and populations [2]. The prototype, PSR B1931+24, shows a quasi-periodic on/off cycle in which the spin-down rate increases by ∼ 50% when the pulsar is in its on state compared to the off state! While the behaviour of this pulsar appears to be linked to the increase in magnetospheric currents when it is on, there is no satisfactory explanation for this effect. Since PSR B1931+24 is only visible for 20% of the time, we can readily estimate that there should be at least five times as many similar objects. We believe this number may be severely underestimated. It is important to establish how many similar objects exist, and what the related timescales of their non-emitting state are. These pulsars, and their cousins the rotating radio transients (discussed in Section 4.1), remain a very exciting area of current research.

2 Correcting the biases in the observed sample How can we account for the effects discussed above and recover the properties of the underlying pulsar populations? While some progress can be made analytically (see, e.g. the early work of Gunn & Ostriker [6]), the non-uniform nature of all the above effects more readily lends itself to a Monte Carlo approach to modeling pulsar populations and their detection. The two main ways to implement such models can be thought of as either a fully dynamical approach or a static “snapshot” model. For the former case, a simulation is created in which a model galaxy of pulsars is seeded according to various prescriptions of birth locations and initial rotational parameters. Each of these synthetic pulsars is then “evolved” both kinematically in a model for the Galactic gravitational potential and rotationally using a model for neutron star spin-down. The properties of the resulting population are then saved.

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Using detailed models for the pulsar surveys, it is possible to compute whether each synthetic pulsar is actually detectable and the properties of these “observable” pulsars are saved. These samples may then be compared to the real observed sample to asses the validity of the Monte Carlo model. The process is summarized in Fig. 2. The snapshot approach differs from the fully dynamical approach in that the pulsars are seeded at their final positions in the model galaxy without assuming anything about spin-down or kinematic evolution and thus form a picture of the current-day population. To model pulsar detectability, both approaches are based around the well-known pulsar radiometer equation [16] which has been demonstrated to provide an adequate description of the sensitivity of pulsar surveys [17]. The advantage of the snapshot approach over the dynamical one is that it is simpler, requiring fewer assumptions about motion in the galaxy or spindown and can often be optimized to form a model with a unique best solution. Its major downfall, however, is that its simplicity means that it says very little if anything about the progenitor population. Fully dynamical models provide insights into these details, and can for example describe the distribution of pulsars in P and P˙ space about which the snapshot approach is blind to. However, as discussed below, a major point to keep in mind is that there is often no unique model that can describe the data and some care needs to be exercised when interpreting the conclusions.

3 Recent results With these caveats in mind, we now briefly review some of the latest findings of studies which adopt either the snapshot or full dynamical modeling approach.

3.1 Pulsar space distribution Models of the Galactic distribution of pulsars have been constructed from observationally biased samples for many years [18, 19, 20]. These studies typically follow the snapshot approach in which the population can be represented in terms of four independent distribution functions: Galactocentric radius R, vertical dispersion from the Galactic plane z, pulse period P and luminosity L. In a recent approach of this kind [21], we investigated models which accounted for the observed distribution of pulsars seen by the Parkes Multibeam Pulsar Survey [22] which provides the largest uniform sample (over 1000 Galactic pulsars) for such analyses. Using an iterative Monte Carlo approach, we found that it is possible to find a unique model which converges to the same functional form regardless of the initial shape of the distribution functions in R, L, z and P. An example of the model output is shown in Fig. 3 which contrasts the underlying and observed distribution functions for the final model. The L, z and P distributions show the number of pulsars as a function


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of each parameter. For R, the results are shown as the projected surface density of objects on the Galactic plane, ρ(R).

Fig. 3 Observed number distribution from our input sample (upper panels) and derived distributions (lower panels) for the parameters: (a) ρ(R); (b) z; (c) L; (d) P. The solid curves are smooth analytic functions fitted to the data (see [21] for details). The dotted curves show: (a) the assumed radial density function of free electrons (from the NE2001 electron density model); (b) an exponential z distribution with a scale height of 350 pc; (c) a log-normal fit to the optimal pulsar population model derived by [23]; (d) a period distribution derived from studying pulse-width statistics [24].

One important limitation of this approach is that the form of the spatial distributions R and z depends heavily upon the assumed model for the Galactic distribution of free electrons. The model shown in Fig. 3a assumes the commonly used “NE2001” model [25]. An example of this dependence is the R distribution in which the pulsars naturally follow the R distribution of free electrons. While the NE2001 model achieves a high level of sophistication, including electron density enhancements in spiral arms, and can account for a wide variety of observations, it is known to have a number of shortcomings [26, 27] which are currently being addressed in a new model (Cordes, private communication). In Fig 3b, for example, it is seen that the optimal model z distribution is significantly larger than observed — this is a direct result of the NE2001 electron scale height [21]. It is conceivable that future population studies with larger samples of pulsars could be carried out where the distribution of free electrons is allowed to vary. At the current time, however, one

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should be mindful of the fact that any conclusions about the spatial distribution of pulsars are strongly coupled to models of the free electron density.

3.2 Pulsar velocities A number of studies of the birth velocities of pulsars have been carried out over the years and there has been much debate as to whether the distribution for nonrecycled pulsars is unimodal [28] or bimodal [29, 30] Recent studies [31, 23] find no compelling evidence to model the distribution with multiple components and the individual 1-D components of the pulsar’s birth velocity vector follow either a Gaussian [31] or exponential form [23] with a mean value in the range 400–500 km s−1 .

Fig. 4 Normalized 3-D velocity probability density functions obtained from the observed 1-D (left) 2-D (right) distributions using a deconvolution technique [31]. The uncertainties on each histogram bin are calculated as the square root of the number of pulsars in each bin. The dotted curve shows the 3-D distribution favoured by Arzoumanian et al. [30]. The solid curve is the bestfitting Maxwellian distribution to the histogram from the 2-D distribution with σ = 265 km s−1 .

Fig. 4 shows the results of a deconvolution process from Hobbs et al. [31] where the 3-D space velocity distribution may be derived self consistently by appropriately deprojecting either the 1-D or 2-D distributions of young pulsars (defined to be those with characteristic ages less than 1 Myr). As can be seen, a previously suggested two-component model is not implied by these data. While it is found for millisecond and binary pulsars that the velocity distribution is different to the normal pulsars shown here, the main conclusion to take away from current results is that the distribution of velocities for isolated radio pulsars is unimodal.

3.3 Pulsar luminosities Because of the strong connection between distance and luminosity, any uncertainty in the pulsar distance scale propagates through to an uncertainty in the luminosity function [32]. Two critical questions concerning pulsar luminosities we wish to an-


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swer are: (1) what, if any, evolution in luminosity is there with pulsar age? (2) what is the shape of the luminosity function? The idea of a decay in luminosity has been in the literature for some time. Taylor & Manchester [19] have pointed out that the simple fact that the distribution of pulse periods tails off at long periods demands that the luminosity decays with time. If the luminosity were constant, many more pulsars would be observed. This can be readily shown via simulations in which assigning the luminosity to a pulsar at random results in a pile up of pulsars at high P and low P˙ which is not observed in the real sample [23]. The exact form of the luminosity decay remains contentious, however. While the best dynamical models can account for the observed data with a simple power law model in which L ∝ Pα P˙ β , the values of the exponents α and β are neither readily found from fits to the observed population [33] nor are uniquely constrained from the dynamical modeling [34].

Fig. 5 Results from Faucher-Giguére & Kaspi [23] which show the underlying luminosity function (defined to be at a frequency of 1.4 GHz) for their optimal model of the isolated pulsar population. The solid line shows a Gaussian fit to the data where the mean of the distribution in log L is –1.1 and the standard deviation is 0.9.

One result that does appear to be robust is the form of the luminosity distribution. While the snapshot models typically favour some sort of power-law distribution for the number of pulsars N(L) in which d log N/d log L ∼ −1, they remain agnostic about the distribution of luminosities below the minimum value in the observed sample, Lmin . The dynamical approach suggests that the underlying shape of the luminosity function is log-normal in form [23]. The parent luminosity distribution from this simulation is shown in Fig. 5. Simulations with different spin-down models all appear to show the same basic shape [34, 35] Whether this distribution applies to millisecond pulsars is currently unclear.

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3.4 Magnetic alignment Recently, two groups have provided strong evidence that the angles between the magnetic and spin axes of neutron stars are not random and, in fact, appear to decay on a timescale of 107 yr or less. Weltevrede & Johnston [36] provide strong empirical evidence for such magnetic alignment based on the statistics of pulsars which exhibit interpulses. They point out that the fraction of pulsars whose profiles can be described by viewing an orthogonal rotator is strongly linked to the stars’ rotational period, with a much higher interpulse fraction observed at longer periods than would be expected from randomly inclined lighthouse beams. Unless the observational sample is in some way biased, their conclusions appear to be irrefutable. In an independent approach, Young et al. [37] also find evidence for magnetic alignment from an analysis of the pulse width statistics of pulsars. They argue, from graphs of pulse width versus characteristic age (see examples in Fig. 6) which show a turn-up at long periods, that only alignment on a timescale of a few million years can explain the increase in pulse width. The two competing effects which shape these curves are the narrowing of pulse widths with period, and the alignment of the magnetic axis which means that older pulsars are more likely to be seen as aligned objects where the emission occupies a larger fraction of the rotational period.

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Both the above studies suggest that some sort of alignment is taking place in isolated radio pulsars. As pointed out by Ridley & Lorimer [34] however, this observation throws up a conundrum when one attempts to construct a self-consistent model of spin-down evolution. The standard magnetic dipole model, in which the braking torque is proportional to the square of the sine of the inclination angle, does not do a good job of reproducing the P − P˙ diagram if this angle evolves with time in the manner expected above. Furthermore, the hybrid spin-down model of Contopoulos & Spitkovsky [38] which can account for alignment, appears to provide a very poor description of the observed distribution in P − P˙ space. A more sophisticated model for pulsar spindown is needed which can reconcile these differences.

3.5 Magnetic field decay No discussion of pulsar statistics would be complete without a mention of magnetic field decay — a contentious issue that has raged for the past 30 yr. For many years, it was believed that the magnetic fields of isolated pulsars decayed exponentially on a 1/e timescale of 10 Myr or less [20]. Popular opinion switched toward favouring models with essentially no field decay in the 1990s [39, 40].

Fig. 7 Results of simulations by Popov et al. [35] which show how comparable results can be found by modeling the population without field decay (upper panels, following the prescription given by Faucher-Giguére & Kaspi [23]) and with field decay (lower panels, following a magnetothermal model of Popov et al. [35]). Both models give statistically equivalent results. The observed distributions in period and magnetic field strength are shown by the red histograms. KolmogorovSmirnov probabilities that the model and observed data are drawn from the same parent population are shown on the top right hand corner of each histogram. The model distributions are shown with statistical error bars. Both models appear to provide equally viable descriptions of the data.

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Nowadays, the community is split between no significant magnetic field decay [23, 34] and a decaying field [41, 35]. The simulations shown in Fig. 7 present models of the radio pulsar population with and without the effects of magnetic field decay. Is this another example of covariance between model parameters, or fundamental differences in modeling techniques? For me, the answer remains to be found.

4 Final thoughts and future prospects In this review, I have focused on a number of recent results concerning the population of isolated pulsars. While we have come a long way in understanding the distribution of these object in the Galaxy, their initial velocity dispersion and luminosity function, much remains to be understood in terms of their spin-down behaviour. A model which can account for the observed magnetic alignment, nulling, beaming and spin-down evolution is a major goal for any future study. Some further areas that are ripe for research are summarized briefly below.

4.1 Rotating radio transients An even more extreme class of intermittent neutron stars are the so-called rotating radio transients [3]. Their detection was made possible by searching for dispersed radio bursts [43] which often do not show up in conventional Fourier-transform based searches [44]. Since the initial discovery, a significant effort has gone in to searching for and characterizing more RRATs. Over 30 are currently known [45, 46, 47, 48, 49] but only seven have timing solutions, with four of these only recently achieved [49]. Recently, Lyne et al. [50] reported the detection of two glitches in RRAT J1819−1458. While these events are similar in magnitude to the glitches seen in young pulsars and magnetars, they are accompanied by a long-term decrease in the spin-down rate, suggesting that it previously occupied the phase space populated by the magnetars. Further observations are needed to confirm this “exhausted magnetar” hypothesis. The Galactic population of such objects is potentially significant and it remains to be determined whether alternative evolutionary scenarios need to be invoked other than core-collapse supernova [51]. Further work will certainly clarify this issue as known sources are better characterized.

4.2 Millisecond pulsars For many years, studies of the Galactic population of millisecond pulsars have been plagued by small-number statistics [52]. More meaningful results were obtained during the 1990s with the advent of all-sky surveys of the local population [53]


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where it was found that the velocity distribution of millisecond and binary pulsars is significantly lower than that of the normal isolated population discussed above. Presently, with an exponentially growing sample of millisecond pulsars we are in an era where it is possible for the first time to carry out full population syntheses of the Galactic population. Story et al. [54] have carried out much work in this area and have paved the way for future studies, though many questions remain to be answered including: (i) what is the overall Galactic distribution of millisecond pulsars?; (ii) is the millisecond pulsar luminosity function comparable to normal pulsars?; (iii) are all millisecond pulsars produced in low-mass X-ray binary systems?; and (iv) what is the origin of isolated millisecond pulsars?

4.3 Pulsars in the Magellanic Clouds Currently 19 radio pulsars are known in the Large and Small Magellanic Clouds [55]. Ridley & Lorimer [56] recently carried out a snapshot analysis of this population assuming the log-normal luminosity function for Galactic pulsars described above. We found that there are roughly 18,000 and 11,000 normal pulsars in the large and small clouds respectively. After accounting for beaming effects, and the fraction of high-velocity pulsars which escape the clouds, the estimated birth rates in both clouds appear to be comparable and in the range 0.5–1 pulsar per century. Although higher than estimates for the rate of core-collapse supernovae in the clouds, these pulsar birth rates are consistent with historical supernova observations in the past 300 yr. A fully dynamical model incorporating the kinematics and spindown of the pulsars in the Magellanic Clouds would be a logical extension of this work. A substantial population of active radio pulsars (of order a few hundred thousand) have escaped the clouds and populate the local intergalactic medium. For the millisecond pulsar population, the lack of any detections from current surveys leads only upper limits of up to 40,000 sources in the two clouds. A new survey with greatly improved time and frequency resolution currently underway at Parkes could detect a few of these sources (if they exist) and place valuable constraints on the total population. Giant-pulse emitting neutron stars could also be seen by this survey.

4.4 Globular cluster pulsars The first pulsar in a GC was found over 20 years ago [57]. Currently, there are 140 radio pulsars in 26 GCs [58]. Progress towards the current sample has proceeded in two phases. In the late 1980s and early 1990s, searches uncovered about two dozen of the brightest objects [59]. Further progress was only made later, around the year 2000, when a combination of advances in high-frequency broadband receivers, software algorithms, computing power and data storage capabilities led to a resurgence of discoveries [60, 61, 62, 63, 64] and interest from observers and theorists [15].

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While much of the recent focus on the observational results mentioned above has been on revealing unique systems and their applications for fundamental physics, relatively little attention has been paid on understanding the population of GC pulsars as a whole. In fact, the last major study into GC pulsar statistics were carried out in the late 1980s [80]. A major finding of this work was that the birth rate required to sustain the population of ∼ 104 MSPs estimated in all GCs was 100 times higher than the birth rate of their proposed progenitors [68], the LMXBs. Since then, the discovery of large numbers of quiescent LMXBs[81] has decreased this disparity, but another potential problem has emerged. If NSs are formed as in the Galaxy, i.e. in the core collapse supernovae of massive stars, then the large resultant velocities observed among the young pulsars [31] would eject the vast majority of all NSs from GCs. This would result in a very small number of primordial NSs in clusters. How do GCs retain enough NSs to form all the quiescent LMXBs and MSPs we observe? Are there other NS formation mechanisms at work? We anticipate significant progress in many of these areas in the near future.

Acknowledgments My research is funded by the West Virginia Experimental Program to Stimulate Competitive Research, the Research Corporation, the Smithsonian Astrophysical Observatory, the National Radio Astronomy Observatory and the National Science Foundation. I thank the Physics Department, Eberly College of Arts & Sciences and the Senate Research Committee for supporting my travel to this meeting.

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51. Keane, E.F.; Kramer, M. 2008, MNRAS, 391, 2009. 52. Kulkarni, S.; Narayan, R. 1988, ApJ, 335, 755. 53. Lyne, A. G.; Manchester, R. N.; Lorimer, D. R.; Bailes, M.; D’Amico, N.; Tauris, T. M.; Johnston, S.; Bell, J. F.; Nicastro, L. 1988, MNRAS, 295, 743. 54. Story, S.A.; Gonthier, P.L.; Harding, A.K. 2007, ApJ, 671, 713. 55. Manchester, R.N.; Fan, G.; Lyne, A.G.; Kaspi, V.M.; Crawford, F. 2006, ApJ, 649, 235. 56. Ridley, J.P.; Lorimer, D.R. 2010b, MNRAS, 406, L80. 57. Lyne, A.G. et al. 1987, Nature 328, 399. 58. P.C.C. Freire, Pulsars in globular clusters (http://www.naic.edu/∼pfreire/GCpsr.html). 59. Kulkarni, S.R.; Anderson, S.B. 1996 Dynamical Evolution of Star Clusters - Confrontation of Theory and Observations P. Hut, J. Makino, eds. (Kluwer, Dordrecht, 1996), 181. 60. Camilo, F.; Lorimer, D.R.; Freire, P.C.C.; Lyne, A.G.; Manchester, R.N. 2000, ApJ 535, 975. 61. D’Amico, N.; Lyne, A.G.; Manchester, R.N.; Possenti, A.; Camilo, F. 2001, ApJ 548, L171. 62. Ransom, S.M. et al. 2001, ApJ, 546, L25. 63. Possenti, A. et al. 2003, ApJ, 599, 475. 64. Ransom, S.M. et al. 2005, Science, 307, 892. 15. Camilo, F.; Rasio, F.A. 2005 in Binary Radio Pulsars (Astronomical Society of the Pacific, San Francisco), F. Rasio, I. H. Stairs, eds., 147. 66. Freire, P.C.C.; Wolszczan, A; van den Berg, M.; Hessels, J. 2008, ApJ, 679, 1433. 67. Lattimer, J., Prakash, M. 2007, Physics Reports, 442, 109. 68. Alpar, M.A.; Cheng, A.F.; Ruderman, M.A.; Shaham, J. 1982, Nature, 300, 728. 69. D’Amico, N. et al. 2001, ApJ, 561, L89. 70. Lyne, A.G.; Biggs, J.D.; Brinklow, A.; Ashworth, M.; McKenna, J. 1988 Nature, 332, 45. 71. Sigurdsson S.; Richer, H.B.; Hansen, B.M.; Stairs, I.H.; Thorsett, S.E. 2003, Science, 301, 193. 72. Prince, T.A.; Anderson, S.B.; Kulkarni, S.R.; Wolszczan, A. 1991, ApJ, 374, L41. 73. Lyne, A.G.; Manchester, R.N.; D’Amico, N. 1996, ApJ, 460, L41, 74. Lyne, A.G.; Biggs, J.D.; Harrison, P.A.; Bailes, M. 1993, Nature, 361, 47. 75. Rasio F.A.; Heggie, D.C. 1995, 445, L133. 76. Sigurdsson, S.; Hernquist, L. 1992, ApJ, 401, L93. 77. Sigurdsson, S. 2003 in Radio Pulsars (Astronomical Society of the Pacific, San Francisco, M. Bailes, D. J. Nice, S. Thorsett, eds., 391. 78. Devechhi, B.; Colpi, M.; Mapelli, M.; Possenti, A. 2007, MNRAS. 380, 691. 79. Kramer, M. et al. 2006, Science, 314, 97. 80. Kulkarni, S.R.; Narayan, R.; Romani, R.W. 1990, ApJ, 356, 174. 81. Heinke, C.O. et al. 2003, ApJ, 598, 501.

Pulsar Results with the Fermi Large Area Telescope Paul S. Ray and Pablo M. Saz Parkinson for the Fermi LAT Collaboration, the LAT Pulsar Timing Consortium, and the LAT Pulsar Search Consortium

Abstract The launch of the Fermi Gamma-ray Space Telescope has heralded a new era in the study of gamma-ray pulsars. The population of confirmed gamma-ray pulsars has gone from 6–7 to more than 60, and the superb sensitivity of the Large Area Telescope (LAT) on Fermi has allowed the detailed study of their spectra and light curves. Twenty-four of these pulsars were discovered in blind searches of the gamma-ray data, and twenty-one of these are, at present, radio quiet, despite deep radio follow-up observations. In addition, millisecond pulsars have been confirmed as a class of gamma-ray emitters, both individually and collectively in globular clusters. Recently, radio searches in the direction of LAT sources with no likely counterparts have been highly productive, leading to the discovery of a large number of new millisecond pulsars. Taken together, these discoveries promise a great improvement in the understanding of the gamma-ray emission properties and Galactic population of pulsars. We summarize some of the results stemming from these newly-detected pulsars and their timing and multi-wavelength follow-up observations.

1 Introduction 1.1 Gamma-ray Pulsars in the Year 2000 Ten years ago, on 4 June 2000, the Compton Gamma Ray Observatory (CGRO) was de-orbited, ending nine years of operation, during which it revolutionized Paul S. Ray Naval Research Laboratory, 4555 Overlook Ave., SW, Washington DC 20375-5352 USA e-mail: [email protected] Pablo M. Saz Parkinson Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064 USA e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_3, © Springer-Verlag Berlin Heidelberg 2011

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P. S. Ray and P. M. Saz Parkinson

gamma-ray astronomy. In particular, the Energetic Gamma Ray Experiment Telescope (EGRET) surveyed the sky at energies > 100 MeV with much better sensitivity than previous experiments. The landmark Third EGRET (3EG) Catalog [35] reported the characteristics of 271 gamma-ray sources. The largest class of identified sources were blazars, with 66 sources, followed by 5 pulsars (Crab, Vela, Geminga, PSR B1055−52, and PSR B1706−44), 1 solar flare, the Large Magellenic Cloud, and one probable radio galaxy (Centaurus A). Interestingly, the majority of the 3EG sources (170 of them) were not associated with any known classes of gamma-ray emitting objects. It was widely believed that a large number of the unidentified EGRET sources, particularly along the Galactic plane, could be pulsars [e.g. 63], and several radio pulsars were, in fact, discovered by searching the error circles of EGRET unidentified sources [e.g. 32, 54]. Further work on EGRET data revealed one more high-confidence pulsar (PSR B1951+32) and several candidates, including one millisecond pulsar [46]. An excellent observational summary of what was known about gamma-ray pulsars at the end of the EGRET era was presented by Thompson [59]. It is also worth noting that a 7th gamma-ray pulsar (PSR B1509−58) was detected by the COMPTEL experiment up to 10 MeV [45], though it was never seen with EGRET. Pre-launch predictions of the number of gamma-ray pulsars that Fermi LAT would detect (as well as the fraction of those that would be radio quiet) are highly dependent on the assumed gamma-ray emission model, ranging from a few tens to many hundreds [e.g. 50], with the larger number (and fraction of radio-quiet pulsars) usually predicted by outer-magnetosphere models, where the gamma-ray beam is expected to be broader [39, 34]. It should be noted that the detection of a gamma-ray pulsar, in this context, does not necessarily imply the detection of its pulsations; most models, for example, “predict” that EGRET detected far more than the 6 gamma-ray pulsars for which high-confidence pulsations were actually observed, a view that is supported by the subsequent detection of pulsations from many formerly unidentified EGRET sources by the LAT.

1.2 Fermi and AGILE After almost a decade without an orbiting GeV telescope, two new satellites were launched in 2007–2008, ushering in a new era of gamma-ray astronomy. AGILE (an Italian acronym for Astro-rivelatore Gamma a Immagini LEggero) was launched on 23 April 2007 and the Fermi Gamma-ray Space Telescope (formerly GLAST) was launched on 11 June 2008. The prime instruments on both spacecraft are pair production gamma-ray telsecopes, like EGRET. However, instead of a gas spark chamber, they employ more modern solid-state silicon strip detectors to track the gamma-ray and particle events. While AGILE had a 14-month head start on Fermi, and has made many important contributions, it represents a modest improvement in sensitivity compared to EGRET. In this paper we focus on the pulsar results made possible by the enormous leap in sensitivity afforded by Fermi.

Pulsar Results with the Fermi Large Area Telescope

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The primary instrument on Fermi is called the Large Area Telescope (LAT) [24]. The LAT is a pair conversion gamma-ray telescope where incoming gamma rays are converted to electron-positron pairs in a set of tungsten foils. The resulting electronpositron pair and shower of secondary particles are tracked by a stack of silicon strip detectors to determine the incident direction of the photon before the energy of the shower is recorded in a CsI calorimeter. The instrument is wrapped in a segmented anti-coincidence detector that aids in the separation of events due to charged particles from those resulting from photons. This is critical because charged particle events outnumber photon events by a factor of 104 . The LAT is sensitive to photons in the energy range 30 MeV to > 300 GeV, with an effective area of ∼ 8000 cm2 at 1 GeV. The point spread function is ∼ 0.8◦ at 1 GeV and is a strong function of energy, scaling like E −0.8 until the resolution becomes limited by position resolution in the tracker at about 0.07◦1 . Compared to EGRET, the LAT represents a major improvement in effective area, field of view, and angular resolution. In addition, it operates in a sky survey mode which avoids loss of observing efficiency from Earth occultations and covers the sky nearly uniformly every two orbits (∼ 3 hours). These characteristics give the LAT unprecedented sensitivity for discovery and study of gamma-ray pulsars. The First Fermi LAT catalog [1FGL; 16] of 1451 gamma-ray sources detected during the first 11 months of science operations contains 56 sources that have been firmly identified as pulsars through their gamma-ray pulsations. Several additional gamma-ray pulsars have been identified since the release of the catalog, bringing the total number to more than 60. In the following sections, we describe the various populations of gamma-ray pulsars being explored by the LAT, and the different techniques employed in their detection, as well as some of the new insights being gained through these new findings. We end with a brief summary and some thoughts on the future goals and expectations for pulsar astrophysics with the LAT in the coming years.

2 The EGRET Pulsars in Exquisite Detail The EGRET experiment represented a major improvement relative to previous gamma-ray missions (e.g. SAS-2 and COS-B). In addition to increasing the number of high-confidence gamma-ray pulsars from 2 to 6, the higher sensitivity of EGRET led to a better understanding of the known gamma-ray pulsars (at the time, only the Crab and Vela). Similarly, the LAT, with its improved sensitivity and broader energy range is not only enabling the discovery of a large number of new gamma-ray pulsars, but is also greatly expanding our knowledge of the previously known EGRETdetected pulsars. Because these pulsars are among the brightest known gamma-ray sources, the LAT is able to accumulate enough statistics to allow for detailed (and phase-resolved) spectral analyses, in many cases answering some questions left over 1

This is the individual photon angular resolution. Bright sources can be localized more precisely via centroiding.

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from the EGRET era, or challenging some of the previous EGRET results which in most cases were based on limited statistics. Early LAT observations of Vela, the brightest steady gamma-ray source, confirmed some of the basic features of this pulsar: It has two asymmetric peaks that evolve differently with energy, and a phase-averaged spectrum well modeled by a hard power-law with an exponential cutoff in the 2–4 GeV energy range. In addition, the much better statistics and time resolution of the LAT data reveal pulse structures as fine as 0.3 ms, and a hitherto unknown third peak in the light curve, which evolves with energy (see Figure 1). Spectral fits to the LAT data suggest that a simple exponential cutoff is preferred over a super-exponential one, indicating that outer-magnetosphere emission models are favored over polar cap type models [6]. More recent results on Vela, using 11 months of observations, show detailed phaseresolved features which confirm the EGRET results on the spectral evolution of the two main peaks. In addition, while the first peak is seen to fade at higher energies, the newly-discovered third peak, along with the second peak, are present up to the highest detected pulsed energies [21]. LAT results on the Crab pulsar confirm that it shares many of the properties of Vela, with two asymmetric peaks evolving differently with energy. The Crab pulsar spectrum is also best modeled with a power law with an exponential cutoff, but the cut-off energy in this case is much higher than Vela (∼6 GeV), with pulsed gammaray photons being detected at least up to ∼20 GeV [18]. One of the new features uncovered by the LAT is an apparent phase shift between the main radio peak and the first gamma-ray peak. Previously, it was thought that these two were aligned, but the fine time resolution of the LAT allows us to determine that the first gamma-ray peak leads the main radio pulse by (281 ± 12 ± 21) µs (see Figure 1). In addition to being the second brightest non-variable source in the GeV sky, Geminga was the first known radio-quiet gamma-ray pulsar. As such, it cannot be timed in radio and until now, a good timing solution relied on X-ray observations. Using ∼1 year of observations, consisting of over 60,000 photons, a timing solution was obtained based solely on gamma rays [11]. Geminga shows many similarities to Vela and the Crab. The phase-averaged spectrum is also well represented by a

Fig. 1 Pulse profile of the Vela pulsar, as a function of energy. The different behavior of the two main peaks is evident. A third peak is seen to appear at higher energies, with its position shifting in phase, as a function of energy [from 21, reproduced by permission of the AAS].


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power law with exponential cutoff, with a hard spectral index and a cutoff energy between 2–3 GeV, leading to pulsed gamma rays being detected up to at least 18 GeV [11]. Detailed phase-resolved spectroscopy shows an evolution of the spectral parameters with phase and appears to indicate that there is emission coming from the pulsar at all rotational phases, favoring, once again, outer-magnetospheric emission models [11]. The remaining EGRET pulsars, J1057−5226, J1709−4429, and J1952+3252, while still bright, were not as bright as Vela, the Crab, and Geminga. LAT observations of these pulsars shed light on some of the key questions left over from the EGRET era. All three pulsars, once again, can be fit with a power law with a simple exponential cutoff. This contradicts earlier EGRET results that indicated that PSR J1709−4429 could be fit with a broken power law and PSR J1952+3252 showed no signs of a cutoff below 30 GeV [12]. It is interesting to note that the conclusion about the EGRET spectrum of PSR J1952+3252 was based on the detection of 2 photons above 10 GeV. Finally, although not detected by EGRET, PSR B1509−58 was seen by the COMPTEL instrument, and is therefore one of the 7 gamma-ray pulsars detected by CGRO. More recently, its detection has also been reported by the AGILE collaboration [10]. Using 1 year of data, the LAT was able to detect pulsations from PSR B1509−58 up to 1 GeV, and confirmed that, unlike the EGRET-detected pulsars, PSR B1509−58 has an energy spectrum that breaks at a few tens of MeV [14]. The high precision phase-resolved spectral measurements made possible with the LAT will be critical for theoretical modeling efforts, which must confront these new data. With the simple question of polar cap vs. outer magnetosphere origin now largely resolved, the important questions become more subtle: Where exactly in the outer magnetosphere is the acceleration occurring? Which magnetosphere geometry is appropriate (e.g. vacuum dipole or force-free magnetosphere)? Fig. 2 Folded light curve of the Crab pulsar [from 18, reproduced by permission of the AAS]. The statistics provided by the LAT allow us to observe structure in the light curve with incredible precision. For example, it is now clear that the main radio pulse (red) and the gammaray pulse (black) do not line up, and in fact are separated by approximately 0.3 ms.

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3 Young Pulsars Found Using Radio Ephemerides In addition to the 7 young (or middle-aged) gamma-ray pulsars previously detected by CGRO, the LAT has also detected gamma-ray emission from an additional dozen or more “young” (non-millisecond) radio-selected pulsars. PSR J2021+3651 holds the distinction of being the first new gamma-ray pulsar in the post-EGRET era. The pulsations were detected with the LAT during the commissioning phase of the instrument [9], although the original discovery of the gamma-ray pulsar was independently reported using AGILE data [33]. Other pulsars detected early in the mission include PSR J1028−5819, shown to be at least partly responsible for the EGRET source 3EG J1027−5817, the single-peaked PSR J2229+6114 in the “Boomerang” pulsar wind nebula (PWN) [5], and the very energetic PSR J0205+6449, in SNR 3C 58 [4]. Several of the newly-detected gamma-ray pulsars were already proposed as marginal EGRET detections, including PSRs J1048−5832 and J0659+1414. Figure 3, for example, shows the folded light curves of PSR J1048−5832, including that generated with EGRET data. While the significance of the EGRET pulsation is clearly limited by the much lower statistics, the perfect alignment of the peaks with the LAT profile confirms that this was, indeed, a real detection, as originally reported by Kaspi et al. [40]. Other young pulsars now seen by the LAT were originally discovered in radio searches of EGRET unidentified sources, and thus proposed as the energetic radio counterparts of the known gamma-ray sources (e.g. PSRs J2021+3651 and J2229+6114). Many, however, had no previous gammaray associations. While the brightest new gamma-ray pulsars (particularly those coincident with formerly-unidentified EGRET sources) could have been detected in blind searches of LAT data (or searching around the extrapolation of the original radio timing solution), the detection of pulsations from fainter gamma-ray pulsars (e.g. PSR J0205+6449) requires contemporaneous phase-connected timing solutions spanning the entire LAT data set. In anticipation of such needs, a comprehensive pulsar monitoring campaign (known as the Pulsar Timing Consortium) was set up, prior to launch, between the LAT collaboration and the major radio telescopes, to ensure periodic monitoring of hundreds of pulsars with large spin-down energies, with the goal of providing the necessary ephemerides [57].

4 Millisecond Pulsars At first glance, millisecond pulsars (MSPs) might not seem like great candidates for gamma-ray emission. After all, they are several orders of magnitude older than the gamma-ray bright young pulsars and their surface magnetic fields are about four orders of magnitude weaker. On the other hand, their very rapid rotation rates give them open field line voltages that are competitive with the young pulsars and their magnetic fields at the light cylinder (BLC) are at about the median value for the young gamma-ray pulsars. This, plus the marginal detection of PSR J0218+4232 with EGRET [46], gave some reason to be optimistic. One particularly prescient pa-


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Fig. 3 Folded light curves of the young energetic pulsar PSR J1048−5832 [from 5, reproduced by permission of the AAS]. The second panel from the bottom shows the EGRET light curve. The Fermi LAT data allow us not only to confirm the marginal EGRET detection (note that the peaks line up), but also to study much finer time scales, as well as the energy evolution of the light curve.

per [58] used a detailed population study based on the pair-starved polar cap model to predict that the LAT should be sensitive enough to detect tens of gamma-ray millisecond pulsars, most of which should be radio quiet and thus form a high-latitude population of unidentified gamma-ray pulsars. They also pointed out that, since the high latitude regions have been very poorly covered by millisecond pulsar surveys so far, radio searches of LAT point sources with pulsar-like spectra should be an efficient way to find new MSPs. Over the first 18 months of the Fermi mission, it has become abundantly clear that millisecond pulsars are a significant contributor to the population of high latitude gamma-ray sources being detected with the LAT. Figure 4 shows the distribution, in Galactic coordinates, of all the MSPs detected to date with Fermi LAT. We describe these discoveries in the following subsections.

4.1 Radio MSPs The first LAT results on MSPs came from folding the gamma-ray data using radio ephemerides for the ∼ 72 field MSPs (i.e. P < 30 ms and outside of the globular cluster system). Within the first 8 months of data taking, significant gamma-ray pulsations were discovered from 8 MSPs, including confirmation of the EGRET detection of PSR J0218+4232 [10, 1]. In addition to the 8 pulsed detections, it was

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noted that there were significant LAT point sources positionally coincident with 5 other MSPs [1]. With continued exposure accumulating, 3 of those 5 now have reported pulsation detections above the 5 σ significance level: PSR J0034−0534 [15], PSR B1937+21 and PSR B1957+20 [42], bringing the total number of radiotimed millisecond gamma-ray pulsars to 11. The initial 8 MSP discoveries tended to resemble the normal pulsar population in most of their characteristics, including the peak separations, fraction that showed single vs. double peaks, and radio lags. This led to the conclusion that MSPs had essentially the same gamma-ray emission mechanism operating in the outer magnetosphere as the young pulsars, as suggested by the similar values of BLC. Interestingly, the three latest discoveries all have gamma-ray light curves that appear to have peaks that are aligned in phase with the radio pulses. This characteristic is very rare among the normal pulsars, with the primary counter-example being the Crab pulsar (where the radio peaks overlap the gamma-ray ones, even though they aren’t perfectly aligned, as described above). It has been suggested that these are cases where the gamma-ray and radio emission are coming from nearly co-located regions of the magnetosphere and that both result from caustic formation [15].

4.2 Searches of LAT Unassociated Sources As mentioned earlier, a promising technique for discovering new MSPs is to perform radio searches in the direction of gamma-ray point sources that have pulsar-like characteristics (e.g. lack of variability and exponentially cutoff spectra). This technique was used, with modest success, on many of the EGRET unidentified sources [29, 27, 41, for example]. These searches were challenging because the EGRET error boxes were many times larger than a typical radio telescope beam, requiring many pointings to cover the source region. With the LAT, the unassociated source localizations are a much better match to radio telescope beam sizes and can generally be searched in a single pointing. The Fermi Pulsar Search Consortium (PSC) was conceived to organize search observations of LAT-discovered pulsars and unassociated sources using several large radio telescopes around the world. Thus far, over 100 LAT unassociated sources, mostly at high Galactic latitudes (See Figure 4), have been searched at 350, 820, or 1400 MHz resulting in the discovery of 18 new millisecond pulsars [51]. These searches are ongoing, and there is no apparent strong correlation between the gamma-ray and radio fluxes of these pulsars, so more discoveries can be expected as fainter LAT unassociated sources2 are searched. These discoveries represent a ∼25% increase in the number of known millisecond pulsars outside of the globular clusters, which is an impressive achievement considering the enormous effort that has gone into radio MSP searches over the last three decades. The new pulsars include several highly interesting sources. Five of 2

The 1FGL catalog, compiled with 11 months of data, lists 630 unassociated sources and many more are expected as the LAT pushes down in sensitivity. Note, however, that AGN (which represent about half of the current associations) will likely comprise a significant fraction of these.


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them are so-called “Black Widow” pulsars, with minimum companion masses of 0.01–0.05 M⊙ and one other has a more typical mass companion, but exhibits radio eclipses. These more than double the known population of such pulsars in the field of the Galaxy and will be important systems for understanding the formation and evolution of millisecond pulsars as well as excellent systems to look for unpulsed gamma-ray emission from intra-binary shocks. Several others are very bright with sharp radio profiles that have the potential to be important additions to pulsar timing array projects that seek to detect nanoHertz gravitational waves via their effect on pulse arrival times [18]. Since all of these pulsars are positionally coincident with LAT gamma-ray sources, it is expected that once sufficiently accurate timing models are available, they will all be found to be gamma-ray pulsars. Indeed, LAT pulsations have already been discovered for the first 3 of the new MSPs [51].

4.3 Globular Cluster MSPs Although there are some 140 pulsars known in globular clusters3 , most of which are MSPs, there have been no reported gamma-ray pulsations from individual millisecond pulsars in globular clusters with the LAT. However, in at least 8 cases, there are point-like gamma-ray sources spatially coincident with globular clusters [3, 43, 13].

J1231-14

J1302-32 J0751+1807 J1745+10

J1614-2230

J1810+17 J1744-1134

J1514-49

J1103-53

B1937+21 J2215+51 J0340+41 J0218+4232

J1658-53 J0613-0200

J2302+44

B1957+20

J1747-40

J2214+30

J0614-33

J2017+06 J1902-51 J2124-3358

J0437-4715 J2241-52

J0023+09

J0100-64

J0030+0451 J0034-0534

Fig. 4 Sky map, in Galactic coordinates, showing millisecond pulsars detected with the Fermi LAT. The background image is made from 16 months of LAT data (2008-08-04 through 2009-1202) with E > 100 MeV. The white crosses mark the 11 previously known radio pulsars found to be gamma-ray pulsars with the LAT. The yellow circles indicate the 18 new radio MSPs discovered in searches of pulsar-like LAT unassociated sources.

3

http://www.naic.edu/˜pfreire/GCpsr.html

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In general, these 8 LAT sources are consistent with being the combined emission of a population of millisecond pulsars in each cluster. Most have spectra that show an exponential cutoff in the few GeV range, as seen with MSPs, but for a couple the significance of the cutoff is too low for it to be considered evidence for an association of the gamma-ray source with the cluster. The fluxes are largely consistent, within the substantial uncertainties, with estimates of the total number of MSPs in each from from radio and X-ray observations. However, in three cases, there are no known MSPs in clusters with associated LAT sources, providing a strong motivation for deeper radio pulsar searches of those clusters. It is worth noting that the AGILE collaboration reported the detection of pulsations from PSR J1824−2452, in the globular cluster M28 [10], but the detection was marginal and appeared in only one subset of the AGILE data. Thus far, this result has not been confirmed by Fermi. In general, the detection of individual gamma-ray pulsars in globular clusters will likely be difficult because of the typically large distances to the clusters (4–12 kpc for the likely LAT-detected clusters) and because of the background provided by the rest of the pulsars in the cluster. However, in ˙ it cases where there is one pulsar (like PSR J1824−2452) that has a very large E, may outshine the rest of the pulsars in the cluster and be detectable individually. Searches with the LAT are ongoing, using radio timing models for a large number of individual pulsars in globular clusters.

5 Blind Periodicity Searches As described in previous sections, it was long thought that many of the EGRET unidentified sources could, in fact, be pulsars—in particular radio-quiet pulsars like Geminga. Previous attempts to carry out blind searches on EGRET data using coherent FFT techniques were unsuccessful [e.g. 28]. The sparse data sets and sensitivity to timing irregularities make such searches incredibly challenging. A new technique was developed to try and ameliorate the problem, by calculating the FFT of the time differences (instead of times of arrival) of events. Time differences are calculated between all events in the time series with respect to events lying within a relatively short sliding window (∼weeks). The lower frequency resolution of the resulting FFTs make these searches less sensitivite to frequency shifts (such as those caused by the spindown of the pulsar), while at the same time resulting in great savings in computational time [23]. This new time-differencing technique was shown to work with EGRET data [64], and has since proven extremely successful with the LAT data, leading to the discovery, so far, of 24 pulsars found in blind searches [2, 56]. Figure 5 shows an example of the output from a successful blind search of a formerly unassociated LAT source, now identified as PSR J1957+5033 [56]. After determining that the highly significant peak at 2.668 Hz is promising, standard pulsar


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packages such as PRESTO4 , and tempo2 [38], are used to refine the result and obtain a final timing solution for the pulsar. Most of the initial 16 pulsars found in blind searches of LAT data were associated with formerly unidentified EGRET sources. In fact, only 3 of the 16 had no EGRET counterpart [2]. Many of these sources were long-suspected of hosting pulsars, including 3EG J1835+5918, the brightest unidentified EGRET source off the Galactic plane, which was even dubbed the ‘Next Geminga’ [31]. Six out of the sixteen pulsars were discovered by assuming a counterpart position derived from observations at other wavelengths (mostly X-ray), instead of the less precise LAT position. A prime example is the discovery of PSR J1836+5925 powering 3EG J1835+5918 [17]. More recently, the last 8 pulsars found in blind searches have mostly been found from newly-discovered LAT sources, with no corresponding EGRET counterpart, except in some cases where the EGRET source might have been confused and is now being resolved into multiple separate gamma-ray sources by the LAT [56]. Although radio beaming fractions for MSPs appear to be large [44], there are still expected to be radio quiet millisecond pulsars detected as point sources with the LAT. A discovery of a radio-quiet MSP in a blind search would be an important result. Unfortunately, the parameter space that needs to be searched is vast. For the case of binary MSPs the problem may be essentially intractable. However, about 25% of MSPs are isolated, including at least two of the LAT-detected radio MSP. For these pulsars the search is daunting, but not impossible. On the plus side, MSPs have low period derivatives and are extremely stable rotators, so the pulse will remain

Fig. 5 Results from a blind search on a formerly unassociated LAT source [now PSR J1957+5033; 56], indicating the presence of a highly significant pulsation at 2.668 Hz. The FFT has been computed using the differences between binned photon arrival times up to a maximum difference of 262,144 s, and the power at each frequency has been normalized to represent the inverse of the probability that it could be due to a random fluctuation, as described in Ziegler et al. [64]. Note that the logarithmic scale results in the majority of the 33,554,432 FFT bins not showing up in the figure. 4

http://www.cv.nrao.edu/∼sransom/presto/, [49]

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phase coherent for a long integration time. Counteracting this is the fact that the fast spin rates require that the pulsar position be known very precisely (∼ 0.1 arcsec). For a typical LAT point source position uncertainty of 3 arcmin, this requires 3.2 × 106 trial positions to cover the region, and each trial position requires a search over frequency and frequency derivative. Current efforts on blind searches of LAT data are concentrating on both searching deeper for young and middle aged pulsars as well as expanding the search parameter space to include isolated MSPs.

6 Pulsar Timing with the LAT Pulsar timing is a powerful technique that involves fitting a model to measured pulse arrival times that can account for every rotation of the neutron star over a time span of years [47, chap. 8]. Of course, such timing yields extremely precise measurements of the spin period and spindown rate of the neutron star, quantities from which estimates of the magnetic field, age, and energy loss rate of the pulsar can be derived. In addition, because of the motion of the Earth around the solar system barycenter, the pulse arrival times are highly sensitive to the pulsar position on the sky. Once those major effects are accounted for, timing is sensitive to a host of other parameters of the system including binary orbital parameters, timing noise, glitches, and even proper motion and parallax in some cases. Traditionally, pulsars have been discovered and timed using radio telescopes. Working in the gamma-ray band, EGRET was not very effective for pulsar timing both because of its limited sensitivity and because of its pointed viewing plan that meant that most pulsars were only observed for a few 2-week observations scattered over the mission. The situation is completely different with Fermi, which now has both the sensitivity to detect a large number of pulsars and a sky survey viewing plan that allows observations of every pulsar in the sky continuously. For most of the 24 blind search pulsars, timing using the LAT data is the only option since they are undetectable or extremely faint at radio wavelengths. In addition there are some very faint radio pulsars, such as PSR J1124−5916 where the observation time required to do radio timing is prohibitive, but which can be readily timed with the LAT. There are several key differences between pulsar timing with the LAT and radio pulsar timing. First, the satellite is not affixed to the Earth, like a ground-based radio telescope. Second, the data are very sparse, with often fewer than 100 photons being used to make a pulse time-of-arrival (TOA) measurement. The first issue is dealt with by transforming the photon arrival times as observed at the satellite to a fictional observatory at the geocenter, thus removing the effects of the spacecraft motion on the measurement. The second difference drives one to adopt a TOA measurement technique different than the traditional radio method of cross correlating a folded pulse profile with a high signal to noise binned template. Instead, TOAs are


49

determined by a maximum likelihood fit to the offset between the measured photon times and an analytic template profile [53]. What is impressive is that even with so few photons, timing models can be determined for most detectable LAT pulsars with RMS residuals of order a millisecond using TOAs spaced by a few weeks. This enables arcsecond position determinations as shown in Figures 6 and 8 (right panel). In addition to these precise positions that enable multiwavelength counterpart identifications, pulsar timing with the LAT has provided spindown measurements for the gamma-ray selected pulsars, detection and measurement of glitches, and studies of the timing noise observed in these systems. The precise long-term timing models are also critical for other studies such as blanking a pulsar to remove confusion in the study of a nearby source, as was required for Cygnus X-3 [8] or searches for off-pulse emission, such as from an SNR or PWN [30]. Fig. 6 Comparison of position determinations of PSR J1836+5925. The large ellipse (0.45 arcmin semimajor axis) is the 95% confidence region from positional analysis of 18 months of LAT data (M. Kerr, private communication). The small ellipse (0.8 × 0.4 arcsec) is from the pulsar timing model fit over the same interval [53]. The background image is a Chandra X-ray image showing the point source at the location of the pulsar.

7 Multiwavelength Connections The 24 blind-search pulsars were all discovered in gamma-ray searches and thus are gamma-ray selected pulsars, but targeted radio observations are required to determine if they are also radio quiet, or could have been discovered in radio surveys independently. Radio detections also yield distance estimates from dispersion measure, information on the emission region from radio to gamma-ray offset, and geometry from radio polarization studies. In addition, the population statistics of radio quiet vs. radio loud gamma-ray pulsars have important implications for gamma-ray emission models. Deep radio searches have now resulted in the detection of radio pulsations from three of the 24 blind search pulsars, with strong upper limits on the others [53, 56]. The pulsations from J1741−2054 were found in archival Parkes Multibeam survey data and confirmed using the Green Bank Telescope (GBT) [26]. For J2032+4127,

50


Fig. 7 Pseudo-luminosities of the gamma-ray selected pulsars that have since been detected as radio pulsars (red stars), compared to the general population of radio pulsars (blue dots).

the pulsations were discovered using the GBT [26]. The third radio pulsation discovered was from PSR J1907+0602 [19] using a very deep observation with the 305-m Arecibo telescope. The detections provide distance estimates from the dispersion measure, which allow conversion of the radio fluxes into pseudo-luminosities. As shown in Figure 7, two of these pulsars are exceptionally faint, with luminosities about an order of magnitude lower than the faintest radio-discovered young pulsars. This is forcing a reevaluation of what is meant by a ‘radio quiet’ pulsar. Observations of PWNe at TeV energies go back to the very first firm detection of emission from the Crab nebula [62]. Since then, over 100 TeV sources have been detected5 and more than half of these have associated LAT sources [16], which is perhaps not altogether surprising given that the energy ranges of the LAT and groundbased Cerenkov detectors overlap. PWNe represent the largest class of Galactic TeV sources. In fact, the first unidentified TeV source, discovered by the HEGRA telescope in the Cygnus OB2 region, is associated with PSR J2032+4127, one of the pulsars found in blind searches of LAT data [2, 26]. HESS observations of the Galactic plane uncovered a large number of unidentified TeV sources, and many of these are thought to be associated with PWNe. In some cases, the discovery of new LAT pulsars coincident with known TeV sources can put into question previous interpretations of the TeV emission. Figure 8, for example, shows the positional coincidence of the highly energetic pulsar PSR J1023−5746 [56] with the bright TeV source, HESS J1023-575. Located in the vicinity of the young stellar cluster Westerlund 2, the TeV emission from this source was previously thought to be due mainly to the wind interaction from massive stars [22]. The presence of such a pulsar, however, must lead to a re-examination of such conclusions. Furthermore, the identification of the counterpart (right panel in Figure 8) shows that the association with the Westerlund 2 cluster is highly questionable. 5

For an up-to-date catalog of TeV sources, see http://tevcat.uchicago.edu/


51

Fig. 8 Left – Fermi LAT counts map of the region around PSR J1023−5746. The green contours represent the HESS significance. Right – Chandra X-ray image of the Westerlund 2 cluster. The X-ray counterpart of PSR J1023−5746 is approximately 8 arcminutes away from the core of the cluster. Inset: Zoomed-in image of a 1 square arcminute region around the location of the pulsar. Note that the 95% (statistical) error ellipse obtained from pulsar timing (shown in white) overlaps with the X-ray source. Figures from Saz Parkinson et al. [56], reproduced by permission of the AAS.

At higher energies still, the Milagro observatory detected significant (> 5σ) TeV emission at a median energy of 35 TeV from the location of 6 gamma-ray pulsars detected by the LAT, and evidence for emission (3 − 5σ) from the location of an additional 8 sources from the Bright Source List [7]. Four of those sources are gamma-ray pulsars, and two more are associated with supernova remnants. This strong connection between young energetic GeV pulsars and their TeV PWNe can play an important role not only in understanding the nature of the emission from such sources, but also as a means to identify likely candidates for gammaray pulsars, ultimately leading to the identification of both TeV and GeV sources. X-ray observations of gamma-ray pulsars and pulsar candidates are particularly important. First, the precise positions of neutron star candidates allow for more sensitive blind searches to take place (as in the case of PSR J0007+7303 or PSR J1836+5925). Secondly, for those pulsar candidates found using the less precise LAT position, X-ray positions can serve to refine the candidate and determine whether it is a real detection. In 4 out of the original 16 pulsars discovered in blind searches, a short observation with the Swift satellite was enough to identify a plausible X-ray counterpart which resulted in a much higher significance of the pulsation [2]. In several other cases (e.g. Gamma Cygni SNR, Cygnus OB2 association), archival observations could be analysed in search of the best possible counterpart.

1


10 39 erg 10 38 s -1 erg 10 37 s -1 erg 10 36 s -1 erg 10 35 s -1 erg 10 34 s -1 erg s-

52

-10

-12

3

y

4

y

5

y

6

y

7

y

8

y

10

Log[dP/dt]

-14

10

10

-16

10

10

-18

10

-20

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Log [P(s)]

Fig. 9 Period-Period Derivative diagram showing the LAT-detected pulsars. Included are 24 young or middle-aged radio-timed pulsars (green circles), 25 gamma-ray selected pulsars (blue squares), where all but Geminga were discovered in LAT blind searches, and 14 millisecond pulsars (red triangles), for a total of 63 gamma-ray pulsars. Note that this does not include 15 of the radio millisecond pulsars discovered in searches of LAT unassociated sources, essentially all of which can be expected to be detected as gamma-ray pulsars once their timing models are well determined.

8 The LAT Pulsar Population A Period-Period Derivative diagram showing all 63 gamma-ray pulsar detections made with the LAT to date is shown in Figure 1. This is an update of Figure 2 from the Fermi LAT First Pulsar Catalog [20], which summarizes the characteristics of the 46 gamma-ray pulsars detected with the LAT in the first 6 months of the Fermi mission. The LAT-detected pulsars generally have high values for the detectability metric E˙ 1/2 /D2 and large E˙ and BLC . Which one of these is really telling us about the gamma-ray emission physics at work in these sources remains to be seen. With a large number of detections spanning a range of E˙ from 1033.5 to > 1038 erg s−1 , we can start to address the evolution of gamma-ray luminosity (i.e. efficiency) with ˙ Unfortunately, the large distance uncertainties for most pulsars combined with E. the model-dependent uncertainty in the beaming factor (see below) prevent strong conclusions from being drawn at present [20].


53

The spectra of LAT pulsars are well characterized by exponentially cutoff power laws with photon indices near 1.5. The cutoff energies are in the 1–4 GeV range with a small number of outliers on the high and low side. The observed pulse profiles frequently evolve with energy, but generally fall into one of three categories: two peaks separated by ∼ 0.4 − 0.5 in phase, two overlapping peaks separated by ∼ 0.2 in phase, and single peaked profiles. Most of the LAT pulsars are consistent with being 100% pulsed in the gamma-ray band. However, a few (e.g. Geminga and PSR J1836+5925) seem to show magnetospheric emission across all rotational phases. In other cases, an analysis of the ‘off-pulse’ region of pulse phase reveals GeV emission from a pulsar wind nebula, typically with a much harder spectrum than that of the pulsar itself. A review of LAT observations of PWNe is presented elsewhere in this volume [30]. The large number of radio and gamma-ray selected pulsars found with the LAT, combined with deep radio searches of the new gamma-ray selected population will enable population studies that will help shed light on the beaming fractions in the two bands and test predictions of the various models for the emission region geometries. One such early study [52] finds that the radio beaming fraction is near unity for the the highest E˙ pulsars and decreases to ∼ 0.5 for the lower E˙ gamma-ray pulsars, implying that very high- E˙ pulsars may produce their radio emission in the outer magnetosphere. If confirmed, this would have major implications. The current challenge is to use the abundance of well-measured light curves to constrain the geometry of the emitting region and the relevant magnetospheric physics. The favored approach is to choose an emission region location (e.g. polar cap (PC), outer gap (OG), or two-pole caustic (TPC)), combine it with an assumed magnetic field geometry and compute an ‘atlas’ of predicted gamma-ray light curves that can be compared with observations. This has been done for vacuum dipole field geometries [61], as well as for numerically-modeled ‘force-free’ geometries [25]. Other groups have specifically targeted millisecond pulsars [60]. The predicted light curve morphologies are sensitively dependent on both the misalignment between the spin and magnetic axes of the neutron star (α) and the viewing angle (ζ) between the spin axis and the line of sight. Without a priori knowledge of these angles, it can be hard to discriminate among models based on light curve fits. However, if the angles can be constrained by other methods, such as radio polarization measurements or Xray PWN geometry, the degeneracies can be broken. An important output of these model fits is the ‘flux correction factor’ fΩ , defined such that the true gamma-ray luminosity, Lγ of a pulsar is Lγ = 4π fΩ F obs D2 ,

(1)

where F obs is the observed gamma-ray flux and D is the distance. In the EGRET era it was commonly assumed that fΩ ∼ 1/4π, but current models predict values much closer to 1. This parameter is crucial for understanding the energetics of these systems and the efficiency (η) with which they convert rotational energy into gammarays. Recent model comparisons with a few LAT pulsar light curves [55] suggest that OG models with alternate field geometries are preferred in these cases. How-

54


ever, other objects may be consistent with lower altitude emission, and additional comparisons are needed to see if the data are consistent with emission beyond the light cylinder, as suggested by the force-free models. With many more high quality light curves being collected by the LAT, it should be possible to make powerful tests of these models, especially if when angle constraints from radio and X-ray observations are available.

9 Future Expectations The next few years promise a continued stream of exciting pulsar results from the LAT. With the very reasonable assumption that the 18 new millisecond pulsars found in radio searches of LAT unassociated sources will all turn out to be gamma-ray pulsars, there will soon be more than 75 solid gamma-ray pulsar detections. This number is not totally unexpected, according to several pre-launch predictions. What is more surprising is that the population is divided into three essentially equal groups: young or middle-aged radio-selected pulsars, young or middle-aged gamma-ray selected pulsars, and millisecond pulsars. Modeling the spectra, light curves, and population statistics of the LAT pulsars will be extremely important over the next few years to turn the powerful observations into improved understanding of the physical mechanism for pulsar gamma-ray emission. But, since this is a primarily observational review, we close with a few of the important observational questions that we expect to be addressed in the coming years. • Are there radio quiet millisecond pulsars? This is both a great challenge for the observers and has very important implications for the emission mechanisms and geometry. • If the ‘gamma-ray binaries’ LS I +61 303 and LS 5039 (see review in this volume Hill et al. [36]) are powered by energetic pulsars, can we detect the gamma-ray pulsations with the LAT? • What are the non-detections of known pulsars telling us? While the new pulsar discoveries have grabbed most of the attention, it may be that one or more key non-detections will tell us something important about what drives gamma-ray pulsars. However, these studies are critically reliant on accurate distance determinations, so this is really a reminder that improved VLBA or timing parallax measurements for as many pulsars as possible will be of great value in increasing the science return from LAT pulsar studies. Acknowledgements The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat a` l’Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto


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Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged ´ from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Etudes Spatiales in France. Pablo Saz Parkinson acknowledges support from the American Astronomical Society and the National Science Foundation in the form of an International Travel Grant, which enabled him to attend this conference. Basic research in astronomy at the Naval Research Laboratory is supported by 6.1 base funding.

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Fermi view of the EGRET pulsars F. Gargano for the Fermi-LAT collaboration

Abstract The six EGRET gamma ray pulsars are among the most interesting objects in the sky observed by Fermi: they are bright galactic gamma ray sources and they have good and updated timing solutions. EGRET has studied these pulsars up to an energy of 10 GeV, and at least for the brightest three it has analyzed the evolution of the emission with phase. The Large Area Telescope (LAT) on Fermi, thanks to its excellent sensitivity, has collected, in only one year, more photons then EGRET in its entire lifetime. The increased photon statistic and the outstanding timing capability, has allowed us to build detailed pulse profiles of all these six pulsars and to deeply study the changes of the emission spectrum with phase. Moreover we have obtained an excellent timing solution for Geminga using only gamma rays, and for all these pulsars we have observed that the emission spectrum is consistent with a power law with simple exponential cut-off. The study of the six EGRET pulsars with Fermi is therefore very important to improve our understanding of the pulsed gamma ray emission from neutron stars and, thanks to the very rich details of the analysis, it is a good test bench for different emission models.

1 Introduction Before Fermi only six pulsars were known as high-confidence gamma-rays emitters above 100 MeV. After the launch of the Fermi Gamma-ray Space Telescope on 11 June 2008 our view of the gamma-ray pulsar-sky is dramatically changed, since we now know more then 60 pulsars that emit above 100 MeV. EGRET data has allowed to build the gamma-ray light curves and the spectral emission spectra up to 10 GeV, but with only a handful of photons above 5 GeV the high energy emission wasn’t well studied and understood. Compared with its predecessor, the Fermi-LAT [1] has a larger effective area (8000 cm2 on-axis, 1GeV) and an improved angular resoluIstituto Nazionale di Fisica Nucleare, sez. Bari, Via Orabona 4, 70126 Bari, Italy e-mail: fabio. [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_4, © Springer-Verlag Berlin Heidelberg 2011

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F. Gargano for the Fermi-LAT collaboration

tion (θ68 =0.6◦ at 1 GeV for events in the front section of the tracker). The large field of view (2.4 sr) allows the LAT to observe the full sky in survey mode every 3 hours. This excellent sensistivity has allowd, after only one year of survay mode observations of these six pulsars, to collect over an order of magnitude photons more than EGRET in its nine year lifetime. This unprecedented high statistics (more then 150000 photons for Vela) allowed us to construct high-quality pulse profiles and study their evolution with energy. Moreover, we have constructed detailed phase-resolved spectra of these pulsars revealing a complex evolution of the spectral parameters with phase. As a result, the study of the six EGRET pulsars has improved our understanding of pulsed emission and is allowing us to test the predictions of the current high-energy pulsed emission models.

2 Analysis results The analysis for the different pulsars have been done using different datasets ranging from 8 to 13 months, and for all of them photons from the Diffuse class are selected, i.e. the highest quality photon data, having the most stringent background rejection. In addition, we exclude the events with zenith angles greater than 105◦ due to the Earth bright γ-ray albedo. All the results shown in this review come from the following papers, where it is possible to find all the details of the analysis: [2] for Vela, [3] for Crab, [4] and [5] for Geminga and [6] for PSR J1057−5226, PSR J1709−4429, and PSR J1952+3252 The light curves are a powerful tool to study the mechanism hidden behind the pulsed emission, at all wavelengths. For this reason a great effort has been put in building good and accurate timing solution, that completely cover the observational periods of the six pulsars. For Crab, PSR J1057−5226 and PSR J1952+3252 the timing solution has been built from radio observations, while for Vela, Geminga and PSR J1709−4429 we have used a timing solution based on Fermi data. Before Fermi-LAT the ephemeris for Geminga, the fist known gamma-selected pulsar, were maintained by RXTE, but since the Fermi-LAT operates in sky-survey mode, it observes Geminga on a daily base and it can provide very accurate and updated timing solutions. For Vela we have chosen to use γ-ray data because it has been demonstrated that they give a more accurate solution than the radio observations. For PSR J1709−4429 the situation is slightly different, since a glitch has occurred around 2008 August 14, and so all the previous timing solution were not valid any more: we have then built a valid timing solution using only LAT data. The complete timing solutions are available at the Fermi Science Support Center (FSSC) website1 . In Table 1 are summarized the main parameters of the light curves and in Fig. 1 are shown the light curves for PSR J1057−5226, J1709−4429 and J1952+3253. With the exception of PSR J1057−5226, all the pulsars show well defined light 1

http://fermi.gsfc.nasa.gov/ssc/data/access/lat/ephems/

Fermi view of the EGRET pulsars

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curves with two main peaks, well described by lorentzian functions both symmetric or asymmetric. The ratio between the two peaks tends to change with energy, and in particular there is always a peak that almost disappears at high energy. Instead PSR J1057−5226 is different, since its light curve is very complex and we can barely point out the two peaks. For this pulsar a longer observation period is needed to study the details of the pulsed emission. All the pulsars show light curves in agreement with the one observed by EGRET [7]. For all the radio-selected pulsars it’s evident that there is a shift in phase between the radio and the gamma pulsation, and this could be explained if we assume a different location for the two different kind of emission. Pulsar Name

Observer

RMS ∆

δ

Vela Crab Geminga PSR J1057−5226 PSR J1709−4429 PSR J1952+3252

LAT Nançay [8] LAT Parkes [9] LAT Nançay [8]

63µs 21µs 251µs 62µs 378µs 228µs

0.13128±0.00016 0.095±0.002 — 0.31±0.03 0.242±0.002 0.154±0.001

0.4332±0.0002 0.398±0.003 0.497±0.004 0.28±0.03 0.250±0.004 0.485±0.017

Table 1 The main contributor to the timing solution is in the 2nd column, the post-fit RMS of the timing solution is in the 3rd one. The parameters derived from the fits to the pulse profile, the peak separation and phase lag between the radio and the first γ-ray pulse, are listed in the 4th and 5th columns.

The high statistic and the excellent performance of the LAT, has allowed to study in great details the γ-ray emission of all the six pulsars from 100 MeV to 100 GeV. For all the pulsars we can now safely reject the hypotesis of a phase averaged emission modeled by a power-law or a broken power-law, in favor of a power-law with simple exponential cutoff. The spectral parameters are summarized in Table 2. Pulsar Name

Γ

Ecutoff (GeV)

Photon Flux Energy Flux 10−7 ph cm−2 s−1 10−4 MeV cm−2 s−1

Vela Crab Geminga PSR J1057−5226 PSR J1709−4429 PSR J1952+3252

1.51±0.01 1.97±0.02 1.30±0.01 1.20±0.05 1.71±0.02 1.57±0.31

2.857±0.089 5.8±0.5 2.46±0.04 1.50±0.09 4.45±0.23 2.80±0.37

95.0±7.1 20.9±0.3 41.4±0.2 3.36±0.10 15.97±024 1.89±0.12

49.10±2.05 8.17±0.12 25.7±0.12 1.77±0.01 6.698±0.08 0.92±0.03

Table 2 Spectral parameters obtained from fitting the energy spectra with a power-law with expo−Γ e(−E/E cutoff ) The last two parameters are the integrated photon flux nential cutoff dN/dE = KE GeV and the integrated energy flux above 100 MeV. Only the statistical errors are reported, for the systematics please refer to the papers of the single pulsars.

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It is worth pointing out that for almost all the pulsars we get a better fit if we use a power law with super-exponential cutoff, with the super-exponent value ranging from almost 1 for PSR J1057−5226 to almost 0.5 for PSR J1709−4429: in any case lower then 1. In our opinion this is due to the fact that the phase averaged spectrum can be a combination of several spectra exhibiting simple-exponentialcutoff shape with different cutoff energies. This has been verified performing for all the six pulsars a phase resolved spectral analysis that for all of them has shown a trend of both spectral index and energy cutoff with phase. For the details please refer to the single pulsar papers.

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3 Conclusion Fermi has confirmed and extended all the results of EGRET, both for the light curves and the spectral shapes, moreover it has given an answer to some of the question left open by EGRET, especially related to the high energy emission. It is interesting to point out that while Vela, Crab and Geminga are among the brightest sources in the γ-ray sky, the other three pulsars aren’t so bright, so an interesting question could be why these three pulsars have been the only ones observed by EGRET. Now we know ([10] and [11]) that they have nothing of really peculiar with respect to all the others known γ-ray pulsars: a possible reason to account for their detection could be that they were the ones with the best timing solution at the EGRET time and this has allowed to clearly detect the γ pulsation. The observation of these 6 well known gamma-ray pulsars has provided a great improvement in our knowledge of the highenergy emission mechanism. We now have an answer to some of the questions left open by EGRET: the gamma-rays are produced in the high magnetosphere of the neutron star and the radio and gamma emission are loacted in different region around the pulsar. For a detailed analysis on the implication of the observed light curves and the spectral behavior of these pulsars on the validation of different emission models please refer to the cited papers. Acknowledgements The Fermi LAT Collaboration acknowledges support from a number of agencies and institutes for both development and the operation of the LAT as well as scientific data analysis. These include NASA and DOE in the United States, CEA/Irfu and IN2P3/CNRS in France, ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board in Sweden. Additional support from INAF in Italy and CNES in France for science analysis during the operations phase is also gratefully acknowledged. The Parkes radio telescope is part of the Australia Telescope which is funded by the Commonwealth Government for operation as a National Facility managed by CSIRO. The Nançay Radio Observatory is operated by the Paris Observatory, associated with the French Centre National de la Recherche Scientifique (CNRS). We thank our colleagues for their assistance with the radio timing observations.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Atwood, W. B., et al. 2009, ApJ, 697, 1071 Abdo A. A. et al. 2010, accepted for publication in ApJ. arXiv:1002.4050 Abdo, A. A. et al. 2010, ApJ, 708, 1254 Abdo A. A. et al. 2010 submitted to ApJ. Razzano, M., Dumora, D. & Gargano, F. 2009, arXiv:0912.5442 Abdo, A. A. et al. 2010, submitted to ApJ. Kanbach, G. 1998 Adv Space res, Vol 21 N◦ .1/2 pp. 227-235 G. Theureau, N. Coudreau, N. Hallet, M. Hanski, L. Alsac, et al., 2005, A&A 430, 373 R.N. Manchester, 2008, AIP Conf. Ser. 983, 584 Ray, P. these proceedings Abdo, A. A. et al. 2010, ApJS, 187, 460

“Garden-variety” Gamma-ray Pulsars J0248+6021 & J2240+5832 David A. Smith for the Fermi LAT Collaboration

Abstract PSRs J0248+6021 & J2240+5832 are “typical” young, radio-loud pulsars detected in GeV gamma rays using the Large Area Telescope (LAT) on the Fermi satellite. “Typical” because their P, P˙ lie mid-range of those of the new gamma-ray pulsars, but also because of some nagging little observational problems. This paper focusses on the observables available to help interpret the wave of new gamma-ray pulsar findings, and some of their limitations.

1 Introduction We did it! Ray & Saz Parkinson (these proceedings) describe the ten-fold increase in the number of known gamma-ray pulsars, over a broad range of radio-loud to radio-quiet, of young and old, of fast and slow, of isolated pulsars and of pulsars grouped in globular clusters or in binary systems. Many power pulsar wind nebulae (PWN, Grondin & Lemoine-Goumard, these proceedings). In the lean years between EGRET and Fermi it was said these discoveries would enable us to understand pulsar emission and to explain the role of pulsars in a variety of Galactic processes. So, how do we actually go about it? The LAT’s “First Pulsar Catalog” [3] is a good start: it tabulates a series of gamma-ray observables for the first 46 gamma-ray pulsars seen with Fermi as uniformly as possible, and makes some simple, global comparisons with model predictions. The LAT team aspires to a more ambitious “Second Pulsar Catalog” in 2011, with not only more gamma-ray pulsars but also considering good gamma-ray candidates not seen, and comparing with expectations David A. Smith Centre d’Etudes Nucléaires de Bordeaux-Gradignan, CNRS-IN2P3, Université Bordeaux I, BP 120, 33175 Gradignan, France. e-mail: [email protected] Co-workers (please see Acknowledgements section) N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_5, © Springer-Verlag Berlin Heidelberg 2011

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of population models updated using the insights acquired since the Fermi and AGILE [10] discoveries. Conducted in parallel is the also necessary approach of detailed study of single objects: our second paper on Vela [1] and our paper on the 9th millisecond pulsar, PSR J0034-0534 [2], are just two examples. This article highlights some observables to illustrate some recurring issues. A detailed article on these two pulsars is [16].

2 Two Not-So-Typical Pulsars Pulsars PSR J0248+6021 and PSR J2240+5832 were discovered in 1998 with the Nançay radiotelescope [5] in a northern Galactic plane survey [12]. Figure 1 shows the radio pulse profile for PSR J0248+6021, along with the polarization and position angle. Like > 80% of radio pulsars, it has a single, narrow radio pulse. The radio profile of PSR J2240+5832 is similar except for the absence of scatter broadening seen in the trailing edge of J0248’s pulse. Both pulsars have the same large spindown power, E˙ = 2.1 × 1035 erg/s, similar rotation periods (217 ms and 140 ms, respectively), and comparable surface magnetic fields (∼ 1012 G) and characteristic ages (∼ 100 kyr). They both have large Dispersion Measures (DM): 370 pc cm−3 for J0248+6021 and 263 pc cm−3 for J2240+5832. For these DMs, the NE2001 model [6] places J2240 very far from the Sun (> 7 kpc), and places J0248 even farther (beyond the Galaxy’s edge, > 9 kpc). Figure 1 also shows the pulse profiles for PSR J0248+6021 in different gammaray energy bands. Only a single peak is prominent, offset from the radio peak by δ = 0.4 in phase, unusual for gamma-ray pulsars, > 80 % of which have two peaks. Here too, the two pulsars are strikingly similar: J2240 also has only one peak, with a larger offset, δ = 0.6. The six gamma-ray pulsars discussed in [18] all have a single gamma-ray peak. As in that paper, we exploit radio polarization data to try to unravel the pulsar geometry. PSR J0248+6021 is in the “First Pulsar Catalog”, whereas PSR J2240+5832 had not yet been detected. Why should the nearer of these two similar pulsars be fainter in gamma rays? Both are at low latitude (|b| < 0.7◦), but in fact the background from diffuse Galactic emission and neighboring sources is much higher for J0248. Might beam geometry be a key difference? Is it “just” the distance? Something else?

3 About those distances DM’s provide a valuable first estimate of a pulsar’s distance. But NE2001’s assumptions about the electron densities in and between the Galaxy’s spiral arms and in a small number of tabulated clouds are easily overwhelmed by the complexity of the star-forming regions hosting massive stars and ,often, their pulsar progeny. For J0248 it is easy to see what’s fooling NE2001: it lies in one of the thickest parts of

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the “Soul” nebula, the giant HII region W5, 0.8◦ west of the center of the open cluster IC 1848 in the Galaxy’s Perseus arm (see the beautifully detailed WISE infrared photograph1.) NE2001 predicts DM = 61 cm−3 pc for 2 kpc for that direction. The excess needed to make up the difference is a quite plausible 18 electrons cm−3 . Twelve years of pulsar timing provides more distance constraints. One example is the proper motion: including uncertainties, PSR J0248+6021 has µ > 48 mas/yr. The largest neutron star velocities due to supernova “birth kicks” are ∼ 1000 km s−1 [7], implying d < 4.4 kpc. But if it is in W5 at 2 kpc then it has a typical transverse velocity vT ∼ 500 km/s. Another example is that the DM of PSR J0248+6021 increased by 0.3 cm−3 pc per year for three years, and then decreased at the same rate for another two years: the pulsar is indeed moving through a cloud. Both pulsars are noisy (J0248 had five glitches in 12 years). The long lever-arm helps constrain degenerate parameters in the timing model. Radio polarization data give a Rotation Measure RM = −158 ± 6 rad m−2 from which the parallel component of the magnetic field along the line-of-sight is Bk = 1.23RM/DM = 0.5µG. This matches nicely the expectation from Figure 6 of [8] and therefore the pulsar is most likely within the Perseus arm. We assign to PSR J0248+6021 the distance of IC 1848, d = 2.0±0.2 kpc. VLBI parallax measurements for all Fermi pulsars are being undertaken and will let us check these arguments in the years to come2 . Turning to PSR J2240+5832, no clouds are obvious in archival images and the NE2001 average electron distribution may be fine. The proper motion measurement gives half the apparent speed and < 1000 km s−1 jives with the Galaxy’s Outer arm. An average vT ∼ 400 km/s would place the pulsar in the Perseus arm. We have RM = 24 ± 4 rad m−2 , but the magnetic fields are poorly known in this direction, so that it only weakly supports the pulsar being so distant. The beautiful “anatomically correct” drawing of the Milky Way in [13] shows that the Outer arm is somewhat closer ( < 8.3 kpc in this direction) than what was known when NE2001 was created. Neutron stars are likely born within arms and, since vT τc < 0.1 kpc, the pulsars should still be there. We conclude with two hypotheses for the distance to PSR J2240+5832: Outer arm (d = 7.7 ± 0.7 kpc) versus the Perseus arm (d = 3.8 ± 0.8 kpc). The gamma-ray luminosity Lγ is plausible in both cases.

4 Understanding the Beams Theorists approach pulsar beam modeling in two steps. First is to think deeply about the underlying physics, to choose simplifying assumptions about the essentially intractable 3-D problem that will lead to realistic, feasible calculations. The next is to distill these meditations such that an observer can compare his data with pre1 2

2010 June 1 NASA APOD (“Astrophysical Picture of the Day”) Fermi Cycle 3 proposal, S. Chatterjee et al.

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dictions. One hopes for an iterative process converging to a clearer, truer vision of neutron star magnetospheres. The “Atlas” approach of [14] is exemplary in this regard: different models are treated uniformly, large numbers of pulse profiles are generated, and a “recipe” guides comparison between data and theory. Spitkovsky & Bai (these proceedings) and Harding & Grenier (these proceedings) have similarly begun to provide Atlas-like tools. See also [17]. It is hoped that alternative theoretical approaches (e.g. Petri ; Arons ; Cheng ; Hirotani, these proceedings) will also lead to direct comparison with the data as we approach 100 varied gamma-ray pulsars. The existing theories mainly address pulse profile shapes. We observers would love to test predictions of how, for example, the photon spectral index Γ or the energy cut-off Ec depend on other measurable parameters. The gamma-ray luminosity ˙ via the beam-correction factor fΩ , albeit with limited discrimLγ is linked to (P, P) inating power at this time (in part due to the huge uncertainties imposed by the distance problem). Self-consistent treatment of radio beams, including polarization, may come in the near future. For PSRs J2240+5832 and J0248+6021, we fit the radio linear polarization Position Angle (PA) versus rotation phase to the Rotating Vector Model [RVM, 11]. The goal is to obtain independent constraints on the inclination ζ of the neutron star rotation axis to the line-of-sight to Earth, and the angle α between the rotation axis and the magnetic axis. The narrow, single radio pulses make RVM fits difficult, and the scattering tail on J0248 makes it even harder. Nevertheless, the magnetic impact parameter β = ζ − α is constrained to β ≈ 5◦ for J0248 and to β ≈ 16◦ for J2240. The “Atlas” approach is to find the (α, ζ) combination for which the predicted gammaray pulse profile (including absolute phase relative to a radio pulse assumed to be centered on the magnetic axis) best matches the observed profile. The (α, ζ) ranges favored by RVM overlap those preferred by “Atlas”, with some difficulties detailed in [16]. Detailed X-ray images of PWN can constrain ζ [9], which is one of several motivations for finding new PWN (Slane, these proceedings). Neither J0248 nor J2240 show evidence for off-pulse gamma-ray emission in the Fermi data. For J0248, nearby radio and optical structures led us to look a bit harder. Mostly to no avail, although see [16], which do give some upper limits and TeV speculations that will interest some readers.

5 Conclusions Pulsars lie at the crossroads of varied domains of astrophysics. Comparing observed properties with model predictions for individual pulsars over as wide a range of parameter space as possible allows theorists to more accurately describe these cosmic particle accelerators. One can then improve the fidelity of neutron star population syntheses, integrating reliable predictions for gamma-ray and electron emissions. The stakes may be high – an example is whether the cosmic electron spectrum

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(Moiseev, these proceedings) has a partial Dark Matter origin, or is instead totally dominated by pulsars. The long-term aim of the ongoing multi-disciplinary work on gamma-ray pulsars, illustrated here with PSRs J0248+6021 and J2240+5832, is to better fit pulsars into the Galactic puzzle. Acknowledgements The authors of the full paper describing this work [16] are members of the LAT Collaboration [4] and/or the Fermi Pulsar Timing Consortium [15]. The immense groundwork laid by the full team made these results possible. The paper authors are: G. Theureau, D. Parent, I. Cognard, G. Desvignes, D. A. Smith, R. W. Romani, J. M. Casandjian, C. C. Cheung, H. A. Craig, D. Donato, L. Guillemot, A. K. Harding, J.-F. Lestrade, P. S. Ray, D. J. Thompson, W. W. Tian, K. Watters. We thank Simon Johnston for useful discussions about the radio polarization data.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Abdo, A. A. et al. 2010a, ApJ, 713, 154 Abdo, A. A. et al. 2010b, ApJ, 712, 957 Abdo, A. A. et al. 2010c, ApJS, 187, 460 Atwood, W. B. et al. 2009, ApJ, 697, 1071 Cognard, I., Theureau, G., Desvignes, G., & Ferdman, R. 2009, ArXiv e-prints Cordes, J. M., & Lazio, T. J. W. 2002, ArXiv e-prints, (arXiv:astro-ph/0207156) Hobbs, G., Lorimer, D. R., Lyne, A. G., & Kramer, M. 2005, MNRAS, 360, 974 Mitra, D., Wielebinski, R., Kramer, M., & Jessner, A. 2003, A&A, 398, 993 Ng, C.-Y., & Romani, R. W. 2008, ApJ, 673, 411 Pellizzoni, A. et al. 2009, ApJ, 695, L115 Radhakrishnan, V., & Cooke, D. J. 1969, ApJ, 3, 225 Ray, P. S., Cadwell, B. J., Lazio, T. J. W., Foster, R. S., Backer, D. C., Cognard, I., & Lestrade, J.-F. 1999, in BAAS, Vol. 31, Bulletin of the American Astronomical Society, 903 Reid, M. J. et al. 2009, ApJ, 700, 137 Romani, R. W., & Watters, K. P. 2010, ApJ, 714, 810 Smith, D. A. et al. 2008, A&A, 492, 923 Theureau, G., Parent, D., Cognard, I., & Smith, D. A. 2010, A&A, submitted Venter, C., Harding, A. K., & Guillemot, L. 2009, ApJ, 707, 800 Weltevrede, P. et al. 2010, ApJ, 708, 1426

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Fig. 1 Phase-aligned γ-ray and radio profiles for PSR J0248+6021 obtained with the Fermi Large Area Telescope and the Nançay Radio Telescope. The bottom panels show three radio frequencies, as well as the linear (red dashed) and circular polarizations (blue dotted) and the position angle sweep with an RVM fit. Other panels show phase-folded γ-ray data in different energy bands. The black histogram in the > 1GeV panel shows photons with > 3 GeV. Two rotations are shown. For details see [16].

Extension studies of galactic sources with Fermi Francesco Giordano on behalf of the Fermi-LAT Collaboration

Abstract The Fermi data analysis tools have been developed on maximum likelihood minimization routine. This analysis technique is extensively used to determine the spectral parameters as the flux and the spectral index of a gamma-ray source, crucial aspects in determining how particles are accelerated, but it may also be used to measure the extension of not pointlike emission regions obtaining precious information about the sites where the acceleration takes place. The capability of the analysis presented here has been deeply studied with simulations varying the source flux, the spectral index, and the position within the galactic plane. This analysis procedure has been applied for determining the extension of the Vela X [1] and the MS H 1552 [2] [3] PWNe, as well as the extension of the W51C [4], W44 [5] and the IC443 [6] SNRs.

1 The simulated cases A simulation based on the Fermi Science Tool gtobssim has been run to investigate the extension determination of gamma-ray galactic sources. Two different cases have been studied. The first concerned the study of the extensions of galactic sources located in very crowded region like the ridge or in less noisy regions like the anticenter. The second test case was a simulation of an extended source emitting underneath a bright pulsar located in the Vela region. The aim is to study the effect of the Nebula on the pulsar spectrum and to test the capability of detecting the Nebula selecting the off-pulse phase of the pulsar as done in the detection of VelaX and MS H1552[3]. Extended Sources analysis. The detection of a possible extension of a galactic source is a crucial aspect in those cases where the gamma-rays emission is suspected to come from the shell of a SNR rather than from a compact object within Francesco Giordano Dipartimento Interateneo di Fisica dell’Universita’ e del Politecninco di Bari and INFN Sez. Bari, Via Amendola 173, I-70126 Bari (Italy); e-mail: francesco.giordano.ba.infn.it N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_6, © Springer-Verlag Berlin Heidelberg 2011

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the SNR. Some examples of these pulsar-SNRs complex are the two middle aged W44 and W51 SNRs as well as the IC443 SNR. A simulation has been developed in order to study the effect on the extension determination depending on the brightness, the hardness and the background contamination. Three different integral fluxes (10−8 cm−2 s−1 , 10−7 cm−2 s−1 and 10−6 cm−2 s−1 for E>100MeV) and two different spectral indexes (-1.5, -2.5) have been simulated, locating the sources both in the very dense galactic ridge and in the lower noisy MilkyWay anticenter. The analysis is based on the binned gtlike [7] Fermi Science Tool. A region of 10◦ around the source has been selected and a cut at 100MeV has been applied, extending the energy range up to 100GeV. For each test case it was assumed a pointlike hypothesis and different extended gaussian templates with a width ranging from 0.1◦ to 1.5◦ and a maximum likelihood fit was done. For each different template hypothesis the Test Statistic (TS), which is an estimator of the significance of the detection, is evaluated from the fit and the trend versus the template extension is reconstructed. The extension is then quoted as the dimension of the template which maximizes the TS value if significantly higher than the pointlike hypothesis (TSext -TS ptlike > 5σ) and the uncertainty is estimated looking at the width of the curve around the maximum according to TSle f t =TSright =TSext -25. As a general behaviour (Table1), the detection of the extension of weak and soft sources especially in very crowded regions (like the galactic ridge) was found to be very hard. However, due to the spectral shape of the galactic diffuse emission, and mostly due to the Fermi PSF which improves at high energy (∼0.5◦ at 1GeV), hard sources are easier to be detected even at low longitude. Table 1 Measured extension as a function of background, spectral index Γ, integral flux F above 100MeV (ph cm−2 s−1 ) and extension σext . Low Background High Background Γ=-1.5 Γ=-2.5 Γ=-1.5 Γ=-2.5 σext F=10−6 F=10−7 F=10−8 F=10−6 F=10−7 F=10−6 F=10−7 F=10−6 0.25◦ 0.25±0.002 0.25±0.03 0.25±0.15 0.25±0.03 0.25±0.2 0.25±0.004 0.25±0.05 0.2±0.1 0.5◦ 0.5±0.005 0.5±0.04 0.5±0.2 0.5±0.04 0.5±0.3 0.5±0.007 0.5±0.1 0.4±0.15 1.0◦ 1.±0.01 1±0.05 0.8±0.4 1±0.08 0.8±0.4 1±0.01 1±0.3 1.3±0.4

An extended source behind a pulsar. The second simulation was developed to study the capability of detecting an extended emission behind the pulsation of a bright pulsar and at the same time to study possible effects on the pulsar spectrum if the contribution from the Nebula is neglected. A Vela-like pulsar (Fig.1 left) has been simulated assuming for the spectral shape a power law with an exponential cutoff with an integral flux for E>100MeV of 9×10−6 cm−2 s−1 , index equal to −1.62 and energy break at 8GeV. For the Nebula was assumed an isotropic extended source of 0.8◦ centered at the pulsar location with a power law emission with a flux of 10−7 cm−2 s−1 and an index of -2.1. Fig.1 shows the timing solution and the spectra results. It is worth to note that the fits of the pulsar obtained including the Nebula in the model (solid line) or neglecting its diffuse contribution (dashed line) are different. The integral flux of

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Fig. 1 Top: Pulsar phasogram. Bottom: The pulsar spectrum and the off-pulse detection.

the pulsar fitted neglecting the Nebula is higher than the flux measured considering its contribution (8.7 ± 0.3 ×10−6 cm−2 s−1 vs 9.4 ± 0.1×10−6cm−2 s−1 ). Concerning the break and the index, the values obtained including the Nebula are 8.6 ± 0.3 GeV and -1.63 ± 0.01 closer to the simulation if compared to 10.5 ± 0.3 GeV and -1.72 ± 0.05 obtained fitting the pulsar alone. A possible explanation of these differences may be that lower energy photons have the responsibility to make the spectrum softer, higher energy gamma-ray photons, especially those above the pulsar break, clearly belong to the Nebula but if the extended source is not taken into account, the fitting procedure force them to be attributed to the pulsar, resulting in a spectral

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function with a higher break. In the same figure is also shown what has been detected in the narrow Off-Pulse window (from 0.4 to 0.6): an extended emission has been detected at 6σ level, with an integral flux 0.2 times lower than the simulated value and a spectral index of approximately -2.1.

2 Galactic extended SNRs: the W51C, the W44 and the IC443 Two galactic classes of objects are expected to be extended: the SNRs and PWNe. The Fermi detection of the extension of the VelaX and the MSH1552 PWNe are deeply presented in [3]. Concerning the SNRs, fermi has detected the extension of three SNRs: the W51C, the W44 and the IC443. The W51C is a middle-aged supernova remnant (∼104 yr) with intense radio synchrotron emission in its shell. It is well known that the W51C is interacting with a surrounding molecular cloud. For running binned gtlike it was assumed a two-dimensional gaussian template [4], detecting an extension of σext = 0.22◦±0.02◦ . The extension of the source support the idea of precluding gamma ray radiation from the CXOJ192318.5+143035 pulsar as a dominant component of the observed spectrum. The W44 is another middle aged SNR known to be interacting with a molecular cloud. The analysis for extended sources has been applied and it has revealed that the GeV emission is significantly extended. It was also applied a deconvolution technique [5] for determining a precise morphology of the acceleration site. According to these considerations, the hypothesis that the gamma-rays may come from the radio pulsar PSR B1853+01 or from its small PWN (1′ − 2′ in X-rays and radio) is disfavoured. A hadronic scenario with the molecular cloud acting as an active dump for pion production seems to be more plausible. The last case of an extended SNR is the IC 443. This SNR located in the outer Galactic plane, has an angular extent of ∼ 45′ in the radio with an age still uncertain (3-4 ky ÷ 20-30 ky). In the IC443 complex it is well known to be the CXOU J061705.3+222127 compact object and also a PWN. A blind frequency search has been performed but also in this case no pulsation has been discovered. EGRET first (3EGJ0617+2238) and MAGIC (MAGIC J0616+225) and VERITAS (VER J0616.9+2230) later have all found a gamma-ray emission from the IC443 SNR and the centroids of the three sources are all displaced from that of the PWN. The extension of the IC443 measured with the Fermi LAT is 0.27◦ ± 0.03◦ and it overlaps almost completely with the VERITAS detection. For all these reasons the GeV-TeV data points have been fitted together favouring a hadronic scenario, even though a possible contribution from the PWN at low energy (E νcr we have a = 1/2 (Jackson 1975). Therefore, the merging index a is likely to corre-

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Fig. 2 The origin of bifurcated components in radio pulse profiles. The double-lobe shape of instantaneous microbeam of curvature-radiation is shown at three positions along electron trajectory. The outward motion of electrons smears out the radiation pattern into a split-fan beam. Fig. 3 Merging rate index a in the relations ∆ ∝ ν−a , where ∆ is the observed separation of maxima/minima in double features. ‘DN’ stands for double notches, whereas ‘BFC’ for bifurcated emission components. The range of a expected for the CR is marked with vertical dashed lines. The errors are statistical 1σ.

late with the spectral index α, defined through Fν ∝ ν−α (a is expected to decrease with decreasing ν and α). Evidence for this is provided by the data: the BFC of J1012+5307, with the smallest merging index measured so far, has a very flat (hard) radio spectrum, with α ≃ 0.8. Within the errors, most of the measured values of a are consistent with the range of (0.33 − 0.5), appropriate for CR (Fig. 3). The unimodal nature of the beam is consistent with the observed high polarisation degree of the emission that contains double features. The BFC of J1012 is expected to have the shape of the ⊥-mode CR beam (eq. 4 in DRD09), convolved with the profile of stream density, and geometric effects, and with some contribution of the second (k) mode. Fig. 4 shows that a frequencyintegrated CR beam can imitate these factors fairly well. The BFC of J1012+5307 is ten times wider than the intrinsic bifurcation angle of CR, 2ψmax = 0.8◦(ρ7 ν9 )−1/3 , calculated for dipolar radii of curvature ρ7 = ρ/(107 cm) ∼ 1, and ν9 = ν/(1 GHz). The BFC might have been enlarged by geometrical viewing effects (cutting the stream at a small angle δcut or a near alignment of sightline with the rotation axis). In a forthcoming paper we show that in the case of the non-orthogonal cut, the BFC is near symmetrical only at a single ‘frequency of symmetry’ νsym . For ν , νsym the BFC becomes asymmetric, because

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Jarosław Dyks, Bronisław Rudak and Paul Demorest

Fig. 4 Best fit of the νintegrated and ⊥-modedominated curvature beam to the BFC of J1012+5307 at 0.82 GHz. The fit has χ2 /dof ≃ 3.6. Dashed verticals mark the phase interval of the fit.

of residual radius-to-frequency mapping. Peaks of such a BFC dominate alternatingly below/above νsym , which agrees with the observations (see fig. 5 in Kramer et al. 1999). We do not expect the double features to be visible in single pulses. This can be understood from Fig. 2: before the line of sight moves from the left to the righthand-side lobe of the microbeam, the electrons observed through the left lobe (contributing to the leading peak of the BFC) are ‘gone’. Radiation of the trailing peak of the BFC comes from different (new) electrons, which in the meantime have approached the line of sight. If the electrons are being ejected in the form of random sparks, the instantaneous flux in the two peaks of BFC will not be the same. It will resemble the normal noisy single-pulse signal of pulsars. Acknowledgements This work has been supported by the grant N203 387737 of the Ministry of Science and Higher Education.

References 1. 2. 3. 4. 5. 6. 7. 8.

Dyks J., Rudak B., & Rankin J. M., 2007, A&A, 465, 981 (DRR07) Dyks J., Rudak B., & Demorest P., 2009, MNRAS, 401, 1781 (DRD09) Jackson J.D., 1975, “Classical Electrodynamics”, John Wiley & Sons Inc, New York Kramer M., Lange C., Lorimer D., Backer D.C., Xilouris K. M., et al., 1999, ApJ, 526, 957 McLaughlin M. A., & Rankin J. M., 2004, MNRAS, 351, 808 Navarro J., Manchester R. N., Sandhu J. S., Kulkarni S.R., Bailes M., 1997, ApJ, 486, 1019 Perry, T.E., & Lyne, A. G. 1985, MNRAS, 212, 489 Rankin J.M., & Rathnasree N., 1997, J. Astrophys. Astron., 18, 91

Emission from the Polar Cap and Slot Gap Confronting Fermi Pulsar Observations Alice K. Harding and Isabelle A. Grenier

Abstract High-energy emission from pulsar polar caps is expected to occur in connection with electron-positron pair cascades close to the neutron star surface in rotation-powered pulsars. The abundant new results from Fermi, however, strongly suggest that the observed emission from pulsars originates in the outer magnetosphere and we have yet to observe any significant component of emission coming from the polar cap. The polar cap model also predicted a high-altitude emission component from electrons undergoing continuous acceleration from the polar cap to near the light cylinder in the slot gap. Emission from the slot gap will form caustics due to aberration and time delays that bunch the radiation on the trailing field lines of both magnetic poles. While the resulting light curves can account for the variety and distribution of observed Fermi light curves, the slot gap model falls short of accounting for the total luminosity implied by observations, requiring either a larger current of accelerated particles or a larger electric field in the gap. Population synthesis and phase-resolved spectral modeling can help us build improved emission models and constrain global magnetosphere structure.

1 Introduction Rotation-powered pulsars are one of the major source classes detected by the Fermi Large Area Telescope (LAT) and they dominate the identified source population in the Galactic Plane at low latitudes [3]. Since launch in 2008, the rate of discovery of new gamma-ray pulsars has exceeded expectations and the discovery of new pulsars Alice K. Harding Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, e-mail: [email protected] Isabelle A. Grenier AIM, Service d’Astrophysique, CEA Saclay, 91191 Gif Sur Yvette, France e-mail: Isabelle. [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_8, © Springer-Verlag Berlin Heidelberg 2011

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Alice K. Harding and Isabelle A. Grenier

through blind frequency searches of γ-ray data alone has been a huge success [1]. Radio-quiet or radio-weak pulsars may in fact dominate the γ-ray pulsar population, which would suggest that the space density of pulsars could be substantially larger than was implied by radio pulsars alone. Another new γ-ray source population discovered by Fermi in its first six months of operation are the millisecond pulsars (MSPs) [4]. All of these have been discovered through their radio pulsations, as the fact that 80% of MSPs are in binary systems makes blind period searches in γ rays very difficult if not impossible. However, many new radio MSPs have been recently discovered in Fermi unidentified sources (Ransom et al. 2010). These new Fermi-assisted searches have so far netted 18 new MSPs, increasing the number in the Galactic Field by nearly a third in a few months. The majority of these are very nearby (< 1 kpc), at high Galactic latitude, and in binary systems, including four “black-widow” MSPs that are interacting with and ablating their companions. The combined population of gamma-ray pulsars presently numbers about 68, a factor of ten larger than before Fermi. With the tremendous increase in new data, the time has never been better for uncovering the secrets of pulsars: the global current circulation in their magnetosphere, where they accelerate particles, how they radiate, the shape of their magnetospheres and their energetics. For more than forty years, the development of a variety of pulsar emission models has progressed slowly, in the absence of enough data to rule any out or distinguish among them. The emission developed along two major paths. Polar cap models [57, 19] assume that acceleration takes place near the neutron star surface at the magnetic polar caps, where large electric fields are induced. Acceleration also takes place in a slot gap along the last open field line up to high altitudes. The high-energy radiation occurs within a few stellar radii of the surface since the particles lose their energy rapidly, and also in the slot gap from the neutron star surface up to the light cylinder. Outer gap models [54, 18] assume that particle acceleration and high-energy emission take place in vacuum gaps that develop along the last open field lines above the null charge surface to very high altitude. A subset of models assume emission from below the null surface. In this review, we will discuss the the polar cap and slot gap model for high-energy radiation, and its predictions in light of the new Fermi data. Complementary reviews of the outer gap model by Hirotani [40] and Cheng [17] also appear in these proceedings.

2 Polar cap and slot gap electrodynamics Polar cap accelerators are based on the concept of “starvation” electric fields, where the space charge above the polar cap is not sufficient to maintain force-free (E · B = 0) conditions. The force-free charge density was first introduced by Goldreich & Julian (1969), and can be derived from −∇ ·

(Ω × r) × B = ∇ · E = 4πρGJ , c

(1)

Emission from the Polar Cap and Slot Gap

81

where Ω is the pulsar rotation rate. For a dipole field and r ≪ Rlc , where Rlc = c/Ω is the light cylinder radius, Ω·B ρGJ = − . (2) 2πec Even for a current density, ρGJ , of electrons or ions extracted from the neutron star surface, the space charge ρ < ρGJ above the surface since a continuous current density falls off faster with r than ρGJ in a dipole field due to field line curvature. Therefore, an electric field develops parallel to the magnetic field, E k , in the absence of any other sources of charge [14] ∇2 Φ = ∇ · Ek = −4π(ρ − ρGJ)

(3)

A plausible source of charge is electron-positron pair production by single photons in the strong magnetic field of the neutron star [27, 20]. However, the photons must have energies and angles above threshold E γ sin θkB > 2mc2 to pair produce and for the surface fields around 1012 − 1013 G the cross section is proportional to exp (−4/3χ), where χ = ǫB′ sin θkB /2, where ǫ is the photon energy E γ in units of mc2 , B′ ≡ B/4.4 × 1013 G and θkB is the angle of photon propagation to the field. Since the photons are initially emitted nearly parallel to the magnetic field so that > 0.1, thus requires that the photons sin θkB ≪ 1, the condition for pair production, χ ∼ have very high energies ǫ > 100 MeV. Such high energies require particle acceleration to Lorentz factors of at least γ ∼ 105 − 107 .

2.1 Polar cap pair cascades The two main types of polar cap accelerator are vacuum gaps [57, 62] and spacecharge limited flow (SCLF) gaps [14, 35]. Which of these form in a particular pulsar depends on whether the neutron star surface temperature is high enough to overcome the binding (or cohesive) forces on charged particles due to the lattice structure in a strong magnetic field [43]. If the surface temperature is not high enough, vacuum gaps can form above the surface [62]. The surface temperatures of most pulsars are thought to be high enough that charges are “boiled off” the surface layers and can flow along the open field lines in SCLF. The E k in SCLF accelerators is computed using Eqn(3) assuming that ρ(R) = ρGJ (R) at the neutron star surface. Since ρGJ (r) is modified by inertial frame-dragging [49], Ek is significantly larger than it is for flat space. Acceleration will be self-limited by the development of pair cascades, at altitudes where the particles reach high enough Lorentz factors to radiate γ-ray photons. The pair cascades can be initiated either by curvature radiation (CR) [19] or by resonant or non-resonant inverse-Compton scattering (ICS) of stellar thermal X-rays by primary electrons [59]. The polarization of pairs above the pair formation front (PFF) may short out the Ek by reversing a small fraction of the positrons, halting any further acceleration at higher altitude. These accelerators can thus maintain a steady

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current of upwardly accelerating electrons, at j−k ≃ cρGJ , and a downward current of positrons, at j+k ≪ cρGJ , which heat the polar cap. It was found that in dipole field geometry, the E k is screened above the PFF very effectively by CR-initiated pair cascades but the ICS-initiated pair cascades produce multiplicities too low to completely screen Ek [36]. Pulsars older than ∼ 107 yr and most of the millisecond pulsars cannot produce pair cascades through CR since the E k does not grow fast enough to accelerate particles as the dipole field falls. These pulsars are “pairstarved” and since their Ek is unscreened, particles continue to accelerate on all open field lines to high altitude. The stability of SCLF accelerators has not yet been verified through time-dependent models, and some simplified studies [41] have in fact shown that some oscillations in the pair creation rate could exist. This is certainly an issue that needs further investigation. Stability of vacuum gaps has also been studied by Gil et al. [31] and more recently time-dependent vacuum gaps have been modeled by Timokhin [61]. The pairs are produced in excited Landau states that decay through emission of synchrotron/cyclotron photons, many of which will produce more pairs in excited states. The pairs can also produce ICS photons, through scattering surface thermal X-rays, which may produce pairs [70]. Radiated spectra from CR-initiated [19] and ICS-initiated [59] cascades are very hard (roughly power laws with indices 1.5 2.0) [33] with cutoffs due to magnetic pair production attenuation at energies around several GeV [34]. Since the pair production attenuation coefficient is exponential in photon energy, the spectral cutoffs have a very sharp,“super-exponential” shape and are therefore a distinguishable prediction of polar cap models. The polar cap cascade radiation produces a hollow cone of emission around the magnetic pole, with opening angle determined by the polar cap half-angle, θPC , at the radius of emission r. The characteristics of emission from this type of polar cap model [21] could reproduce some features of γ-ray pulsars, including the wide double-peaked pulses observed from γ-ray pulsars like the Crab, Vela and Geminga, and the phase-revolved spectra. However, the polar cap opening angle is very small (a few degrees) unless the emission occurs more than a few stellar radii above the surface [23]. Daugherty & Harding[21] had to assume extended acceleration to 3 stellar radii and an artificial enhancement of primary particle flux near the polar cap rim in order to reproduce the Vela pulsar spectrum and pulse profile.

2.2 The slot gap Due to the geometry of the field lines and the assumed boundary conditions of the accelerator, the altitude of the PFF varies with magnetic colatitude across the polar cap [13, 35]. Near the polar cap rim, which is assumed to be a perfectly conducting boundary, the electric field is decreasing and a larger distance is required for the electrons to accelerate to the Lorentz factor needed to radiate photons energetic enough to produce pairs. The PFF thus curves upward as the boundary is approached, forming a narrow slot gap near the last open field line [13]. Since Ek


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is unscreened in the slot gap, particles continue to accelerate and radiate to high altitude along the last open field lines. The accelerating E k in the slot gap can be determined by solving Poission’s Equation in the narrow flux tube bounded on the inner edge by the PFF and on the outer edge by the fully-conducting last open field line. Muslimov & Harding have found solutions for the SG E k , including inertial frame-dragging, both near the neutron star surface [46] in dipole field geometry " # 3 κ θ0 2 E ||,low ≃ − B0θ04 ∆ξSG cos α + sin α cos ϕ [1 − ξ∗2 ] (4) 4 η4 2η1/2 and at large altitudes [47]. In Eqn (4), α is the angle of the magnetic axis to the rotation axis, ϕ is the magnetic azimuth, B0 is the surface magnetic field strength, ξ∗ is the magnetic colatitude in the SG, where ξ∗ = 0 at the gap center, and κ = 0.15I45/R36 , where I45 = I/1045 g cm2 is the neutron star (NS) moment of inertia and R6 is the neutron star radius in units of 106 cm. The luminosity of the SG from each magnetic pole is LSγ G

= εγ c

Z

2π 0

dϕ

Z

θ0 θ0 (1−∆ξSG )

ρ(η)Φ(η)r2 sin θdθ

(5)

where ρ(η) and Φ(η) are the primary charge density and potential as a function of radius η ≡ r/R, in units of NS radius and εγ is the radiation efficiency. The width of the slot gap, ∆ξSG , is a function of pulsar period, P, and surface magnetic field, B12 ≡ B0 /1012 G [46], and can be expressed as a fraction in colatitude ξ ≡ θ/θ0 of the polar cap opening angle, θ0 ≃ (ΩR/c)1/2. Young Crab-like and Vela-like pulsars have widths ∆ξSG ≈ 0.05 − 0.1 which increase with age as P B−4/7 approximately. 12 Using the expressions for the low-altitude SG in Eqn (12) for Φ and Eqn (4) for ρ from [46], we have ∆ξSG 1 )[κ(1 − κ)(1 − 3 ) cos2 α + 2 η s    9 2 ∆ξSG 2  H(η) f (η) θ0 (1 − )H (1)  η − 1 sin2 α] 8 2 H(1) f (1)

3 LSγ G,low = εγ E˙ sd ∆ξSG (1 −

(6)

where E˙ sd = Ω4 B20 R6 /6c3 f (1)2 is the spin-down power, and H(η), f (η) are functions given in Muslimov & Tsygan [49] (see also [35]). The high-altitude SG luminosity from each pole can also be determined from Eqn (5) using Eqn (52) for Φ and Eqn (21) for ρ from [47], ( ∆ξSG 1 η 3 LSγ G,high = εγ E˙ sd ∆ξSG β(1 − ) [κ(β − κ)(1 − 3 ) + 1 − β](1 + ) cos2 α 2 ηlc ηc  s      H(ηc )   9 f (1)  + θ2 H 2 (1)  ηc − β sin2 α (7)   8 H(1) f (ηc ) 

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where β = (1 − 3η/4ηlc)1/2 and ηlc = rlc /R = c/ΩR. The electrons that accelerate in the slot gap will radiate curvature, inverse Compton and synchrotron radiation at high altitudes. Initially, their Lorentz factors will be limited by curvature-radiation reaction, to γCRR = ((3/2)E ||ρ2c /e)1/4 ∼ 3 × 107 and 3 /ρ ≈ 3 GeV. Musthe peak energy of their CR spectrum will be εCR = 2λC γCRR c peak limov & Harding[46] found that pair cascades on the inner edge of the slot gap occur at altitudes of 3-4 stellar radii and have higher multiplicities M+ ∼ 104 − 105 than the polar cap cascades. As the electrons reach higher altitude, where the local magnetic field has dropped to B ∼ 106 − 108 G, they may be able to resonantly absorb radio photons of energy ε0,GHz that are at the cyclotron resonance in their rest frame [42]. The condition for resonant absorption is γR = 3 × 105 B8 ε0,GHz /(1 − βµ0) where B8 ≡ B/108 G and µ0 is the cosine of the angle between the radio photon and the electron momentum. The electrons are then excited to higher Landau states and radiate synchrotron emission. Petrova [50] concluded that this process could be a significant source of radiation for young pulsars [39]. It could also be significant for millisecond pulsars with high radio luminosities like PSR J0218+4232 [38].

3 Geometry of high-energy radiation The geometry of emission at high altitude is strongly influenced by special relativistic effects of aberration, time-of-flight and retardation of the magnetic field. Aberration and time-of-flight each produce phase shifts of comparable magnitudes ∆φ ∼ −r/Rlc in radiation emitted at different altitudes rem to the light cylinder radius Rlc . Morini [45] first noted that the combined phase shifts from aberration and timeof-flight, of photons radiated tangent to a magnetic dipole field from the polar cap to the light cylinder, nearly cancel those due to field line curvature on the trailing edge of the open-field region. Radiation along such trailing field lines bunches in phase, forming a sharp emission peak or caustic in the pulse profile. On the leading side, these phase shifts add up to spread photons emitted at various altitudes over a large range of phases. The effect is most pronounced for large α and emission between altitudes rem ∼ 0.2 − 0.8 R LC . Sweepback of the magnetic dipole field due to retardation [22, 68] affects photon emission directions near the light cylinder, and also distorts the polar cap and open field volume [12, 24], even at the stellar surface. Most observer angles sweep across caustics from both magnetic poles, resulting in a double-peaked pulse profile where the peaks generally have phase separation less than 180◦ [26]. Furthermore, emission occurs at all phases in the profile. Such profiles are very similar to those of the bright γ-ray pulsars, Crab and Vela. The predicted polarization characteristics of such a “two-pole caustic” (TPC) model in a retarded vacuum dipole [22] geometry can also explain the observed optical polarization of the Crab pulsar [25]. Radiation from the slot gap has a geometry very similar to that of the “twopole caustic” model and thus displays caustics in the intensity phase plots as well as Crab-like pulse profiles [47]. The high-altitude slot gap thus may be a viable


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model for high-energy emission from young pulsars. However particle acceleration in the slot gap, as derived for dipole fields, may not operate at all inclination angles. The low altitude E k , shown in Eqn (4), is a function of both α and ϕ. For large α and cos ϕ < 0 (field lines curving away from the rotation axis), the second term in Eqn (4) can become large and negative at large r, causing the E k to reverse sign. This would cause a buildup of charge at that location, and would clearly be an unstable situation. The charge flow along those field lines might then be either time-dependent or nonexistent. The solution for E k at high-altitude in the slot gap [47] may moderate > 70◦ the E reverses sign at low this effect somewhat, but for fast rotators and α ∼ k altitude. A possible resolution to this problem may require opposite signs of charge being accelerated in different parts of the polar cap (see Section 5). Until recently, the retarded vacuum dipole was the only geometry used to model high-energy pulsar light curves. Although it was obvious that the Deutsch solution was not a realistic model for pulsar magnetospheres filled with currents and charge, it was relatively simple and easily implemented. In the last few years, solutions for the force-free magnetosphere have been computed for oblique rotators [58, 60]. Since such geometries assume that E · B = 0 everywhere and there is no particle acceleration, they are still not realistic. Yet they are thought to be closer to the magnetospheric geometry of a young pulsar in which pair cascades screen the Ek throughout most of the open field volume except in small or narrow charge-depleted regions. The first light curve models using force-free geometry [15] show that the caustic patterns are somewhat different from those in in vacuum dipole geometry. Since the force-free field lines at large radii are straighter than dipole field lines, due to distortion by the toroidal currents, the footpoints of the open field lines define a wider polar cap. The caustics of the TPC and OG emission are less sharp and stronger caustics appear near or across the light cylinder. The light curves resulting from this “separatrix layer” (SL) model, emission in a narrow gap between ξ = 0.9 or 0.95 and 1.0 very similar to the SG except extended beyond the light cylinder, produce similar double-peaked shapes to those of the SG. Pair starved polar cap models (PSPC) produce very different emission patterns, with radiation concentrated near the polar caps but extending to high altitude [26]. The predicted light curves will consist of narrow peaks in phase with the radio pulse if the viewing angle crosses near the magnetic axis, but will consist of a single broad peak leading the radio pulse if the viewing angle to the magnetic axis is large, since the high-altitude emission will be shifted to earlier phase by aberration [26].

4 Confronting the Fermi observations Since its launch in 2008, Fermi has discovered many new gamma-ray pulsars, increasing the known population by a factor of ten [53]. Several classes have emerged: young and energetic radio-loud gamma-ray pulsars, young radio-quiet or radioweak gamma-ray pulsars, and old gamma-ray millisecond pulsars. Surprisingly, each of these classes comprises about a third of the population. With its increased

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sensitivity, Fermi has also measured the spectra and light curves of the known and bright pulsars with much greater detail. We now have the prospect of discriminating between emission models and magnetospheric geometry as was never before possible.

4.1 Spectra One of the most important measurements that Fermi was anticipated to make early in the mission was of the spectral cutoff shape of Vela and other bright pulsars. Determining whether the cutoff fit better with a simple or a super-exponential could confirm or rule out gamma-ray emission in the strong near-surface magnetic fields predicted by PC models. Within the first few months of data collection, Fermi measurement of the spectra cutoff of Vela [2] was able to rule out the super-exponential fit with a significance of 16σ. The cutoffs of other bright pulsar spectra such as Geminga [7] and the Crab [8] also fit a simple exponential shape, indicating that the gamma rays are emitted far above the neutron star surface. In fact, the fits even prefer a shape that is more gradual than a simple exponential. Measurements of the pulsar spectra across the profile in small phase bins is revealing new details about the emission. Both the photon index and particularly the cutoff energy vary with phase. The cutoff energy undergoes rapid changes in the peaks and in the interpeak region, in the case of Vela [5], by factors of 2 - 3. Such changes in cutoff energy can account for the gradual shape of the phase-average spectra and also indicate rapid changes in characteristics affecting the radiation, such as altitude or magnetic field line curvature. In most outer magnetosphere (OM) models, the accelerating particles are radiation-reaction limited (i.e. their rate of energy gain from acceleration is balanced by their curvature radiation losses), so that the steady-state Lorentz factor is γCR =

"

3 Ek ρ2c 2 e

#1/4

,

(8)

where ρc is the local field line radius of curvature, and the expected spectral cutoff energy is ! E k 3/4 1/2 3λ –c 3 ECR = γ = 0.32 λc ρc . (9) 2 ρc CR e

where λc = 2πλ–c is the electron Compton wavelength. The cutoff values roughly agree with those predicted for curvature radiation in the outer magnetosphere since the Ek is similar for SG and OG models. So, the variation in E c with phase would reflect variations in radius of curvature, E k or both. It opens the possibility of testing emission models and magnetospheric geometry, in particular force-free versus vacuum field geometries, by comparing their prediction of E c phase variations with the data.


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4.2 Population synthesis and light curve fitting With the much larger population of detected gamma-ray pulsars, both radio-loud and radio-weak, population synthesis becomes a more powerful tool for comparing the distributions of various properties with those predicted by models. If the different emission models such as SG, OG, PC or SL models predict distinct distributions of measurable gamma-ray pulsar properties, such as age, spin-down luminosity, gamma-ray vs. spin-down luminosity, light curve peak separations and radio lags, then observed distributions will distinguish between these models or constrain their parameters. Pierbattista et al. [52] have simulated a population of normal isolated pulsars using a Gaussian distribution for the initial period and a log-normal distribution for the initial magnetic field. The neutron star motions have been evolved in the Galactic potential. Geometrical and luminosity models of the core and cone components of the radio beam have been implemented to compare with the observed properties of the radio pulsars in the ATNF11 catalogue. We discuss here the case of neutron star evolution with magnetic field decay. Details of the population synthesis are given in Gonthier et al. 2010 [30], while details of the light curve simulations and early results are given by [51] and [52]. We have modeled the gamma-ray emission from the simulated pulsars for four cases: • PC: low-altitude pair cascade radiation from the slot gap above the polar cap • SG: radiation from particles accelerating in the slot gap to 95 % of the light cylinder radius • OG: radiation from the outer gap, following Zhang et al. [69] • OPC: radiation from the one-pole caustic outer-gap geometry, from the null surface up to the light cylinder, following Watters et al. [67] The main difference between the OG and OPC cases is twofold: 1) the gammaray luminosity scales as Lγ = w3OG E˙ sd for the OG and Lγ = wOPC E˙ sd in the OPC case; 2) the gap width in the OG case is computed according to the physical model of Zhang et al. [69] whereas it is simply the gamma-ray efficiency wOPC = (1033erg s−1 / E˙ sd )1/2 in the OPC case. The actual OG width changes with magnetic obliquity α and it varies with altitude, so we compute its average along the last closed field line. To locate the PFF that defines the inside gap boundary, the calculation uses the E|| (r) structure and the radiation-reaction limited Lorentz factor of the primary CR gamma rays, as well as the angle dependence of the 2-photon pair production cross-section. The assumed geometry is simple (the X rays leave radially the heated polar cap and the gamma rays are produced tangent to the last closed field line), but it captures the evolution of the gap width with P, B, and α. To determine the gap width in the SG case we find the value of ξ where the PFF at location zPFF (ξ), in units of stellar radius, begins to rise sharply,

1

http://www.atnf.csiro.au/research/pulsar/psrcat/

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Fig. 1 Slot gap phaseplots for different choices of gap widths, 0.1 (left panels) and 0.5 (right panels) and magnetic obliquities (α = 20◦ , 50◦ and 80◦ from top to bottom).

dzPFF dξ

!

=λ

(10)

ξ=ξSG

where λ ∼ 0.1 − 0.3 is a free parameter [46]. We find that a value λ = 0.2 provides the best match to the Lγ vs. E˙ sd seen in the Fermi pulsars. For the PC case, we use an emission distribution on the low-altitude field lines that approximates that of simulated pair cascades [46]. A simple radiative efficiency has been used to convert particle power into gamma-ray luminosity (100%, 400%, 30%, and 20% for the PC, SG, OG, and OPC models, respectively, to match the Fermi luminosity constraints). The need for an efficiency in excess of 1 is discussed below. To describe the radiation pattern across the sky resulting from the sweeping of each beam, we have computed 2D phaseplots or skymaps in the (ζ, φ) plane of the observer viewing angle ζ and rotational phase φ (Figures 1 and 2 show examples). The calculation includes field retardation assuming the vacuum solution [22], light travel delays, and relativistic aberration [25]. The sharp peaks seen from the OG profiles in Figure 2 result from the assumption of a very thin radiative layer along the gap inner edge (away from the last closed field line). The SG peaks in Figure 1 appear more smeared because we have assumed a broader photon distribution across the gap width. Their density profile perpendicular to the field lines peaks in the middle of the gap and falls to zero along the last closed line and along the gap inner edge. A grid of phaseplots has been produced to fully sample the magnetic obliquities and pulsar characteristics relevant to each radio and gamma-ray beam model (period and its derivative, magnetic field, gap width, radio frequency). The phaseplot of a particular pulsar has been obtained by careful interpolation within the


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Fig. 2 Outer gap phaseplots for different gap widths and magnetic obliquities.as in Fig. 1.

grid, preserving the continuous transformation of pattern shapes from one choice of parameter to the next. The phaseplot has then been normalized to twice the total luminosity per pole that the pulsar can sustain for a given model. Light curves, at the viewing angle of the simulated star, have been integrated to compare the average point-source gamma-ray flux with the 6-month sensitivity map given in the Fermi pulsar catalogue [9]. The population synthesis results can be used to probe both the energetics of the gamma-ray emission, by comparing simulated and observed distributions of gamma-ray vs. spin-down luminosity, and the geometry of the gamma-ray emission, by comparing simulated and observed light curve characteristics. One important quantity we can determine (and in fact requires a particular emission model to determine) is the beam correction factor fΩ [67], which allows us to derive the total luminosity radiated by a pulsar Lγ = 4π fΩ Fγ d2 , from its measured phase-averaged energy flux Fγ . Figure 3 shows the computed beam correction factors for the simulated pulsars in the PC, SG, OG and OPC models as a function of spin-down luminosity. The PC model has very small values of fΩ because all of the visible emission is concentrated in a small region near the magnetic poles. The SG, OG and OPC models have larger values of fΩ since emission is distributed over a large part of the sky. In the SG case, fΩ ∼ 1, and can even be larger than 1, with small dispersion and a very small trend decreasing fΩ with E˙ sd . As the SG ages and the gap widens, the centroid of emission moves toward the magnetic pole but the emission pattern on the sky remains extended because emission comes from all altitudes. In the OG and OPC cases, fΩ has a larger range from around 1 down to 0.01, with a distinct trend of smaller fΩ with decreasing E˙ sd . This trend results from the widening of the gap with age, which in OG models moves the emission towards the magnetic axis, and

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collapses the emission in the skymap onto the spin equator (ζ = 90◦ ). This has an effect similar to the PC model and thus produces small fΩ values (but the emission is at very high altitude). The smaller values of fΩ in the outer models allows smaller gamma-ray efficiencies in older pulsars, but the large dispersion can severely impact the derivation of a pulsar luminosity from the observations. The large spread in fΩ values that we find for the OPC model is purely due to the radiation pattern of the pulsed emission since there is no dispersion in the modelled luminosity. 1

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The derived values of fΩ can be used to determine the Lγ for the observed pulsars from their Fγ and we may examine their gamma-ray efficiencies with age. The Fermi pulsars cover five decades of spin-down power and four decades of gamma1/2 > 1034 − 1035 erg s−1 which at E˙ sd ∼ ray luminosity, showing a general trend Lγ ∝ E˙ sd ˙ ˙ breaks to Lγ ∝ Esd at lower Esd . Both PC and SG models predict such a break, since pair screening at high E˙ sd limits the acceleration voltage to about V = 1013 Volt independent of P and B [35]. In that case, the gamma-ray luminosity Lγ = V n˙ p is 1/2 simply proportional to the primary current, n˙ p = ρGJ APC c ∝ E˙ sd [32]. For pulsars ˙ with lower Esd , pairs are not produced efficiently enough to screen the Ek and the 1/2 voltage grows to the entire open field value VPC ∝ E˙ sd . Both the normalization of the Lγ vs. E˙ sd and the position of the break constrain the gap acceleration and the width of the SG as a function of pulsar age. Figure 4 shows the different model predictions plotted with the Lγ of the Fermi pulsars. The OG model also generally 1/2 predicts a trend of Lγ ∝ E˙ sd at high E˙ sd , since the voltage of the OG is limited by pair screening in a similar way to that of the PC and SG. In the simulated pulsar populations, the SG model predicts a slightly higher proportion of young and energetic pulsars than the OG model, so that the SG is in better agreement with


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the data in this respect. As mentioned above, the predicted break can be adjusted to fit the data by varying the parameter λ that determines how the SG widens with age and we find that a relatively large value of λ, giving relatively narrow gaps, produces the best break location. Narrower gaps also produce narrower gamma-ray peaks that provide better fits to gamma-ray pulsar light curves. So both the Fermi lightcurve shapes and the Lγ vs. E˙ sd trend point to narrow gaps. However, smaller gap widths give lower predicted Lγ for the SG that are too low compared to those of the observed pulsars by about a factor of five. This indicates that either the current of radiating particles or the voltage in the SG is higher than currently expected. 29

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Another measure that can discriminate between emission models is the distribution of viewing angle ζ and magnetic inclination angle α. Figure 5 shows the ζ and α of the simulated pulsars for each model. The results are strikingly model dependent, with PC models favoring very small or very large ζ, SG models allowing visible emission at all ζ across the sky, and OG models favoring a small range near the equator ζ ∼ 90◦ . An interesting correlation is that in SG models, the range of ζ decreases with increasing α while in OG and OPC models the range of ζ increases with α. These trends are again due to the different sky patterns in the SG and OG models, with the outer-gap models at smaller α being restricted to small bands near ζ = 90◦, while the SG patterns are not so restricted. The total number of pulsars detectable by Fermi after 6 months, as well as the ratio of radio loud (RL) to radio quiet/weak (RQ), are also shown in Figure 5 for each model. Compared with the number of 38 detected non-millisecond pulsars reported in the Fermi pulsar catalog [9], the number of visible simulated pulsars for the SG is only a few short but the PC, OG and OPC are significantly below the observed number. The mean ages of the

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simulated visible pulsars in all models, however, are greater than for the observed pulsars, as can be seen in Figure 7. PC : 5.1 RL/RQ 2.6

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The Fermi pulsar light curves show a fair degree of diversity, but there are several distinctive patterns that have emerged. About 75% have two peaks and a majority of these have a wide separation between 0.4 and 0.5 of pulse phase. The pulses are very narrow in most cases, with widths of less than 0.1 in phase. The light curve shapes of the simulated pulsars have been analyzed for several key characteristics that can be compared with those of the data. We have built an automated classification scheme based on the number of maxima, minima, and inversion points in the profile. The light curves were first smoothed to keep only the bulk features, i.e. a single peak, two well-separated peaks, a closer double peak, triple peaks, shoulders, etc. that are displayed in Figure 6. The light curves have then been fitted with a combination of Gaussians (for the PC) or of Gaussians and Lorentzians (for the SG, OG, and OPC) in order to locate the peak positions in phase and to derive their intensity and width. The closest magnetic pole is set at phase zero. We have divided the different light curve types into different classes for each model. Figure 6 shows the classes for PC, SG, OG and OPC models and their frequency of occurrence in both the simulated parent population and in the population that would be visible to Fermi as point source after 6 months of sky survey. It is apparent by the similarity of the parent and visible population distributions that there is little loss of morphology information in the visible sample.


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Fig. 6 Typical examples of light curve shapes found for each model. The histograms give the recurrence of each class in the parent sample that shines towards us (in black) and in the visible gamma-ray sample that passes the Fermi detection threshold (in gray).

Since there are many parameters with which to explore the light curve diversity (peak multiplicity and separation, sharpness, skewness, radio-gamma peak lags, etc.) in this multivariate space (E˙ sd , gap width, age, obliquity, orientation, etc.), we present and comment on only a few snapshots taken from two samples, the total parent population of neutron stars with non-zero light curve, and the visible gamma-ray sample with an integrated point-source flux that is larger than the 6-month Fermi sensitivity threshold in the pulsar direction. The comparison between the parent and visible samples is less sensitive to orientation effects than to flux thresholding since the pulsars from both samples do shine in our direction. Figure 7 shows the distribution of peak spacing with characteristic age. It is apparent that all of the models lack widely-spaced peaks. This may tell us that the assumed magnetospheric geometry needs to be revisited [55], but it also reflects the lack of young pulsars that can match the Fermi sensitivity threshold in all the simulated models. The problem is more pronounced for the OG models because the peak separation rapidly shrinks with age as the gap widens. Such a correlation results from the one-pole origin of both peaks of the OG models, where the peak spacing narrows as the inner edge of the gap moves closer to the magnetic axis as the gap width grows with age. The OG peak separation is also very sensitive to α. The SG model predicts more pulsars with peak separations of 0.4 - 0.5 than the PC or OG models and it exhibits little evolution of peak spacing with age, since the two peaks originate from opposite magnetic poles and even as the gap widens with age the peak spacing remains roughly the same for a given inclination and viewing angle. The Fermi pulsars do not seem to show a strong correlation of peak spacing with age, as predicted by the OG and OPC models. The data thus favor two-pole emission models such as the SG, TPC or SL models.

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Alice K. Harding and Isabelle A. Grenier PC : 5.1 RL/RQ 2.6

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4.3 New insights from the increasing γ-ray MSP Population The discovery of gamma-ray pulsations from millisecond pulsars (MSPs) and the extraordinary increase in their number in the last year or two opens up the opportunity for improved understanding of this ancient population of neutron stars. By the same token, the latest results reveal more complicated and varied characteristics than previously imagined. Continued observations will add more MSP members to the high-energy source catalogs of space missions such as Fermi and AGILE, while the non-detection of VHE gamma rays from MSPs to date by ground-based instruments such as H.E.S.S. and MAGIC tentatively rule out spectral components beyond 100 GeV, such as those expected from ICS emission. Pre-Fermi Expectations: PSPC Models MSPs occupy the lower left corner of the ˙ therefore low magnetic fields. PP˙ diagram due to their relatively short P and low P, This region falls below the predicted curvature radiation (CR) pair death line [37], so that MSPs were not expected to have copious pair production in their magnetospheres. Rather, it was believed that most MSPs should have unscreened magnetospheres [38], as is evidenced by modeling of MSPs assuming pair-starved electric fields in the so-called pair-starved polar cap (PSPC) scenario [48, 38], and prediction of single gamma-ray pulses roughly in phase with the radio [63, 28]. In the PSPC model, the low pair multiplicity allows charges to be continually accelerated up to high altitudes over the full open-field-line region. Furthermore, the formation of a PSPC gap is seen as the relaxation of an SG accelerator to a PSPC structure with increasing pulsar age.


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Post-Fermi MSP modeling: OGs, TPCs / SGs, and PSPCs Recent results [26] of 3D emission modeling of 8 Fermi-LAT MSPs [4] led to the surprising conclusion that the radiation of most of the MSPs originate in the outer magnetosphere. A large number of light curves were generated for the standard PC, PSPC, OG, and TPC geometries, for nearly the full range of inclination and observer angles, as well as various periods and gap widths. While PC models do not provide good fits for MSP light curves with a nonzero phase lag between radio and gamma-ray peaks, most of the light curves are best fit by TPC and OG models. This indicates that narrow accelerating gaps limited by robust pair production exist even in MSPs with very low spin-down luminosities. The gamma-ray light curve lags the radio for six MSPs (PSR J0030+0451, PSR J1614−2230, PSR J0218+4232, PSR J0437−4715, PSR J1613−0200, and PSR J0751+1807), and are well fit by TPC and OG models. The very thin TPC / OG gaps needed to model the Fermi-LAT MSP light curves indicate that new pair creation mechanisms (or different magnetospheric conditions) are needed for low-E˙ sd pulsars. For two other MSPs (PSR J1744−1134 and PSR J2124−3358) the gammaray curves lead the radio by 0.15 in phase, and these two cases are exclusively fit by the PSPC model, where we are viewing the high-altitude emission. Lastly, several new MSPs now exhibit phase-aligned radio and gamma-ray light curves (see next section), so that three mutually exclusive gamma-ray MSP subclasses are now emerging. The gamma-ray spectra of MSP detected by Fermi are also similar to those of the younger gamma-ray pulsars: hard power laws with simple (not super-) exponential cutoffs around several GeV [4]. This finding is consistent with emission from the outer magnetosphere although, because MSP surface fields are so low, one does not expect magnetic pair production to cut off the spectrum below the CR cutoff at least for the low- E˙ sd sources [38]. The fact that the magnetic field strength at the light cylinder is similar for MSP and young gamma-ray pulsars though lends support to the outer magnetosphere emission hypothesis. Phase-aligned MSP light curves The discovery of three MSPs (PSR J0034−0534, PSR J1939+2134, and PSR J1959+2048) with phase-aligned radio and gamma-ray light curves [6, 4] argues for co-located emission regions for the radio and gammaray radiation. While these light curves may be reproduced by (faded) PC models (low-altitude geometric models with modulated gamma-ray emissivities which mimic results from pair cascade modeling; see section 4.2) [25], there are also very reasonable fits provided by so-called ‘altitude-limited TPC / OG’ models [66]. In the latter models, we limit the minimum, rmin , and maximum, rmax , radius of emission of the TPC and OG gaps which provides a greater variety of pulse shapes. The extended radio emission ( rmin = 0.6Rlc, rmax = 0.8Rlc ) is enveloped by the gamma-ray emission regions ( rmin = R, rmax = 0.9Rlc) for the case of PSR J0034−0534, and is typically situated very close to the light cylinder, which is relatively near the stellar surface when compared with of younger pulsars (e.g., a 2 ms MSP’s light cylinder occurs at ∼10 stellar radii).

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VHE Expectations Since the observed CR spectral cutoffs occur around a few GeV (section 4.1), it is very unlikely that these GeV components will be seen by Cherenkov detectors. Rather, it is hoped that ICS components due to the scattering of thermal X-ray photons by relativistic electrons may be visible in the upper GeV to TeV range. However, modeling of ICS components for MSPs using PSPC electric fields [16, 38] reveal that these components are expected to be at a much lower level than the CR radiation, although such ICS calculations should be redone using SG / OG electric fields in the light of the the new results described above. Still, the order-of-magnitude sensitivity increase of the CTA and AGIS over the current ground-based observatories might lead to the detection of VHE emission from MSPs [56].

5 Learning from Nature - Future pulsar modeling In the two years since the launch of Fermi, we have learned much about pulsar emission. Predictions of a number of different models have now confronted the data and, although some have provided encouraging fits to observed light curves, all have failed in some aspects. Polar cap models where emission originates near the NS surface do not seem to be producing the main gamma-ray pulsations from any detected Fermi pulsars. This result does not, however, imply that near-surface acceleration and pair cascades are not occurring. Such cascades are in fact thought to be necessary for observed radio emission, to establish force-free conditions over most of the open magnetosphere in young pulsars and to create narrow accelerator and radiation gaps. We just need to understand why the gamma-ray emission that accompanies the pair cascades is not yet seen. If it is a matter of viewing geometry, the PC emission should cross our line-of-sight eventually. If the luminosity is simply below present sensitivity levels, detecting the PC emission may require deeper observation of faint off-pulse bumps. If PC emission remains invisible, population modeling will be able to give interesting limits of PC cascade activity. The observed gamma-ray pulse shapes and phase lags with respect to the radio pulses point to high-altitude emission from narrow gaps being dominant for all geometries. In general though, the SG/TPC and OG models that seem to provide reasonably good fits to Fermi pulsar light curves do not provide enough power through the thin gaps required for good light curve fits. Does this tell us that these models have the right geometry of emission but the wrong energetics? The population studies also show that none of the models (PC, SG, OG or OPC) produce enough young pulsars compared to observations, and therefore do not produce the numbers of visible gamma-ray pulsars that Fermi is detecting. This problem may be a result the simulated neutron stars evolving too fast toward longer periods (possibly due to the wrong initial period or magnetic field distribution), or result from the SG or OG widths growing too fast with age. In addition, the model fits to MSP light curves seem to also require narrow gap widths. But the standard models predict that


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MSPs should not be producing the high-multiplicity pair cascades necessary to form narrow accelerator gaps. However, all of the acceleration and radiation models developed to date assume dipole magnetic fields and do not incorporate current closure. Perhaps the failure of the models to confront many properties of the data is linked to these approximations and understanding the Fermi observations will require models to include more realistic field geometry and energetics. In the last few years, the “pulsar equation” [44] has finally been solved numerically to produce oblique pulsar magnetosphere models [58] with current closure. The current in these models has a strong effect on the magnetic field geometry, producing currents sheets and large distortions from the vacuum geometry in the outer magnetosphere. Although these models are force-free (E · B = 0) so that there is no particle acceleration, in the case of young pulsars with (apparently) very thin accelerator gaps, the force-free models may provide a more realistic zeroth-order geometry for pulsar acceleration models. It is likely that the accelerating electric fields that exist in the gaps in force-free geometry are quite different from those in vacuum geometry. The force-free magnetospheres have larger polar caps and currents of both sign across the polar cap [15]. The existence and form of slot gaps and outer gaps in force-free magnetospheres will depend on how pair cascades can function and whether they can provide the high pair multiplicity and currents that are required. The next few years will present new challenges for pulsar modeling but also an unprecedented opportunity to make use of a growing data set from Fermi that will provide us with more challenges for years to come. We would like to thank our collaborators, Christo Venter, Marco Pierbattista and Peter Gonthier, for all their help in generating the results for this review.

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Gamma-ray emission and pair creation of outer gap K. S. Cheng

Abstract In this talk we use a simple two dimensional outer gap model, which consists of a primary acceleration region plus a screening region, to calculate the theoretical curvature radiation spectrum. We find that the observed spectra of all mature pulsars detected by Fermi can be explained in terms of three independent gap parameters,i.e. the gap current in the primary accelerator, the outer gap size and the gap ratio between the primary region and the total gap size. The fitting results indicate that (1)the current in primary region is only 10% of Goldreich-Julian current, which ensures the production of multi-GeV photons from the gap and (2)the gamma-ray power of pulsars is a broken power law of spin-down power, which suggests that there are two gap closure mechanisms. We next examine two possible pair creation processes, i.e. photon-photon pair creation and magnetic pair creation, we find that the former should be dominated for Lsd > 1036erg/s and the latter is more important for Lsd < 1036 erg/s. If the magnetic pair creation is the gap closure mechanism we predict that the gamma-ray luminosity (Lγ ) and the cut-off energy of 1/4 the spectrum (Ec ) are given by Lγ ∝ L5/8 sd and Ec ∝ L sd respectively.

1 Introduction Pulsars are rapidly spinning and strongly magnetized neutron stars. They act like monopolar generators. The potential drops for young pulsars can be much higher than 1015 V. It is generally believed that the pulsar magnetosphere should fill with charge separated plasma, which corotates with the star with angular velocity (Ω) up to the light cylinder radius (rL = c/Ω), where the corotation speed equals the speed of light. In equilibrium the Lorentz force of a test charged particle in the magnetosphere should be zero, i.e. E + Ω×r×B = 0. The charge density (ρ) of the pulsar c K. S. Cheng Department of Physics, University of Hong Kong, China, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_9, © Springer-Verlag Berlin Heidelberg 2011

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magnetosphere can be obtained by ∇ · E = 4πρ, which gives ρGJ = Ω·B 2πc and this solution is called the Goldreich-Julian solution (Goldreich and Julian 1969). There is an interesting region called null charge surface, where Ω is perpendicular to B and hence ρGJ = 0. Since the charge carriers in the opposite side of this region is opposite, therefore when the current passes through this surface charges are removed from this region and hence a vacuum region is created. Since this vacuum region deviates from equilibrium situation hence the electric field along the magnetic field lines exist and it is called ”Gap”. The question is ”Would this gap continue to grow when the current continue to across the null charge surface?”. The answer is ”No” because the electric field along magnetic field increases when the vacuum region becomes bigger. Furthermore when charged particles accelerate in this region they emit curvature photons, whose characteristic energy depends on the strength of the electric field. When the vacuum region grows the characteristic energy of curvature photon also increases. Eventually the energy of curvature photons, typically a few GeV, becomes high enough to become electron/positron pairs when they collide with the background soft photons, e.g. soft X-rays emitted from the stellar surface. These pairs can stop the further growth of the ”Gap”. It has been first shown that two slab-like stable outermagnetospheric gaps can exist in the pulsar magnetopshere (cf. Fig. 7 of Cheng, Ho and Ruderman 1986a). Mathematically stable static outergap can exist by adding two boundary surface charge layers on the top and bottom boundary of the gap. Realistically the top boundary of the outergap should be a current layer, which gradually screen out the gap electric field to recover the Goldreich-Julian solution outside the gap (cf. Fig.12c of Cheng, Ho and Ruderman 1986a). Therefore in general the gap should consist of two regions, a primary acceleration region, where the current flow is much lower than the Goldreich-Julian current, and the screening region, where most of gap current is flowing and the current density can exceed the Goldreich-Julian value in order to screen the gap electric field from outside.

2 Two dimensional outergap model Although the detailed observed spectrum, e.g. the phase resolved spectrum, is determined by a three dimensional models (e.g. Tang et. al. 2008, Harding et al. 2008, Hirotani 2008, Bai & Spitkovsky 2010), the phase average spectrum can be determined by two dimensional models. By fitting the phase average spectrum of pulsars we can obtain some very useful key parameters of the gap including the current distribution, size of the gap etc. These information can let us know how the gap evolves. In this section we use a simple two dimensional outergap model to explain all fermi detected gamma-ray pulsars except 4 very young Crab-like pulsars, whose radiation is expected to be synchrotron-self-Compton process because the hot surface and the small light cylinder make the optical depth of curvature photon larger than unity. We believe that high energy photons from most Fermi pulsars are curvature photons except these four young pulsars, whose age is less than 104 yr old.

Gamma-ray emission and pair creation of outer gap

101

2.1 Gap structure Fig.1 illustrates our two-dimensional gap structure. We express the potential in the gap as Φ = Φ′ + Φ0 , where Φ0 is the co-rotating potential, which satisfies ▽2 Φ0 = −4πρGJ with ρGJ being the Goldreich-Julain charge density. In addition, the potential Φ′ is the so called non co-rotating potential, which represents the deviation from co-rotating potential and generates the accelerating electric field. Using the Poisson equation ▽2 Φ = −4πρ, and assuming the derivative of the potential field in the azimuthal direction is much smaller than those in the poloidal plane, we express the Poisson equation of Φ′ in the simple 2-dimensional geometry as ! ∂2 ∂2 + Φ′ = −4π(ρ − ρGJ ), (1) ∂x2 ∂z2 where the coordinates x and z are distance along and the perpendicular to the magnetic field lines, respectively. In the present simple two-dimensional geometry, we ΩBx express the Goldreich-Julain charge density as ρGJ (x) ≈ − 2πcs (cf. Eqs. 3.2 and 3.3 of CHRa), where Ω is the angular velocity, B ≈ B(Rlc) is the magnetic field strength in the outer magnetosphere, Rlc = c/Ω is the light cylinder radius and s ≈ Rlc is the curvature radius of the magnetic field lines.

Fig. 1 Schematic view of the gap structure. (a)The structure of the two-dimensional outer gap. The regions I and II are the primary region and the screening region respectively. (b)The distribution of the charge density in the trans-field (z) direction in the gap. (c)The distribution of the g(z) in z-direction in the gap. (d)The distribution of the potential Φ′ (z), and the accelerating electric field E⊥ ∝ Φ′ (z).

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Since we are interested in the distribution of the accelerating field in the transfield direction (z-direction), we approximately express the deviation of the charge density from the Goldreich-Julian charge density as ρ−ρGJ ∼ g(z)ρGJ (x), where g(z) expresses the deviation from the Goldreich-Julian charge density averaged along the magnetic field line between the inner and outer boundaries. By assuming that the derivative of the potential field in the trans-field direction is larger than that along the magnetic field line and ignoring the variation of the Goldreich-Julian charge density in the trans-field direction, we rewrite the Poisson equation (1) as, ∂2 ′ Φ (x, z) = −4πρGJ (x)g(z). ∂z2 By defining Φ′ (x, z) = ρGJ (x)Φ′ (z), the Poisson equation becomes ∂2 ′ Φ (z) = −4πg(z). ∂z2

(2)

The accelerating electric field is calculated from E || (z) = −∂Φ′ (x, z)/∂x. To solve the equation (2) we impose the boundary conditions on the lower and upper boundaries. We put the lower boundary at the last-open field line, where the condition Φ(z = 0) = 0 (3) is imposed. On the upper boundary, we impose the gap closure conditions that Φ(z = h2 ) = 0 and E ⊥ (z = h2 ) = 0,

(4)

which ensure that the total potential (co-rotational potential + non co-rotational potential) field in the gap is continuously connected to the co-rotational potential field outside the gap. The location of the upper boundary can not be arbitrary chosen, because both Dirichlet-type and Neumann-type conditions are imposed on the upper boundary. We divide the gap into two regions, i.e. the primary acceleration region and the screening region. The main acceleration region is expanding between the last-open field line and the height z = h1 (region I in Fig.1a), and the screening region is expanding between z = h1 and z = h2 (region II in Fig.1a). We note that the averaged charge density must be less than the Goldreich-Julian value, that is |ρ| < |ρGJ |, in the primary acceleration region, while |ρ| > |ρGJ | in the screening region. To simplify the problem, we treat the distribution of the number density and therefore of the charge density in the trans-field direction (z-direction) as a step function (Fig.1b). Because we consider the case that the inclination angle is smaller than α < 90◦ and because the primary acceleration region extends between the null charge surface and the light cylinder, we describe the deviation of the charge density from the Goldreich-Julian charge density as * + ( ρ − ρGJ −g1 , if 0 ≤ z ≤ h1 = g(z) = , (5) g2 , if h1 < z ≤ h2 ρGJ


103

where g1 > 0 and g2 > 0 (cf. Fig.1c). Using the boundary conditions that Φ′z (z = 0) = 0 and Φ′z (z = h2 ) = 0 and imposing the continuity of the potential field Φ′z and ∂Φ′z /∂z at the height h1 , we obtain the solution of the Poisson equation (2)analytically, which is function of four gap parameters, i.e. h1 , h2 , g1 and g2 . However, the gap closure condition E ⊥ = 0 on the upper boundary implies the relation that h2 h1

!2

= 1 − g1 /g2 .

(6)

Therefore a particular solution of the Poisson equation is obtained by specifying any three parameters or their combinations out of four, i.e. h1 , h2 , g1 and g2 .

2.2 Curvature radiation spectrum The charged particles are accelerated by the electric field along the magnetic field lines in the gap, and emit γ-rays via the curvature radiation. The accelerating electric field is approximately computed from E || (z) = −

∂ ′ ∂ρGJ (x) ΩB(Rlc ) ′ Φ (x, z) ∼ −Φ′z (z) ∼ Φz (z), ∂x ∂x 2πsc

(7)

The Lorentz factor, γe , can be estimated from the condition that eEk (z)c = lcur (z), where lcur (z) = 2e2 cγe4 (z)/3s2 is the power of the curvature radiation, as γe (z) =

"

3 s2 E k (z) 2 e

#1/4

.

For a single particle, the spectrum of curvature radiation is described by √ 2 3e γe single F cur = F(x) 2π¯hsEγ

(8)

(9)

where x(z) = E γ /E cur (z), Ecur (z) = (3/2)¯Rhcγe3 (z)/s is the characteristic energy of ∞ the radiated curvature photon and F(x) = x K5/3 (y)dy, where K5/3 is the modified Bessel functions of order 5/3. The total curvature radiation spectrum from the outer gap is computed from Z dN single F cur (E γ ) = F (z)dz, (10) dz cur where dN = n∆V, where the number density of physical particle n(z) = ρ/e = nGJ (1 + g(z)) and the ∆V = ∆A∆l is the total volume of the gap. We choose ∆l ≈ Rlc and the ∆A can be obtained from the magnetic flux conservation, i.e. B(Rlc)∆A = Φgap . The magnetic flux of the gap Φgap is calculated from Φgap ∼ 2πRlc h2 (Rlc )B(Rlc),

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K. S. Cheng 10

-3

10

(a)

-3

1

10

1

1

10

1

2

1

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4

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5

2

1-g1=0.1

10 10

2

h /h =0.96

2

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f=0.76

h /h =0.933

2

h /h =0.90

-3

h /h =0.933

-4

2

h /h =0.80

1-g =0.05

1

1

10

h /h =0.70

1

1-g =0.01

2

2

E F (MeV/cm /s)

10

1-g =0.10

10

(c)

1

f=0.2

1

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1-g =0.30 1-g =0.10

f=0.4

-4

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(b)

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f=0.76

-4

-5

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E (MeV)

3

10

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4

5

10

-5 2

10

E (MeV)

3

10

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E (MeV)

Fig. 2 In above illustration Geminga parameters are used. (a)The gap size f on the shape of the spectrum of the curvature radiation. (b)The charge density of the main acceleration region, 1-g1, on the shape of the spectrum. (c)The ratio of h1/h2 on the shape of the spectrum.

implying ∆A = 2πRlch2 (Rlc ) and ΩB(Rlc )R2lc (1 + g(z)) dN = 2πR2lc n(z) = . dz ec

(11)

The total flux received at Earth is F(E γ ) =

1 F cur (E γ ), ∆Ωd 2

(12)

where d is the distance of the pulsar and ∆Ω is the solid angle.

2.3 Properties of curvature spectra with gap parameters Basically we have three independent fitting parameters, i.e the fractional gap size defined by f ≡ h2 (Rlc )/Rlc , the number density (current) in the primary region (1 − g1) and the ratio between the thicknesses of primary region and total gap size h1 /h2 . In Fig. 2 we show how these gap parameters affect the radiation spectrum. We can see that. (i)When the gap size increases both the radiation power and the electric field increases, hence the cut-off energy of the spectra increases. (ii)Basically the spectrum consists of two components, i.e. the primary region radiates high energy gamma-rays and the screening region radiate softer gamma-rays. When the current in the primary region increases but all other parameters fixed, the flux in the high energy component increases and the spectrum becomes harder. (iii)When the size of the primary region increases but the currents in both acceleration regions are fixed, the charge density in the primary decreases and hence the electric field in this region increases. This make the cut-off energy higher. At the same time the charge density in the screening increases and hence the electric field in this region decreases. The characteristic photon energy in this region becomes even lower. The combined effects make the high energy component and low energy component separate wider and hence the overall spectrum becomes flatter.

Gamma-ray emission and pair creation of outer gap 15

105

16

(a)

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N

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0.8

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fit

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Fig. 3 This figure summarizes the fitting results of 42 Fermi pulsars. (a)The primary region occupies roughly 95% of the entire gap and (b)the current (1-g1 ) in this region is roughly 10% of the Goldreich-Julian value, which mean that the gap electric field in the primary region is closed to the vacuum value. (c)The fractional size of the gap f increases with age of pulsar. (d)The total gap current is only 55% of the Goldreich-Julian value.

2.4 Fitting Results We fit the spectra of the 42 γ-ray pulsars measured by the EGRET and Fermi telescopes with the present model. For the observed spectra, we use information reported in the first Fermi catalogue (Abdo et al. 2010), in which the observed data were fit with a single power law plus exponential cut-off form. In our fitting, we do not include the Crab-like young pulsars (e.g. the Crab pulsar, PSR J11245916) because the radiation mechanism of the Crab-like pulsars are synchrotronself-Compton process instead of curvature radiation process (Cheng, Ruderman & Zhang 2000; Takata & Chang 2007). In the Crab-like pulsars their soft photon density is sufficiently high so that most curvature photons from the outer gap will be converted into pairs within the light cylinder and the observed gamma-rays resulting from the inverse Compton scattering of the synchrotron photons of secondary pairs. This radiation process differs from what we have considered in this paper and therefore we will not consider them. As discussed in section 2.3, our fitting parameters are the fractional gap thickness f , the charge density in the primary region, 1 − g1 , and the ratio h1 /h2 . In fact, given observed phase-averaged spectrum can be uniquely fit with one set of ( f, 1 − g1 , h1 /h2 ) with a small uncertainty. The model fitting was proceeded as following. First, we deduced the typical fractional gap thickness, f , from the observed intensity and the cut-off energy, because the fractional gap thickness f greatly affects the intensity and the cut-off energy. For the next step, we fit the spectral slope

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K. S. Cheng

10

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10

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J0633+1746

J0835-4510

(Geminga)

(Vela)

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J1057-5226 (B1055-52)

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J2021+4026

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1

1

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h /h =0.947 1

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Fig. 4 This figure shows the model results for 6 canonical pulsars. The solid lines represent the best fitting model spectra with the fitting parameters listed in each panel. The circles are the observed data from Fermi LAT, which are taken from Abdo et al. (2009) for the Vela pulsar and Trep et al. (2010) for J2021+4026. The boxes are the observed data from EGERT (Fierro 1995). The dotted lines in the panels of the Geminga and the Vela pulsars are results for the fractional gap thickness (f = 0.7 for the Geminga and 0.145 for the Vela) about 10 % less than the best fitting fractional gap thickness, while the dashed-dotted lines are results for 1-g1 (0.13 for the Geminga and 0.1 for the Vela) and h1/h2 (0.867 for the Geminga and 0.967 for the Vela) about 10-20 % less than the best fitting parameters.

3

10

Canonical Pulsar MSP 2

10

L

L

L

L

1/14 sd 5/8 sd

0

10

fit

(10

34

erg/s)

10

L

Fig. 5 The predicted gammaray luminosity as a function of the spin down power. The circle and triangle represent for the canonical and millisecond pulsars. The solid and dashed lines represent the models by Zhang & Cheng (1997) and Takata et al. (2010), respectively.

1

-1

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erg/s)

below the cut-off energy with the charge density in the primary region, 1 − g1 , which mainly controls the slope of the calculated spectrum. Finally, we determined h1 /h2 , which controls the spectral width between the cut-off energy in several GeV and the spectral break energy in lower energy bands. In Fig. 3 we summarize the fitting results of the gap parameters for 42 Fermi detected gamma-ray pulsars. In Fig. 3a we can see that the primary region occupies 92% to 97% of the entire gap with a mean roughly about 95%. In Fig. 3b the fitted gap current in the primary region is only 10% of the Goldreich-Julian value. It indicates that most the outergap region is still quite empty. This is very important


107

because if the gap current is large it reduces the gap electric field substantially. Consequently multi-GeV photons, which collide with soft photons to make pairs, cannot be produced. The fitting results are consistent with this requirement. In Fig. 3c the gap size increases with age. This is easily to be understood because when the pulsars age, the gap electric field reduces. In order to maintain multi-GeV production, the gap needs to grow larger to compensate the weakening of the gap. In Fig.3d the total gap current is quite constant and close to 55% of the Goldreich-Julian value. First it tells us that the gap electric field is guaranteed non-zero and secondly it may suggest a dynamic gap. We can speculate that the gap may begin with quite empty and once the pair creation occurs, the gap will fill with full Goldreich-Julian current. Since all particles, i.e. photons and charged particles, in the gap are moving with speed of light and hence after the time average the mean current in the gap may close to 55%. Fig.4 presents the fitting results with the observed data for the 6 canonical pulsars. The data points are taken from the EGRET observations (Fierro, 1995) for the Geminga, PSRs J057-5226,J1709-4229 and J1952+3252, and from the Fermi observations for the Vela (Abdo et al. 2009 and 2010) and PSR J2021+4206 (Trep et al. 2010). The grey strips represent the errors of the photon index, cut-off energy and intensity measured by the Fermi observations. The solid lines represent the best fit spectra with the fitting parameters listed in each panel and in Table 1. We use the dashed and dashed-dotted lines in the panels of the Gemiga and Vela pulsars to preset how the best fit parameters include the uncertainties. The dotted lines are results for the fractional gap thickness ( f = 0.7 for the Geminga and 0.145 for the Vela) about 10 % less than the best fitting values, while the dashed-dotted lines are results for 1 − g1 (0.13 for the Geminga and 0.1 for the Vela) and h1 /h2 (0.867 for the Geminga and 0.967 for the Vela) about 10-20 % less than the best fitting values. It is obvious that both dashed and dashed-dotted lines can not explain the observed data, implying the fitting parameters include uncertainties of about 10 % for the Geminga and Vela pulsars. The fitting results of the remaining Fermi pulsars including 8 millisecond pulsars can be found in Yu, Takata and Cheng (2010). In general our model can fit the observed phase average spectrum of all Fermi extremely well. The theoretical gamma-ray power can also be obtained numerically in fitting. In Fig. 5 we plot the the fitting gamma-ray power (Lγ ) versus the spin-down power of pulsars (L sd ). There appears some indication in this figure that the gamma-ray power seems insensitive to the spin-down power for L sd > 1036 erg/s whereas the gammaray power satisfies a simple power law for L sd < 1036 erg/s, which may imply the gap controlling mechanism may be different in these two regions. In next section we will introduce a new gap closure mechanism.

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3 Pair creation mechanisms 3.1 Photon-photon pair-creation process The outer gap accelerator model was proposed by Cheng, Ho and Ruderman (1986a,b), who argued that a large global current flow through the outer magnetosphere causes a charge depletion region around the null charge surface. In the charge depletion region, the non-corotational electric field along the magnetic field accelerates the charged particles, which can emit γ-ray photons. This non-corotational electric field could be screened out by the discharge of the copious electron and positron pairs produced by the pair-creation process of the γ-ray photons. The outer gap would be completely screened out in the trans-field direction, where the noncorotational electric field perpendicular to the magnetic field, En,⊥ , in the poloidal plane is equal to zero. This condition implies that the total potential (corotational + non-corotational) field is continuously connected to the corotational field outside the outer gap. Fig. 6 Schematic view of the outer gap accelerator. In the outer magnetosphere, the photon-photon pair-creation process produce the pairs in the gap uniformly. The pairs created by the magnetic pair-creation process close the outer gap in the outer magnetosphere. The favorable magnetic structure near the stellar surface is depicted in Figure 7.

Ω

µ + e-

+ e+ e- e

X-ray

e-e+

γ-ray

Co-

rota

ting

γ-ray

e+ ma

gne

tosp

her

e

Zhang & Cheng (1997) discussed the gap closure mechanism by the photonphoton pair-creation process between the high-energy γ-rays emitted in the gap and the X-ray photons coming from the stellar surface. They estimated the typical gap thickness from the pair-creation condition Eγ E x ∼ (2me c2 ), where Eγ is the energy of the emitted γ-ray photons in the outer gap and E X is the energy of the soft-photons from the stellar surface, and they obtained the fractional gap thickness as fZC ≡ h⊥ (Rlc /2)/Rlc ∼ 5.5P26/21 B−4/7 , d,12

(13)

where Rlc is the light cylinder radius, h⊥ (Rlc /2) is the gap thickness in poloidal plane at r = Rlc /2 and Bd,12 is the global stellar magnetic field in units of 1012 Gauss. The outer gap closure mechanism with the photon-photon pair-creation process in the trans-field direction have also been discussed by solving the electrodynamics in the outer gap with 2-dimensional and 3-dimensional geometry (Takata, Shibata and Hirotani 2004; Hirotani 2006a,b; Hirotani 2008). For example, Hirotani (2006a)


109 Global field e-

Curvature photons (~100MeV)

Fig. 7 Schematic view of the favorable magnetic structure near the stellar surface.

gne to

γ(

ma ing ot a t

∼5 M

h ,m

co-r

Local field

e+ −

γ(

e+ − α>π/2

eV )

γ

e+ −

sph

∼1 00 M

ere

eV )

Synchrotron photons (~5MeV)

γ

γ

γ

e-

e+ −

Stellar surface

demonstrated that the outer gap for the young pulsar, the Crab pulsar, is almost screened out in the trans-field direction at the fractional gap thickness of f ∼ 0.2 (figure 6 in Hirotani 2006a). For mature pulsars such like Gemiga, on the other hand, Takata and Chang (2009) argued that the photon-photon pair-creation process will be insufficient in the outer magnetosphere and the outer gap could occupy entire region between the last-open field lines and the critical field lines that have the null charge point at the light cylinder.

3.2 New gap closure mechanism Recently Takata, Wang and Cheng (2010) proposed a possible gap closure mechanism, in which the magnetic par-creation process near the stellar surface supplies the electron and positron pairs to close the outer gap in the trans-field direction. It has been proposed that the magnetic field near the stellar surface is enhanced by the strong multiple magnetic field, although the global magnetic field is well described by the dipole field (Blandford et al. 1983; Romani 1990; Ruderman 1991). The neutron star magnetic field will be produced by a current flowing the crust, which has a thickness of δr ∼ 1 − 3 × 105 cm ≪ R s . It was suggested that the magnetic structure near the stellar surface is super position of clumps resolved into multiples of characteristic of the order of R s /δr (Arons 1993). If the clumps cover whole stellar surface, the strength of the stellar magnetic field is order of B s ∼ (R s /δr)n Bd , where Bd is the strength of dipole magnetic field determined by the observed rotation period P and ˙ and n = 1 and 2 represent coherent and incoherent superpothe period derivative P, sition of the magnetic momentum of the clump, respectively. This model indicates the strength of the stellar magnetic field can take easily B s ∼ 10 − 100Bd. Therefore, even in the millisecond pulsar, the magnetic field near the star surface will be close

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K. S. Cheng

to B s ∼ 1011 Gauss, and the magnetic pair-creation process will take place close to the stellar surface. We argue that the γ-rays emitted near the stellar surface is converted into the pairs via the magnetic pair-creation process above the height (h⊥,m ) measured from the last-open field line. In equation (16), we will estimate the height, h⊥,m , above which the pair-creation process takes place. The important conditions for closing the gap by the pairs produced by the magnetic pair-creation process are as follows; (1) the gap was not closed by the photon-photon pair-creation process below the height h⊥,m , (2) the local magnetic field lines near the stellar surface is bending away from the last-open field lines (see Fig.7 below) due to the strong multiple fields, and (3) some of magnetic pairs migrate into outer magnetosphere. The second condition is required to produce outflows of the magnetic pairs. Fig.6 and Fig.7 represents the schematic view of the outer magnetosphere and of the magnetic structure near the stellar surface, which is favored in this study, respectively. In the outer magnetosphere, the photon-photon pair-production process creates pairs, which are separated by the accelerating electric field. Inward propagating particles will emit the γ-ray photons toward the strong magnetic field region near the stellar surface. As demonstrated by the electrodynamic study (e.g. Hirotani 2006a), the electric field below null charge surface are significantly reduced by the pairs and arises with a very weak field. Below the null charge surface, therefore, the curvature energy loss will not be able to be compensated by the acceleration of the electric field in the gap, and the incoming particles loose their energy by the curvature radiation. Takata et al. show that there is a minimum energy of the curvature photons, which does not depend on any pulsar parameters and the curvature 2 radius of the local magnetic field, and it is given by Emin ∼ mαe cf ∼ 100 MeV, where α f is the fine structure constant. Before hitting the stellar surface each gap particle can emit ∼ 104 100MeV curvature photons. Most of these curvature photons can be converted into e± pairs by the strong magnetic field. The mean free path of the magnetic pair-creation process of the photon with the energy Eγ is described as (Erber 1966;Ruderman & Surtherland 1975) ! 4.4 h¯ Bq 4 lm = exp , (14) α f m e c B⊥ 3χ where χ = Eγ B⊥ /2me c2 Bq , α f is the fine structure constant, Bq = 4.4 × 1013 Gauss and B⊥ = B sin θa with θa is the angle between the direction of the propagating for the photon and the magnetic field. The exponential dependency of the mean-free path on the photon energy Eγ and the angle θa implies that most of emitted photons will be converted into pairs if the condition that Eγ B⊥ /(2me c2 Bq ) ∼ χ is satisfied. Using the magnetic pair-creation condition, we can estimate height measured from the last open field line, above which the magnetic pair-creation process of the photons with Emin ∼ 100 MeV becomes important with the dipole magnetic field geometry. The collision angle θa between the trajectory of the curvature photons and the magnetic field line is approximately described as


sin θa ∼

ℓ ∼ s

111

r

2h⊥ , s

(15)

√ where ℓ ∼ 2h⊥ s is the propagating distance of a photon from the emission point, and h⊥ is the thickness of the gap near the inner boundary. The magnetic paircreation condition implies that the curvature photons with an energy ∼ 100 MeV will be converted into the pairs above the height h⊥,m (Ri ) ∼ 104 χ2−1 B−2 m,12 s7 cm,

(16)

where Ri expresses the critical radial distance below which the magnetic paircreation process becomes to be important and it will be Ri ∼ 2 − 3R s for the canonical pulsars and Ri ∼ R s for the millisecond pulsars. In addition, χ−1 = χ/0.1, Bm,12 is the strength of the magnetic field at the pair-creation position in units of 1012 Gauss, and we used E min = 100 MeV. Rescaling the thickness at the stellar radius using the magnetic flux conservation, we obtain h⊥ (R s , m) ∼ (R s /Ri )3/2 h⊥,m (Ri ) with R s being the stellar radius. As we have discussed above, the incoming particles will create pairs above the height h⊥,m , which is described by equation (16), via the magnetic pair-creation process near the stellar surface, and the multiplicity could acquire Me± ∼ 104 − 105 for the canonical pulsars and ∼ 104 for the millisecond pulsars. Although it is expected most of the created pairs have inward momentum and migrate toward the star, it may be possible that a tiny fraction of the created pairs are produced with outward momentum and migrate into outer magnetosphere, as discussed below. In fact, only an extremely small fraction of pairs out of Me± ∼ 104 − 105 will be enough to close the outer gap accelerator in the trans-field direction everywhere in the outer magnetosphere. The magnetic pairs would be produced with an outward momentum if the magnetic structure near the stellar surface is affected by the strong multiple field, as illustrated in Fig.7, which shows how some pairs can acquire the outgoing momentum due to the geometry of the local magnetic field lines. Near the stellar surface, the magnetic field lines (dashed lines) can be bending away from the last-open field line due to a strong multiple field (solid-dashed line). The solid curved lines represent the global field which are not affected by the local magnetic field, and thin dashed-line represent the geometry without the multiple field. The 100 MeV curvature photons (solid arrows) emitted by the incoming particles, which were accelerated inside the outer gap, are converted into the pairs via the magnetic pair-creation above height, h⊥,m described by equation (16). For the canonical pulsars, the synchrotron radiation of the created pairs will produces 10 MeV photons (dashed arrows), which could be converted into new pairs by a strong magnetic field near the stellar surface. If the direction of the magnetic field at the pair-creation positions is bending away from the last-open field line, it is possible that the collision angle (denoted as α in the Fig.7 between the photons and the magnetic field line becomes larger than α ≥ 90◦ , implying the created pair has the outward momentum.

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Lγ/Ec2 (1033 erg/s/GeV2)

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Radio-selected Gamma-ray selected Millisecond Model

101

10

0

10-1

10

Fig. 8 Plot of Lγ /Ec2 as a −1/2 function of B1/2 d,12 P−1 .

2

-2

10-3 10-2

10-1

-1/2 B1/2 d, 12 P-1

100

101

We note that (1) because the position of the pair-creation point is determined by the value B sin α, and (2) because the collision angle changes from a smaller value to a larger value as the photon propagate toward the stellar surface, the position with the collision angle smaller than 90◦ is preferentially chosen as the pair-creation point, although sin α gives the same values with, for example, α = 80◦ and 110◦ . However, the magnetic field also increases as the photons propagate toward the stellar surface, implying the strength of the magnetic field is bigger for the position with α = 110◦ than that with α = 80◦ . As a result, it will be possible that some photons do not have enough energy to produce the pairs with the magnetic field at the position with α = 80◦ , but do to produce the pairs at the position with α = 110◦ . On these ground, some created pairs will be able to have the outward momentum, if the local magnetic field is bending away from the last-open field line. If all field lines in the polar cap region are bending toward the last-open field line, it is not expected outgoing pairs because the collision angle is always α < 90◦ . In such a case, all pairs created by the magnetic pair-creation process will have an inward momentum, implying the photon-photon pair-creation process will be only possible mechanism to close the outer gap.

3.3 Predictions of new outer gap model Our gap closure process is summarized as follows; 1. the incoming particles emit ∼100 MeV photon below the null charge surface, 2. the ∼100MeV photons emitted toward the stellar surface will produce the pairs via the magnetic pair-creation process (Me± ∼ 104 − 105 ) above the height h⊥,m estimated by equation (16), and 3. if some fraction of the created pairs will be produced with an outward momentum due to the geometry of the local magnetic field, and the returning pairs completely close the outer gap in the trans-field direction everywhere in the outer magnetosphere.

Ec; Cut-off energy (GeV)


Fig. 9 Plot of the cut-off energy as a fucntion of the spin down power. The line is the model prediction, Ec ∼ 1/4 0.22K 3/2 B1/4 d,12 L sd,34 GeV with

10

1

10

0

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Radio-selected Gamma-ray selected Millisecond Model ()

10-1 10-1

100

< K 3/2 B1/4 d,12 >= 5.

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103

Lsd ; Spin down luminosity (1034 erg/s)

104

105

Applying equation (16) as the typical gap thickness of the gap we define the fractional gap thickness as fm ≡

h⊥,m (R s ) ∼ 0.25K(χ, Bm, s)P1/2 , −1 rp

with K = χ2−1 B−2 m,12 s7

Rs Ri

!3/2

.

(17)

(18)

By assuming a simple localized dipole field on the surface of neutron star, Takata et al. (2010) have estimated that K ∼ 1 for canonical pulsars and K ∼ 10 for millisecond pulsars. Applying the fractional gap thickness to the acceleration and curvature emission process beyond the null charge surface, we discuss the expected properties of the γray radiation from the outer gap closed by the magnetic pair-creation process. The typical magnitude of the electric field in the gap beyond the null charge surface is given by f 2 Va E|| (K, Bd , P) ∼ m ∼ 8.3 × 104 K 2 Bd,12 P−2 (19) −1 Volt/cm. Rlc which can accelerate the electrons and positrons up to γ(K, Bd ) ∼

3s2 E|| 2e

!1/4

∼ 2.1 × 107 K 1/2 B1/4 , d,12

(20)

where we used s = Rlc in the outer magnetosphere. We find that the maximum Lorentz factor does not depend on the rotational period. The typical energy of the curvature radiation by the accelerated particles in the outer magnetosphere is Ec (K, Bd , P) =

3 hcγ3 ∼ 0.55K 3/2 B3/4 P−1 GeV. d,12 −1 4π s

(21)

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Fig. 10 Plot of the γ-ray luminosity as a function of the spin down power. The line is the model prediction, Lγ ∼ 5/8 2 × 1032 K 3 B3/4 d,12 L sd,34 erg/s with
= 13.

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101

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103

Lsd ; Spin down luminosity (1034 erg/s)

104

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Because the efficiency of the emission is significantly reduced above the energy E c , we expect that the γ-ray spectrum has the cut-off energy of Ec . The total current flowing in the gap is order of Igap ∼ fm IGJ , where IGJ = πBd R s /PRlc is the Goldreich-Julain current. Using the total potential drop in the gap of Vgap ∼ fm2 Va , we can estimate the γ-ray luminosity as Lγ (K, Bd , P) ∼ Igap Vgap ∼ 2 × 1033 K 3 B2d,12 P−5/2 erg/s. −1

(22)

3.3.1 Switching between two gap closure processes We have emphasized that both photon-photon pair creation and magnetic pair creation occur in different regions of pulsar magnetosphere. But there is only one of them will be the dominant gap closure mechanism. The simplest criterion is which mechanism makes the gap smaller. Therefore from the condition fZC = fm , we can determine the switching of gap closure processes taking place at L sd ∼ 2.5 × 1036(K/2)−168/31 B−34/31 erg/s. d,12

(23)

The above equation is consistent with our 2D model fitting results shown in section 2. 3.3.2 Comparison with Fermi observations Takata et al. (2010) have made a detailed comparison between model predictions and the data of Fermi. Here we just discuss three of them. Again we would like to emphasize that K is an unknown parameter, which depends on the surface magnetic field structure of neutron stars. In order to avoid this unknown parameter we can consider −1 2 Lγ /E c2 = 6.6 × 1034 B1/2 (24) d,12 P−1 erg/s GeV ,


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this ratio only depends on the observed pulsar parameters. Fig. 8 shows reasonable linear relation as predicted in above equation. If we recast the cut-off energy Ec (21) and the γ-ray luminosity Lγ (22) as a function of the spin down power L sd = (2π)2 B2d R6s /6c3 P4 , we obtain

and

Ec ∼ 0.22K 3/2 B1/4 L1/4 GeV d,12 sd,34

(25)

Lγ ∼ 2 × 1032 K 3 B3/4 L5/8 , erg/s d,12 sd,34

(26)

respectively. Takata et al. (2010) show that although K and the average mangetic field between canonical pulsars and millisecond pulsars are very much different, it turns 3 3/4 out that the proportionality coefficients K 3/2 B1/4 d,12 in equation (25) and K Bd,12 in equation (26) have less dependency on the pulsar populations. The model predicted values of these two combined coefficients for canonical pulsars and millisecond pulsars only differ by a factor less than 2. Consequently in Fig. 9 and Fig. 10 we can see that both populations can form simple relation with the spin-down power of pulsars.

4 Summary We find that a 2D outergap model with a primary region plus a screening region can explain the phase average spectrum of all mature pulsars detected by Fermi very well.The fitting results indicate that the primary region consists of 10% GJ current and the screening region contains 40%. The low current in primary region ensures the production of multi-GeV photons and hence pair creation can take place. The total current in the gap is 50% of the Goldreich-Julian current may suggest a dynamic gap. The size of the gap increases with age. By plotting the fitted gamma-ray power versus the spin-down power of pulsars suggest that there may be two possible pair creation processes controlling the gap closure, i.e. photon-photon pair creation and magnetic pair creation. The transition takes place erg/s. If the magnetic pair creation is the at L sd ∼ 2.5 × 1036(K/2)−168/31 B−34/31 d,12

respectively. More and Ec ∝ L1/4 gap closure mechanism we predict that Lγ ∝ L5/8 sd sd predictions can be found in Takata, Wang and Cheng (2010). Acknowledgements This work is in collaboration with J. Takata and Y.Wang and is supported by a GRF grant of Hong Kong SAR Government under HKU700908P.

References 22. Abdo A.A. et al., 2009, ApJ, 696, 1084 22. Abdo A.A. et al., 2010, ApJS, 187, 460

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Arons J., 1993, ApJ, 408, 160 Bai, Xue-Ning & Spitkovsky, A. 2010, ApJ, in press Blandford R.D., Applegate J.H. & Hernquist, L., 1983, MNRAS, 204, 1025 Cheng K.S., Ruderman M. & Zhang L. 2000, ApJ, 537, 964 Cheng K.S., Ho C. & Ruderman M. 1986a, ApJ, 300, 500 Cheng K.S., Ho C. & Ruderman M. 1986b, ApJ, 300, 522 Erber T., 1966, RvMP, 38, 626 Fierro J.M., 1995, PhD thesis, Stanford Univ Goldreich P. & Julian W.H. 1969, ApJ, 157, 869 Harding, A. K., Stern, J. V., Dyks, J., & Frackowiak, M. 2008, ApJ, 680. 1378 Hirotani, K. 2008, ApJ, 688, 25 Hirotani K., 2006a, ApJ, 652, 1475 Hirotani K., 2006b, Mod. Phys. Lett. A, 21, 1319 Romani R.W, 1990, Nature, 347, 741 Ruderman M., 1991, ApJ, 366, 261 Ruderman M.A. & Sutherland P.G., 1975, ApJ, 196, 51 Takata J., Shibata S. & Hirotani K. 2004, MNRAS, 354, 1120 Takata J. & Chang H.-K., 2007 ApJ, 670, 677 Takata, J., Wang, Y. & Cheng, K.S. 2010, ApJ in press Tang, Anisia P. S., Takata, J., Jia, J. J. & Cheng, K. S. 2008, ApJ, 676, 562 Trepl, L., Hui, C. Y., Cheng, K. S., Takata, J., Wang, Y., Liu, Z. Y. & Wang, N., MNRAS, 2010 in press 22. Wang, Y., Takata, J. & Cheng, K.S. 2010, ApJ submitted 22. Zhang L. & Cheng K.S., 1997, ApJ, 487, 370

What Pulsar High-Energy Emission Model Survives? Electrodynamical Considerations Kouichi Hirotani

Abstract We explore particle accelerator electrodynamics in the magnetosphere of a rapidly rotating neutron star (NS). We address the importance of a self-consistent treatment of pair production, solving the Maxwell and Boltzmann equations simultaneously. It is demonstrated that the accelerator solution is obtained if we specify only the following four parameters: the NS spin period, magnetic dipole moment, magnetic inclination angle with respect to the rotation axis, and the NS surface temperature. Applying the scheme to the Crab pulsar, we show that the solution reproduces the gamma-ray observations at least qualitatively and that the solution corresponds to a quantitative extension of phenomenological outer-gap models. We also apply it to the slot-gap model, a geometrically thin version of the pair-starved polarcap (PSPC) model, to show that this alternative model predicts too small photon flux compared to observations. It is discussed that the PSPC model is electrodynamically vulnerable to pair production.

1 Introduction Rotation-powered pulsars are excellent laboratories for testing particle acceleration theories. The major advantage of studying pulsars is that we know that they are powered by rotational energy loss. It is generally accepted that the rotating magnetic field works as a unipolar inductor to exert a large electro-motive force on the spinning neutron star (NS) surface and that the resulting potential drop in the rotating magnetosphere leads to the acceleration of charged particles to ultra-relativistic energies. The challenge is then to investigate where and how they convert this energy into radiation that we observe. Kouichi Hirotani Academia Sinica, Institute of Astronomy and Astrophysics (ASIAA) / Theoretical Institute for Advanced Research in Astrophysics (TIARA), P. O. Box 23-141, Taipei, Taiwan, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_10, © Springer-Verlag Berlin Heidelberg 2011

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The pulsar magnetosphere can be divided into two zones (fig. 1). The closed zone is filled with a dense plasma co-rotating with the star, whereas the open zone allows plasmas to flow along the open field lines, escaping to large distances through the light cylinder (LC). Here, the LC is located at the so-called ‘light cylinder radius’, ̟LC = c/Ω, from the rotation axis, where Ω denotes the NS rotational angular frequency and c the speed of light. The last-open field lines, which become parallel to the rotation axis at the LC, form the border of the open magnetic field line bundle. In all the pulsar emission models, particle acceleration and the resulting photon emissions take place within the open zone. Fig. 1 Schematic figure (side view) of the pulsar magnetosphere. The slot gap extends from the stellar surface to the light cylinder on the last-open field line (in the open zone) with trans-field thickness much less than the outer gap. The outer gap is traditionally assumed to be located between the null charge surface and the light cylinder. For middle-aged pulsars, the OG trans-field thickness becomes greater than depicted.

magnetic dipole axis

null surface magnetic field lines

outer gap NS

slot gap polar gap

last-open field line

closed zone

pulsed γ-rays

light cylinder

light cylinder radius

ϖLC= 3 108(Ω /102 rad s-1) cm

Attempts to model pulsar high-energy emissions concentrate on a few scenarios: (i) polar-cap (PC) models with emission above a PC surface [23, 16, 18, 58], (ii) outer-gap (OG) models with emission near LC [10, 11, 14, 15, 55, 56, 68, 13], (iii) emission models from a striped wind [4, 5, 51, 54]. In scenarios (i) and (ii), both PC and OG models predict that e± ’s are accelerated in a charge depletion region, a potential drop, by the magnetic-field-aligned electric field, Ek , to radiate high-energy gamma-rays via the curvature and inverse-Compton processes. Thus, their electrodynamics is more or less common. However, the physical processes taking place in scenario (iii) are quite different from those in scenarios (i) and (ii). Thus, in this chapter, we will focus on scenarios (i) and (ii), and first solve both models from the same set of basic equations under different boundary conditions. It is widely accepted from phenomenological studies that coherent radio photons are emitted from the PC accelerator (or equivalently ‘inner gap’ as depicted in fig. 1). It should be noted that the PC model predicts the so-called ‘pencil beam’ emission with a small solid angle along the magnetic axis, because the emission takes place in the lower altitudes (i.e., near the NS surface). Since the radio pulsation generally exhibits a single sharp peak in each rotational period, we can reproduce the pulse profiles if the observer’s viewing angle, ζobs , with respect to the rotation axis, is close to the magnetic inclination angle, α, with respect to the rotation axis. However, to explain the emissions of incoherent high-energy photons, which generally exhibit

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widely separated double peaks, one has to invoke a very small α and ζobs . Thus, to explain the γ-ray pulsations detected from several brightest pulsars [50, 21, 35, 21, 42, 64, 41, 53, 37], a high-altitude emission, which results in the so-called ‘fan beam’ emission with a large solid angle (∼ 1 ster), drew attention as an alternative possibility. The possibility of a high-altitude extension of the PC accelerator was originally introduced by [2]. Developing this electrodynamical model, and incorporating general relativistic effects [47], [48] began discussing high-energy emission from the pulsar slot gap (SG), a narrow region on the last-open field line where Ek is decreasing and accelerating particles cannot create pairs. Then [49] extended this loweraltitude solution (within a few stellar radii) to higher altitudes (near the LC) and found that curvature radiation of the primary particles forms caustic patterns, as suggested in the two-pole caustic model [19]. Subsequently, [13] examined polarization characteristics and found that fast swings of the position angle and minima of polarization degree can be qualitatively reproduced within their two-pole caustic model. This type of emission, SG emission, fills the whole sky and all phases in a light curve. That is, most observers catch emission from the two poles, if ζobs is in a reasonable range (e.g., 45◦ < ζobs < 125◦ for α > 30◦ ). More recently, [24] investigated the SG emission, adding synchrotron radiation of the gap-accelerated primaries and higher-generation pairs produced at lower-altitude PC region. They applied the model to the Crab pulsar and predicted the pulse profiles and the phaseresolved spectra, which are consistent with the observations from 0.3 keV to 10 GeV. An alternative way to consider a high-altitude emission is the OG model. To examine the OG quantitatively, [28, 29] first solved the set of Maxwell and Boltzmann equations in a pulsar magnetosphere, extending the method originally proposed for a pair-production cascade in a rotating black-hole magnetosphere [6, 27]. Before [28], the accelerator position, strength of E k , and even the existence of the OG itself, have been hypothesized. However, in their one-dimensional analysis of a pair-production cascade along the magnetic field lines, [28] demonstrated that the OG does exist as the solution of the set of the Maxwell and Boltzmann equations. After that, a number of papers appeared in the same context (for one-dimensional solution along the magnetic field lines, see, [30]; for two-dimensional solutions, see [60, 31, 32, 62, 33]), confirming that the traditional OG models give qualitatively good agreement with these self-consistent solutions. In the present chapter, we extend the method presented in [31], which analyzes the OG electrodynamics in the 2-D poloidal plane, into the 3-D magnetosphere. We demonstrate that the OG solution is uniquely obtained if we specify the NS rotational period, P, magnetic dipole moment, µ, surface temperature, kT , and α, without introducing any artificial assumptions. Phase-resolved spectra and pulse profiles can be predicted, if we additionally specify ζobs and the distance to the pulsar, d. In § 2 we present basic equations. Then in § 3, we demonstrate that the OG solution is quantitatively obtained from the set of Maxwell-Boltzmann equations. In § 4, we apply the same method to the SG model and point out its difficulties. We finally discuss another electrodynamical difficulty of PSPC in § 5.

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2 Basic equations Around a rotating neutron star with angular frequency Ω, mass M and moment of inertia I, the background space-time geometry is given by [39] ds2 = gtt dt2 + 2gtϕ dtdϕ + grr dr2 + gθθ dθ2 + gϕϕ dϕ2 , where

rg 2 rg gtt ≡ 1 − c , gtϕ ≡ ac sin2 θ, r r rg −1 grr ≡ − 1 − , gθθ ≡ −r2 , gϕϕ ≡ −r2 sin2 θ; r

(1) (2) (3)

rg ≡ 2GM/c2 indicates the Schwarzschild radius, and a ≡ IΩ/(Mc) parameterizes the stellar angular momentum. At radial coordinate r, the inertial frame is dragged at angular frequency ω ≡ −gtϕ /gϕϕ = 0.15ΩI45r6 −3 , where I45 ≡ I/(1045g cm2 ), r6 ≡ r/10 km, and r∗ represents the stellar radius.

2.1 Poisson Equation for Electrostatic Potential First, we consider the Poisson equation for the electrostatic potential, which is given by the Gauss’s law as "√ # −g µν 1 4π tµ ∇µ F = √ ∂µ g (−gϕϕ Ftν + gtϕ F ϕν ) = 2 (ρe + ρion ), (4) 2 −g c ρw √ where ∇ denotes the covariant derivative, the Greek indices run over t, r, θ, ϕ; −g = q grr gθθ ρ2w = cr2 sin θ and ρ2w ≡ g2tϕ − gtt gϕϕ = c2 (1 − rg /r)r2 sin2 θ. In the right-hand side, ρe denotes the sum of positronic and electronic charge densities, and ρion the ionic one. The six independent components of the field-strength tensor F µν give the electromagnetic fields observed by a distant static observer [8, 9]. Assuming that the electromagnetic fields are unchanged in the corotating frame, we can introduce the non-corotational potential Ψ such that Fµt + ΩF µϕ = −∂µ Ψ (r, θ, ϕ − Ωt),

(5)

where µ = t, r, θ, ϕ. If F At + ΩF Aϕ = 0 holds for A = r, θ, the angular frequency Ω of a magnetic field is conserved along the field line. On the neutron-star surface, we impose Fθt + ΩF θϕ = 0 (perfect conductor) to find that the surface is equi-potential, that is, ∂θ Ψ = ∂t Ψ + Ω∂ϕ Ψ = 0 holds. However, in a particle acceleration region, F At + ΩF Aϕ deviates from 0 and the magnetic field does not rigidly rotate (even though the deviation from the uniform rotation is small when the potential drop in the gap is much less than the EMF exerted on the spinning neutron star surface). The deviation is expressed in terms of Ψ , which gives the strength of the acceleration


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electric field that is measured by a distant static observer as Ek ≡

B Bi Bi · E = (Fit + ΩF iϕ ) = (−∇i Ψ), B B B

(6)

where the Latin index i runs over spatial coordinates r, θ, ϕ, and an identity Br F rϕ + Bθ F θϕ = 0 is used. If Ψ varies along the magnetic field line, charged particles are accelerated along the field line; we call such a gap of electro-static potential a ‘gap’. If the potential variation is large enough, we can expect enough high-energy emissions from the gap. Substituting equation (5) into (4), we obtain the Poisson equation for the noncorotational potential, ! √ −g µν c2 − √ ∂µ g gϕϕ ∂ν Ψ = 4π(ρ − ρGJ), (7) −g ρ2w where the general relativistic Goldreich-Julian (GJ) charge density is defined as "√ # −g µν c2 ρGJ ≡ g gϕϕ (Ω − ω)F ϕν , (8) √ ∂µ 4π −g ρ2w which reduces to the ordinary, special-relativistic expression of the GJ charge density [25, 43] in the limit r ≫ rg . Instead of (r,θ,ϕ), we adopt in this chapter the magnetic coordinates (s,θ∗ ,ϕ∗ ) such that s denotes the distance along a magnetic field line, θ∗ and ϕ∗ represents the magnetic colatitude and the magnetic azimuth, respectively, of the point where the field line intersects the neutron star (NS) surface (fig 2). For explicit expressions of the Poisson equation (7) in the magnetic coordinates (s,θ∗ ,ϕ∗ ), see [31].

θ* sinϕ*

Fig. 2 Magnetic coordinates (θ∗ ,ϕ∗ ) that specify individual magnetic field lines on the polar-cap surface. The dots denote the footpoints of the magnetic field lines along which the simulation is performed; 40 grids are taken in θ∗ direction, and 96 grids in ϕ∗ direction (even though only 8 points are depicted at each ϕ∗ ). The rotation axis resides at ϕ∗ = π. Both axes are in radian unit.

last-open fieldline, h =0

θ*

θ

max

* ϕ *

magnetic axis, h =1

ϕ*=0

θ* cosϕ*

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2.2 Particle Boltzmann Equations Second, we consider the Boltzmann equations for particles. At time t, position r, and momentum p, the distribution function N+ of positrons (or N− of electrons) obeys the following Boltzmann equation, ∂N ∂N± v ± + vi · ∇i N± + qE + × B · = S ± (t, r, p), ∂t c ∂p

(9)

where v ≡p/(me γ); mp e refers to the rest mass of the electron, q the charge on the positron, and γ ≡ 1/ 1 − (|v|/c)2 the Lorentz factor. In a pulsar magnetosphere, the collision term S + (or S − ) consists of the terms representing the appearing and disappearing rates of positrons (or electrons) at r and p per unit time per unit phasespace volume due to pair creation, pair annihilation, and the energy transfer due to IC scatterings and synchro-curvature process. Imposing a stationary condition ∂/∂t + Ω∂/∂φ = 0, utilizing ∇ · B = 0, and introducing dimensionless particle densities per unit magnetic flux tube such that n± = hN± i/(ΩB/2πce), where hi denotes the quantity averaged in a gyration, we can reduce the particle Boltzmann equations as c cos χ

∂n± ∂n± ∂n± 2πce + p˙ + χ˙ = S IC + S p , ∂s ∂p ∂χ ΩB

(10)

where the upper and lower signs correspond to the positrons p (with charge q = +e) and electrons (q = −e), respectively, and p ≡ |p| = me c γ2 − 1. In the right-hand side, S IC represents the difference between the disappearing and appearing rates of e± ’s at Lorentz factor γ due to the inverse-Compton scatterings (ICS), whereas S p denotes the particle production rate due to photon absorption. The characteristics of equation (10) in the phase space are given by p˙ ≡ qE k cos χ −

PSC , c

χ˙ ≡ −

qEk sin χ ∂(ln B1/2 ) +c sin χ, p ∂s

(11)

where the particle position s is related with time t by s˙ = ds/dt = c cos χ. For outward- (or inward-) migrating particles, cos χ > 0 (or cos χ < 0). The radiationreaction force [12, 68], PSC /c, is introduced as a friction term to compute p˙ [31]. If we integrate n± over p and χ, and multiply the local GJ number density, ΩB/2πce, we obtain the spatial number density of particles. Therefore, we can express ρe as ZZ ΩB ρe = n+ (s, θ∗ , ϕ∗ , γ, χ) − n−(s, θ∗ , ϕ∗ , γ, χ) dγdχ. (12) 2πc In equation (10), collision terms are expressed as


S IC ≡ − +

ǫn−1 X 0, which leads to ρGJ < 0 in p the PC region. It is reasonable to evaluate µ with its vacuum2 = 1.012I 1/2 P1/2 P ˙ ˙ −15 1/2 , where P = 2π/Ω dedipole value, µd = 3c3 IP P/8π 45 −15 −1 ˙ ˙ notes the NS spin rate, P is its temporal derivative, and P˙ −15 = P/(10 s s ). We obtain the self-consistent solution by specifying only the three parameters, α, kT , and µ, in addition to an observable, P. For an OG, we adopt α = 60◦ in this section.

3.1 Gap geometry and acceleration electric field Let us begin by presenting the solved gap geometry in the 3-D pulsar magnetosphere. In figure 3 (left panel), the gap trans-field thickness, hm , is plotted as a function of the position (s,ϕ∗ ) on the last-open field line surface. At each point (s,ϕ∗ ), Ek maximizes near the central height, h ∼ hm /2. We present such maximum values of Ek (s, ϕ∗ ) in figure 3 (right panel). It follows that E k is screened substantially in the lower altitudes because of the discharge of produced pairs, forming a striking contrast with previous OG models.

3.2 Photon mapping result and radiation spectrum We plot the photon intensity on the pulse phase Φ versus ζobs plane in figure 4. The photons emitted from the north magnetic pole would appear at Φ = 0 and ζobs = α(= 60◦ ). The left panel shows that the OG connected to the north pole emits outward-propagating photons into the southern hemisphere, ζobs > 90◦ , and into the rotation phase −140◦ < Φ < 40◦ , while inward ones into ζobs < 90◦ and 130◦ < Φ < 300◦(= −60◦). On the contrary, from the south-pole OG, inwardpropagating photons appear in ζobs > 90◦ and −50◦ < Φ < 120◦ . Thus, the intensity around ζobs ∼ 120◦ and Φ ∼ 0◦ consists of both the outward emission from the northpole OG and the inward emission from the south-pole OG (right panel). This result is consistent with phenomenological 3-D OG models [59] and self-consistent 2-D

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OG solution [61]. If we specify ζobs , we obtain the photon count as a function of the rotational phase. In figure 5, we present such light curves for three discrete ζobs . Figure 6 depicts the phase-resolved spectrum for ζobs = 105◦ , indicating that the present scheme reproduces the observations at least qualitatively. The first peak (P1) shows softer spectrum than the second peak (P2), because E k becomes small due to the flaring-up field-line geometry near the LC, because collision angles become greater between the primary γ-rays and the secondary X-rays due to the deformation of the field lines near the LC, and because E k is efficiently screened in the middle altitudes of the leading side (LS) due to the propagation of inward γ-rays towards the LS and their subsequent materialization as pairs. The tendency of soft P1 spectrum is, in fact, commonly predicted for other rotation-powered pulsars. The flux correction factor [57] becomes 3.2, 1.8, 0.88, 0.57 at ζobs = 100◦ , 105◦ , 110◦ , and 115◦ , respectively. Note that the ICS photons are emitted by the primary e+ ’s; however, they are totally absorbed by the magnetospheric IR photons to appear as the secondary synchrotron component between 100 MeV and 10 GeV. The present method (coincidentally) corresponds to a quantitative extension of previous phenomenological OG models, which assumes Ek distribution in the 3-D magnetosphere.

Fig. 3 Left: Gap trans-field thickness hm on the 2-D last-open field line surface (s,ϕ∗ ) in the selfconsistent OG solution. The white curve denotes the intersection of the null surface where ρGJ vanishes with the last-open field line surface. Right: Distribution of the maximum value of Ek [V m−1 ] near the gap center (in the meridional direction) on the last-open field line surface.

4 Slot-gap model: the case of the Crab pulsar We apply the same scheme described in previous sections to the SG model, a geometric thin version of the pair-starved polar-cap (PSPC) model. We briefly review the SG formation in section 4.1, then in 4.2-4.3, we first re-examine the SG model


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Fig. 4 Phase plot of the photons having energies above 90 MeV in the self-consistent OG solution. Left: Emission from the north-pole OG alone. Right: Emission from the both poles.

Fig. 5 Pulse profile for ζobs = 95◦ , 105◦ , and 115◦ for the Crab pulsar with α = 60◦ in the self-consistent OG solution. The ordinate denotes the photon energy flux per rotational phase in MeV s−1 cm−2 deg−1 unit.

[48, 49, 24] by our code, which can be commonly applied to both OG and SG models. To compare the results with [24], we adopt α = 45◦ for the SG model.

4.1 Formation of a slot gap in the polar-cap region For a parallel rotator, in a PC SCLF model, e− ’s are extracted at a slightly smaller rate (in an absolute value sense) than the GJ rate, cρ∗GJ , where ∗ denotes a quantity evaluated at the NS surface. Provided that the particle motion is stationary in the co-rotating frame and that pair production does not take place, we find that the real charge density per magnetic flux tube, j/B ∝ ρe /(ΩB/2πc), conserves along the field line; the situation is depicted by the thin green dashed line in figure 7. How about the GJ charge density per magnetic tube, ρGJ /(ΩB/2πc)? Along the magnetic field

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Fig. 6 Phase-resolved spectrum of the pulsed emission from the Crab pulsar in the self-consistent OG solution. The thin solid curves denote the primary photon fluxes, while the thick red solid ones include absorption and subsequent reprocesses. Interstellar absorption is not considered. The filled circles (LECS), open circles (MECS), filled triangles (PDS) denote the Boppo SAX observations, while the open triangle the Gamma-ray Imaging Spectrometer (GRIS), and inverse filled triangles (OSSE), diamonds (COMPTEL), and filled squares (EGRET) denotes the CGRO observations. Data points are from [38] [http://www.sron.nl/divisions/hea/kuiper/data.html].

lines curving away from the rotation axis, its Newtonian GJ value, −Bζ /B, where Bζ denotes the magnetic field component projected along the rotation axis, increases outwards, as indicated by the thin black dotted line. As a result, at the altitude much less than the stellar radius, ρeff ≡ ρGJ − ρe changes sign from negative to positive outwards, leading to a sign reversal of Ek from negative to positive, thereby terminating the gap. (Exactly speaking, the place where Ek changes sign depends not only on the sign of ρeff but also on the trans-field structure; nevertheless, this argument of gap termination is qualitatively correct in any case.) Thus, it had been considered that a PC accelerator is not active along the polar field lines curving away from the rotation axis because of its localized geometry in the vicinity of the NS surface [2]. Subsequently, [47] pointed out that an energetic PC accelerator can exist along such away-curvature field lines due to general relativistic (GR) effects, because ρGJ /B deviates from the Newtonian value due to the Ω − ω factor (instead of Ω) in the right-hand side of equation (8), as indicated by the thin black solid curve in figure 7, where P = 33 ms, r∗ = 10 km, and α = 60◦ are assumed. Since the SCLF has ρe /(ΩB/2πc) as indicated by the thick green solid line for this revised PC model, a negative-definite ρeff , which ensures a negative-definite Ek , extends up to a greater altitude than the Newtonian case. Thus, a PC accelerator exists within the altitude comparable to the NS radius around a rapidly rotating NS. The resulting potential drop is found be enough to reproduce high energy emissions (for details, see [48] and references therein). In spite of these attractive features on energetics, the GR-PC accelerator is still localized within a few stellar radii even for millisecond pulsars. Thus, the emission solid angle is too small to reproduce the wide pulsed profiles that are observed. They were, therefore, motivated by the need to contrive a higher altitude emission model.

Fig. 7 Charge density per magnetic flux tube along the last-open field line that crosses the NS surface at ϕ∗ = 0, thereby curves away from the rotation axis. The black solid curve denotes the GJ charge density (eq. [8]) for a dipole magnetic field with GR corrections, while the black dotted one the Newtonian value. In the PSPC model, the GJ charge distribution is assumed to change from the actual value (black solid line) to the red solid line.

charge density / (ΩB/2πc)


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c) / 2π B /(Ω

-0.28 -0.32

ρ GJ ual act

GR PC accelerator

assume

ρ /(ΩB/2πc)

ρGJ /(ΩB/2πc) in PSPC model

-0.36 -0.40

Newtonian PC accelerator

1 2 3 distance along fieldline / NS radius

4.2 Lower-altitude slot-gap solution

Fig. 8 PFF height, hm , on the last-open field line surface in the lower-altitude SG model. Note that the abscissa is normalized by NS radius, not by ̟LC . The minimum value is 0.01250. In the reddened region, PFF becomes parallel to the NS surface; thus, the gap exists over the entire PC surface.

magnetic azimuth ϕ* [rad]

We re-examine the SG model of [48] by applying the same numerical code as we used in § 3. [48] demonstrated that the pair-formation front (PFF) becomes almost parallel to the NS surface in the central part of the PC (i.e., near the magnetic axis) and that the PFF rapidly curves up to become almost parallel to the last-open field line above several per cent of r∗ for a rapidly rotating, highly magnetized NS. We confirmed their results by our code as indicated by figure 8, which presents the height, hm , of the PFF measured in meridional direction from the last-open field line as a function of s and ϕ∗ . Close to the star, the SG structure is found to be almost independent of ϕ∗ . It is also confirmed that the potential drop, which attains ∼ 1.5 ×1012 V along the field lines threading the higher-altitude SG (e.g., at h = 0.02, see next subsection for details on the high-altitude SG), is consistent with [48] (their eq. [47]). The electrons are accelerated up to the Lorentz factor of ∼ 3 × 106 at s ∼ 0.08r∗ . 0.017 0.0165 0.01251

distance along field line / NS radius

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4.3 Higher-altitude slot-gap model The SG solution described just above exists only within the region in which ρeff = ρGJ − ρe < 0 holds to guarantee a negative-definite E k throughout the gap. The pair-free SG extends, therefore, only up to the altitude rc ∼ 1.2r∗ in the case of the Crab pulsar, because ρe /B is conserved along the field line, as indicated by the thick green dashed line in figure 7. However, if the SG extends only up to such an altitude, the problem of the small emission solid angle occurs in the same way as in PC models. Thus, [49] examined the possibility of an extension of the SG into the higher altitudes, which corresponds to an hybrid scenario of PC and OG geometrical models. However, unlike the OG solution (§ 3), or unlike the lower-altitude SG solution (§ 4.2), the higher-altitude SG model cannot be constructed without additional assumptions. We thus describe them in sections 4.3.1 and 4.3.2, then turn to a re-examination of the high-altitude SG model of [49, 24] in sections 4.3.3 and 4.3.4. 4.3.1 Additional assumption: GJ charge density To extend the SG into the higher altitudes, [49] assumed that ρGJ /B remains constant with s at higher altitudes, as indicated by the red solid curve in figure 7. Their rationale is that the cross-field toroidal motion of e− ’s would effectively screen out the excessive GJ charges and would maintain ρGJ /B at some constant value in the higher altitudes. However, it is not easy to understand why ρGJ , which is purely defined by the magnetic-field and space-time geometries (eq. [8]), can be modified due to the cross-field motion of charges, or to the surface charges on the last-open field lines. For example, if charges are supplied into the gap or if electrons escape from the SG by cross-field motion, they only change the ρe in the right-hand side of equation (8). The surface charges do result in a jump of E ⊥ across the last-open field lines; however, it does not modify the right-hand side of equation (8) at all in the gap. Nevertheless, it is true that a SG could not be extended into the higher altitudes without assuming a negative-definite effective charge density, ρeff = ρGJ − ρe , from the NS surface to the outer magnetosphere. Thus, we follow the assumption proposed by [49] (their eqs. [28]-[30]), as depicted by the red solid curve in figure 7. In our notation, it is equivalent with adopting (eq.[38] in [49]) (" ! # r3 ρeff Ω =− κ β − ∗3 + 1 − β cos α B 2πc rc  s      H(rc ) rc f (r∗ )   3  + H(r∗ )θ∗max  − β sin α cos ϕ∗  , (21)   2 H(r∗ ) r∗ f (rc )  where rc ∼ 1.2r∗ , κ ∼ 0.15 describes the space-time dragging effect, β, H, f are close to unity, β = (1 − 3r/4̟LC)1/2 , H(r) ∼ 1 − 0.1x − 0.026x2 − 0.075x3 + 0.019x4 , f (r) ∼ 1 + 0.3x + 0.096x2, with x = r∗ /r. Note that equation (21), and hence equation


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(38) in [49], is not derived from any basic equations. It is purely derived by assuming that ρGJ has a spatial dependence as equation (20) in [49], which is valid only near the PC surface, and that ρeff nearly saturates at some negative value above r = rc (see the description just above eq. [37] in [49]). In § 5, we will discuss that the same problem arises in the geometrically thick version of PSPC [66], which was recent proposed. 4.3.2 Additional assumption: trans-field thickness We assume that the co-latitudinal thickness is constant at hm = 0.04 in the higheraltitude SG, in the same manner as in [49, 24]. If e− ’s are extracted and accelerated in the lower-altitude SG, it may be natural to suppose such a small hm is realized in the higher altitudes, because the pairs produced outwardly in the PFF will migrate outwards to efficiently screen Ek in the higher altitudes. For instance, in the lower altitudes, hm < 0.017 is obtained in figure 8, or hm ≪ 0.01 is obtained by [48] (their fig. 2). 4.3.3 Acceleration electric field Let us now turn to the discussion of the results of higher-altitude SG model (or equivalently geometrically thin version of PSPC model), adopting the assumption described in the foregoing two sections, and applying the numerical code used for the OG and the lower-altitude SG models also to the higher-altitude SG model. We present Ek distribution for the Crab pulsar with µ = 4 × 1030G cm3 in figure 9. It follows that |Ek | increases with increasing altitude, because |Ek | given by equation (4) in [24] contains a term that increases with the altitude. Note that the Ek in the PSPC model is directly derived from the assumed ρeff (i.e., eq. [21]), instead of solving it from the particle Boltzmann equations. 4.3.4 Insufficient luminosity from the SG Using both the lower- and higher-altitude SG solutions, we map the photon intensity as a function of the pulse phase Φ and ζobs in figure 10. Only the photons having energies greater than 90 MeV are plotted. The yellow rings around the north pole (at ζobs = α = 45◦ and Φ = 0◦ ) and the south pole (at ζobs = π − α = 135◦ and Φ = 180◦) indicate the photons emitted from the lower altitudes. Because |Ek | increases with increasing altitude, caustic is formed by the emission from the middle and higher altitudes. The photon mapping result is consistent with figure 5 of [24]. If we specify ζobs , we obtain the photon count as a function of Φ. In figure 11, we present the pulse profiles for ζobs = 90◦, 100◦ , and 110◦. It follows that the observed double-peak pulse profile can be reproduced if we adopt ζobs ∼ 95◦ .

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We present the phase-averaged spectra for ζobs = 95◦ , 105◦ , 115◦ , and 125◦ in figure 12. The lower-altitude SG emission that is due to the synchrotron process from the cascaded pairs above the polar-cap PFF and becomes important below 10 MeV, is not depicted to clarify the primary SG emissions. It follows that the SG reproduces only several per cent of the observed flux for a moderate of ζobs. The lack of flux is solely because the SG thickness, hm , is much less than unity. This numerical conclusion is consistent with the analytical one [34]. The same difficulty of insufficient luminosity arises for other pulsars, if we adopt the SG model. This is because the analytic expression (eq. [10] in [34]) can be applied to arbitrary pulsars. In general, a gap having such a thin trans-field thickness as h < 0.05, irrespective of whether it is an OG or a SG, cannot reproduce enough γ-ray flux that is observed, unless the particle number density greatly exceeds the GJ value. The only exception could be nearby, young pulsars, which may emit detectable γ-ray flux from a geometrically thin (hm < 0.05) gap.

-1 16

-2 -1 8

-8 0

Fig. 10 Gamma-ray phase plot in the SG model. The abscissa denotes the NS rotation phase Φ, whereas the ordinate the observer’s viewing angle, ζobs . The red ring around Φ ∼ 0 and ζ ∼ α represents the north-pole, lower-altitude SG emissions, whereas the red caustics do the higher-altitude SG emissions.

[10 MeV s cm deg ]

Fig. 9 Acceleration field E k [V m−1 ] distribution, which is computed by equation (21), in the higher-altitude SG model. The maximum value of Ek in the (meridional) transfield direction is plotted on the last-open field line surface (s,ϕ∗ ). The white solid curve represents the null surface position.


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Fig. 11 Pulse profile for three different viewing angles, ζobs , in the higher-altitude SG model. Only the photons having energies greater than 90 MeV are taken into account. The ordinate denotes the photon energy flux per rotational phase in MeV s−1 cm−2 deg−1 unit.

Fig. 12 Phase-averaged spectrum of the Crab pulsar in the higher-altitude SG model at four discrete observer’s viewing angles, ζobs = 95◦ (black solid), 105◦ (red dashed), 115◦ (blue dotted), and 125◦ (green dash-dotted). The ordinate denotes the photon energy flux in MeV s−1 cm−2 unit.

5 Discussion It is demonstrated in § 4.3.1 that a negative Ek in the higher-altitude SG model is derived under the assumption of a constant ρGJ /B (fig. 7), which is inconsistent with the Maxwell eq. (4). The same problem, in fact, arises in the geometrically thick version of PSPC [66], because they adopt the same Ek . It might be possible to argue that ρe /B (instead of ρGJ /B) changes along field line so that |ρeff /B| ≪ |(ρGJ /B)∗| holds, leading to a weak Ek from lower to higher altitudes, as a small deviation from the force-free magnetosphere. However, if Ek is negative as required in the PSPC model, a small amount of pair production leads to the increase of ρeff /B = (ρGJ − ρe )/B outwards (from a negative value), resulting in the reversal of the sign of Ek . This is because e+ ’s return inwards while e− ’s migrate outwards when the produced pairs discharge, leading to a decrease of ρe /B outwards. The same difficulty of outwardly decreasing ρe /B arises, if positive, negative, or both charges are somehow injected into the PSPC accelerator (e.g., by cross-field motion). Note that such a difficulty does not arise in the OG model. Pairs are produced when inward γ-rays collide with outward X-rays in an OG. Due to the discharge in a positive Ek , e+ ’s return outwards while e− ’s migrate inwards, leading to an outwardly increasing ρe /B, which is self-adjusted so that a small-amplitude, posi-

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tive ρeff /B, and hence Ek , is maintained in the inner part of an OG (as solved and demonstrated in fig. 5 of [31]). Thus, Ek sign does not change in an OG, leading to an extended OG from the vicinity of the NS to the outer magnetosphere. In short, it is a positive Ek that is naturally maintained when ρGJ /B is increasing outwards (as commonly assumed in OG and PSPC models). The PSPC model, which requires Ek < 0, is vulnerable to pair production, or to any injection of charges into the gap. Acknowledgements The author is grateful to Drs. D. F. Torres and N. Rea for support and hospitality. He is also indebted to Drs. K. S. Cheng and A. K. Harding for valuable comments and constructive criticisms. This work is supported by the Theoretical Institute for Advanced Research in Astrophysics (TIARA) operated under Academia Sinica and the National Science Council Excellence Projects program in Taiwan administered through grant number NSC 98-2752-M-007006-PAE.

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Current Models of Pulsar Magnetospheres Anatoly Spitkovsky

1 Introduction Pulsar magnetospheres are filled with plasma, and the presence of plasma affects all macroscopic and microscopic properties of the magnetosphere. Although this simple fact was well known since the early days of pulsar research, the ability to quantitatively model plasma effects has emerged mainly in the last decade. This review highlights the main properties and consequences of the current models of pulsar magnetospheres (or, rather, of “magnetospheric models with currents”). The first part concentrates on the influence of plasma currents on the magnetospheric structure, while the second part discusses the emerging picture of pulsar high-energy emission in which strong magnetospheric currents make a surprising contribution. Generally speaking, the models of pulsar magnetospheres can be classified according to the amount of plasma supply they assume. At one extreme is the vacuum magnetosphere, which is modeled with the magnetic field of a spinning dipole in vacuum [10]. Of course, as this solution has no plasma, it has no possibility of producing any pulsar-like emission. However, the fact that this field is described by an analytic formula, has made it the most widely used framework for calculating pulsar properties. For example, the characteristic spin-down energy loss which yielded the fiducial pulsar field strength of 1012G or the polarization sweep of the rotatingvector model are guided by the vacuum field shape. The next order of approximation are models that allow plasma emission from the surface of the star. These include the original charge-separated model of Goldreich and Julian ([18], hereafter GJ), and the space charge-limited models with pair formation (e.g., [1]). These models have both regions that are filled with plasma that shorts out accelerating electric fields and regions where acceleration is present (so-called “gaps”). This approach allows for more realism in studying plasma creation and acceleration, but at the price of being decoupled from the global structure of the magnetosphere. Finally, the class of Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_11, © Springer-Verlag Berlin Heidelberg 2011

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models that concentrate on the global magnetospheric properties assume that abundant plasma exists throughout the magnetosphere and in the wind. This plasma can short out accelerating electric fields and provide corotation of field lines with the star. These models include relativistic MHD description of the magnetosphere and its limit for magnetically-dominated plasmas, the “force-free” models. Which of these different regimes is applicable for real pulsars may ultimately depend on the way plasma is introduced in the magnetosphere, and we turn to this question first.

2 Plasma supply and charge-separated models The first attempt at solving the magnetospheric structure and the problem of plasma supply was made by Goldreich and Julian (GJ) [18], who noticed that the unipolar induction electric fields on a rotating magnetized star are going to pull particles off the surface and fill the magnetosphere with plasma that has net charge density ηGJ = ∇ · E/4π = Ω · B/2πc. This charge density is needed to maintain corotation of the magnetic field lines with the star by forcing the accelerating fields E|| = E · B/B to zero. The GJ model is charge-separated, meaning the plasma density is assumed equal to the GJ charge density everywhere. If the plasma is moving at c, the associated current density ηGJ c is of the right order to cause the toroidal magnetic field at the light cylinder to be equal to the poloidal field. The corotation induces poloidal electric field E p ∼ (Ωr/c)B p, and the resulting outward Poynting flux E˙ rot = cE × B/4π is dominated by the poloidal electric and toroidal magnetic field and leads to the net energy loss from the system. Thus, even an aligned rotator, which has no time-dependent magnetic or electric fields that are needed for vacuum energy loss, can spin down in the presence of plasma. The magnetospheric structure of GJ model is shown in fig. 1a. The GJ magnetosphere consists of closed and open field lines. The last closed field line touches the light cylinder. The plasma on the closed field lines corotates with the star, and streams away on the open field lines, which are asymptotically straight in the poloidal direction. The open field lines also carry the toroidal field and the current needed for the spin down. These gross properties of the magnetosphere make physical sense, and were held to be true for years, even though the actual self-consistent solution escaped many analytical and numerical attempts. One should note that the GJ density nGJ = ηGJ /e is only the minimum plasma density required for corotation; the magnetosphere most likely is populated by much denser plasma. This plasma is generated from pair creation cascades, initialized by curvature and inverse compton gamma rays emitted by particles that accelerate from the surface [57, 1]. The typical “multiplicity” of such pair cascades can raise the plasma density to 104 nGJ in young pulsars. This is corroborated observationally by the requirement that the particle injection into pulsar wind nebulae exceed the GJ flux by a similar factor [10]. Thus, considerable attention has been devoted to magnetospheres filled with dense plasma. Despite being the foundation of the magnetospheric research, the GJ picture may not be viable, at least in the charge-separated regime. Consider the following setup:

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a)

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b)

Fig. 1 a) Schematic shape of the magnetosphere from the Goldreich-Julian model [18]; b) Chargeseparated electrosphere with domes of electrons and a differentially rotating disk of positrons/ions [52].

given a conducting rotating sphere with a dipole magnetic field and free escape of particles from the surface, can this system generate currents and spin down? At first sight this is the setup for the original GJ model, where a charge-separated outflow is expected to form. The problem, as seen from fig. 1a, is that on some field lines the charge separated flow of electrons should turn into protons (or positrons) at the null surface [27]. Thus the GJ flow without pair formation cannot be in a steady state. Indeed, several simulations [31, 51, 52] found that instead of forming an outflow, the rotating sphere is surrounded by electron “domes” near the poles and an equatorial ion “disk” (fig. 1b). These structures extend out to a few stellar radii, and are separated by vacuum regions. This external charge density compensates the vacuum accelerating field on the surface, and particles are not accelerated to the gamma-ray emitting energies. This solution is also stable to artificially induced bursts of pair formation[51]. The charge-separted plasma is not in complete corotation with the star, and the equatorial disk undergoes a diocotoron (nonneutral Kelvin-Helmholtz) instability because of the differential rotation [52, 43, 44, 45]. Over tens of rotational periods, the equatorial plasma drifts in radius, diminishing the differential rotation. This mechanism forms a way of filling the magnetosphere with GJ-like charge density, even though some of the regions are not directly accessible by appropriately charged field lines from the star. There is even a radial current flow, associated with this transport, although it is not enough to be responsible for pulsar action. Moreover, when the particles reach the light cylinder, the electrostatic diocotron instability switches to the electromagnetic magnetron mode, with smaller growth rates [46, 47]. Where such electrospheres fit into the grand scheme of things is not yet clear. They may represent what happens to neutron stars beyond the death line, or may be the intermittent process for establishing corotation in the closed zone of an active pulsar. The time scale of the instability is also interesting in the context of drifting subpulse phenomena. So far, however, the electrospheres have not been

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demonstrated to drive interesting spin down currents. Perhaps this will change with more realistic simulations, in particular 3D simulations with pair formation. One important property of the GJ magnetosphere is that the energy of the magnetospheric plasma is much smaller than the energy in the magnetic field. Even at the light cylinder, the plasma contribution is one part in 104 for young pulsars. The bending of the field lines at the light cylinder is thus not due to the inertial contribution of the plasma, but rather due to the “inertia” of the field. Magnetic domination allows a simplification of the MHD equations to the low-inertia, or “force-free” limit, described below1 .

3 Force-free models In the presence of dense plasma, all accelerating fields are quickly shorted out so that the ideal MHD condition E · B = 0 holds everywhere. The structure of the magnetosphere is then determined by the equilibrium of forces acting on the plasma. In the limit of small plasma inertia and temperature, the right hand side of the momentum equation becomes ρE + 1c j × B = 0, or “force-free”. Significant effort was directed over the years to finding a steady-state axisymmetric solution for the mgnetospheric structure of an aligned rotator subject to these constraints. Introducing flux function ˆ c and writing the corotation electric field Ψ such that poloidal field is Bp = ∇Ψ × φ/r ˆ the force-free constraint can be reduced to as E = rc Ωc−1 Bp × φ, # ∂2 Ψ ∂2 Ψ 1 + x2 ∂Ψ (1 − x ) + − = −I(Ψ)I ′ (Ψ). x ∂x ∂x2 ∂z2 2

"

(1)

Here, x ≡ rc /R L and z ≡ zc /R L are scaled cylindrical coordinates, and I(Ψ ) is the unknown function proportional to the polodial current enclosed by the flux surface Ψ. Known as the “pulsar equation” [38, 50], eq. (1) is a nonlinear second order elliptic equation with a regular singularity at the light cylinder x = 1. The current distribution I(Ψ ) is a priori unknown and should be determined as part of the self-consistent solution. This nonlinearity makes it a very difficult problem. Analytic solutions for the pulsar equation are known only for a monopolar magnetic field [38], and for a corotating dipole magnetosphere without a current [39]. A great advance was made in 1999 by Contopoulos, Kazanas & Fendt ([15], hereafter CKF) who solved the pulsar equation numerically for a dipole magnetic field. They used an elliptic solver to solve eq. (1) both inside and outside the light cylinder for a trial current distribution. In general, such a solution has an unphysical kink in the magnetic field at the light cylinder. A clever iterative algorithm that adjusted the current function to minimize the discontinuity allowed CKF to find a solution that passed smoothly through the light cylinder. This solution, shown in fig. 2, has a corotating closed zone and an open wind zone, with poloidal fieldlines asymptotically becoming monopolar, and toroidal field dominating at infinity. There are no distributed dissipative regions 1

The following chapter follows closely the discussion in [63]


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where E>B beyond the light cylinder, as was expected when early analytic solutions failed [37]. The last open field line corresponds to Ψopen = 1.36Ψ pc where Ψ pc ≡ µ/RL is the flux through the polar cap for the unperturbed vacuum dipole field. a)

b)

Fig. 2 a) Numerical solution of the steady-state pulsar equation using CKF method [15]. Figure from [20]; b) Steady-state poloidal magnetic field lines from a time-dependent aligned rotator simulation [55]. Toroidal field is marked in shades.

The magnetosphere supports an active current system: current is flowing along the open field lines to infinity, and the bulk of return current flows in the equatorial current sheet and on the boundary of closed and open zones, although a 5% fraction is distributed along a set of open field lines near equator (1.08Ψ pc < Ψ < 1.36Ψ pc). The CKF solution was later studied at finer resolution by Gruzinov [20], who calculated the open flux to be 1.27Ψ pc and the energy loss for the aligned rotator to be (1 ± 0.1)µ2Ω4 /c3 . He also obtained analytical expressions for the opening angle of the tip of the closed zone, where the current sheet splits into two (the Ypoint). The Y-point in these solutions is fixed to be at the light cylinder from the outset. However, this does not have to be the case. In fact, Timokhin [58] numerically found a family of solutions where the Y-point could be anywhere inside the light cylinder. Such magnetospheres spin down faster (according to eq. [??]), but otherwise seem accessible and physical. Besides the expectation that the magnetosphere should choose the lowest energy solution, it was not obvious which of these possibilities would exist in nature. The best way to address this was to solve an evolutionary, rather than a boundary value problem. This was done with the advent of time-dependent simulations. The MHD condition E · B = 0 and Maxwell equations can be combined with the force-free constraint to yield an evolutionary system of equations [40, 19, 6]:

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1 ∂E 4π 1 ∂B = ∇ × B − j; = −∇ × E; c ∂t c c ∂t c E × B c (B · ∇ × B − E · ∇ × E)B j = (∇ · E) 2 + . 4π 4π B B2

(2) (3)

This system has been called “force-free electrodynamics,” “magnetodynamics” [29], or “force-free relativistic MHD.” The philosophy behind the equations is very simple: the evolution is driven by the strong electromagnetic fields; however, the plasma, while having negligible inertia, does affect the fields through charges and currents. Unlike the full MHD equations, the small terms associated with the plasma inertia do not enter, and thus the system is not stiff in the highly magnetized regions. The plasma is assumed to move with the E × B velocity perpendicular to the fields; the velocity along the magnetic field is not defined. Eq. 3 serves as the prescription for the plasma current, and has the contributions from charge advection normal to the field and conduction current along the field. Unlike in the pulsar equation, there are no critical points in the system (2-3); yet the evolution from quite regular initial conditions can form discontinuities, or current sheets, and regions where E > B. The most difficult current sheets are the ones where magnetic field goes through zero. In those cases, the fundamental assumption of magnetic domination implicit in the derivation is invalid, and formally one has to resort back to the full MHD equations. In practice, one can deal with current sheets numerically by adding resistivity [29, 55], although there is some freedom in selecting a viable resistive formulation. Time-dependent magnetospheric simulations of the axisymmetric rotator have now been done by several groups [29, 36, 55, 28]. Typical initial conditions are a rotating conducting sphere with dipole magnetic field immersed in a force-free plasma. All groups generally agree on the outcome, although the details depend on the diffusivity of the codes. The time-dependent evolution settles into CKF-like state after a transient. This transient is interesting because in the ideal force-free formulation the topology of the field lines cannot change, so in order to transition from closed to open geometry, the field lines have to be stretched so that they close at infinity. The initial evolution does try to propagate a pulse that stretches the field lines (in the poloidal plane) and after a quarter of a turn an equatorial current sheet forms, because the field drops to zero in the equator (see ref. [54], fig. 1). After the transient, the Y-point settles very close to the light cylinder (fig. 2b). The spin down power measured in simulations for a star with magnetic moment µ is µ2 Ω4 /c3 . Komissarov [29] addressed the same problem with a full relativistic MHD code. That simulation produced the same gross magnetospheric shape and the Y-point near the light cylinder as the force-free simulations, although the conditions in the inner magnetosphere had to be artificially constrained to be numerically tractable. Simulation by Bucciantini et al. [9] also found similar results in the MHD regime at large magnetizations of thermally driven MHD winds from neutron stars. As a result of many numerical experiments, it appears that all signs point to the CKFtype solution being the natural steady state for an aligned rotator. The consequences of this will be investigated in the next section. Since pulsars must necessarily have finite obliqueness angle between the rotation and magnetic axes in order to pulse, the most general case of interest is that of the


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oblique rotator. The time-dependent force-free formulation allows one to solve the 3D problem as well. The difficulties are again associated with the formation of current sheets. For the oblique rotator, the current sheets are not aligned with the grid, and the numerical method has to be able to capture such structures. In [55] this was done on a 7003 cartesian grid for a range of inclination angles. The resulting magnetospheric shape is shown in fig. 3 for a 60◦ inclined rotator after 1.2 turns of the star. After this time the solution becomes nearly steady in the corotating frame 2 . Although the magnetospheric structure is intrinsically 3D, some insight can be gained from considering the shape of the field lines in the corotating frame in the plane defined by µ and Ω vectors. In this plane the field lines are reminiscent of the CKF solution with a closed and open zone and a current sheet. The main difference is that the current sheet oscillates about the rotational equator in a wedge with the opening angle of 2α and the wavelength of 2πRL . The field lines in this plane become straight beyond the light cylinder, corresponding to the inclined split-monopole solution found by Bogovalov [5]. For comparison, the fieldlines of a rotating dipole in vacuum look dipolar in µ-Ω plane out to two light cylinder radii, with no open zone or a current sheet. In the force-free solution the current sheet starts at the intersection of the light cylinder with the closed zone even in the oblique case. In the perpendicular plane the field is increasingly toroidal, reversing the sign in the current sheet (fig. 3b).

a)

b)

Fig. 3 Oblique pulsar magnetosphere with magnetic inclination α = 60◦ in the corotating frame: a) Magnetic fieldlines traced in the µ-Ω plane. Color is the magnetic field perpendicular to the plane; b) Slices through the 60◦ magnetosphere. Shown are fieldlines in the horizontal and vertical plane, color on the vertical plane is the perpendicular field, on the horizontal plane – toroidal field. Sample 3D flux tube is traced in white. From [55].

Having the global 3D solution, one can numerically integrate the escaping Poynting flux and measure the spin down energy loss as a function of inclination angle. The measured values are well fit by the formula [55]: 2

Kalapotharakos & Contopoulos (2010) tested this assumption with much longer simulations with radiating boundary conditions and converged on essentially the same solution

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a)

b)

Fig. 4 Oblique pulsar magnetosphere with magnetic inclination α = 60◦ in the corotating frame: a) Conduction current parameter λ [21] as color on a plane and on the star, with field lines traced in the µ − Ω plane, demonstrating the structure of the current sheet; b) Several slices through the magnetosphere, showing the λ parameter as color, with traced last closed field lines (white).

Lpulsar = k1

µ2 Ω4 (1 + k2 sin2 α), c3

(4)

with coefficients k1 = 1 ± 0.05 and k2 = 1 ± 0.1, or roughly L ≈ µ2 Ω4 /c3 (1 + sin2 α). This formula is a fit to a numerical result, not an analytically derived formula. The errors come from uncertainties associated with the current sheet, which causes some energy to disappear from the simulation as a function of radius. The angular dependence of the spin down should be compared to the commonly used vacuum result, which scales as 2/3 sin2 α. Obviously, eq. 4 gives the right limit for the aligned rotator, consistent with the axisymmetric simulations, and predicts that the 90◦ rotator loses twice as much energy as the aligned one. In-depth study of the 3D magnetosphere is complicated by difficulties in unambiguously identifying flux surfaces in 3D. While individual field lines can be easily traced, meaningful association of different field lines as belonging to a “flux tube” is more involved. An interesting development on this front was made by Gruzinov [21], who derived an invariant of the 3D analog to the pulsar equation: ∇ × (B + V × (V × B)) = λB,

(5)

where V = Ω × r. The quantity λ is conserved along field lines, B · ∇λ = 0. In the axisymmetric case, λ reduces to the integrated current enclosed by a flux tube, I(Ψ ). In 3D, λ is also related to the conduction current: the quantity λB is the field-aligned conduction current density in the corotating frame. Indeed, in the corotating frame, the electric field vanishes, and the force-free condition reduces to the non-relativistic j × B = 0, so the current flows along B in that frame. Isosurfaces of λ can be used to define flux surfaces in 3D, although these flux surfaces do not correspond to open or closed field line bundles. The quantity λ is very useful in marking the location


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of the current sheets and Y-points in 3D. In Fig. 4a, we plot the values of λ in a plane containing µ and Ω. It is clear that λ is conserved along the field lines and large current appears near the edge of the closed field lines and in the oscillating current sheet beyond the light cylinder. In Fig. 4b I plot several slices through the magnetosphere together with the tracing of the last closed field lines to give the impression of the 3D shape of the current sheet.

Fig. 5 Structure of the current (parameter λ) of the force-free magnetosphere in the Ω − µ plane for magnetic inclination angles α = 0◦ , 30◦ , 60◦ and 90◦ respectively. Arrows show the direction of the projected magnetic field in this plane [3].

Fig. 6 The shape of the polar caps in force-free field (solid lines) and the Deutsch field (dashdotted lines) for magnetic inclination angles α = 0◦ , 30◦ , 60◦ and 90◦ (left to right). Overlaid are the color plots of the current to flux ratio λ on the pulsar surface. To better visualize λ, the size of the pulsar is set to be 0.25RLC [3].

In [3], we analyzed the properties of the force-free solution as a function of inclination of the magnetic axis. The main findings can be illustrated in Figs. 5 and 6, where we show the structure of the current in the µ − Ω plane and the current distribution on the polar cap for different inclinations. The transition of current structure is smooth as inclination angle α increases from 0◦ to 90◦ . In Fig. 5, we see that

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at small inclination angle, α = 30◦, the pattern of λ is similar to the axisymmetric case, and the current sheet inside the LC appears slightly wider and weaker. As the inclination angle increases, the distribution of current becomes very asymmetric, and more current is returned to the polar cap through the distributed flow rather than the current sheet. The current flow in the polar cap is predominantly of one sign (e.g., ingoing) for the aligned rotator, bounded by a strong current sheet of opposite sign (e.g., outgoing), and is symmetric with respect to the equatorial plane. In contrast, when α = 90◦ , the current flow has different signs in the northern and southern halves of the polar cap (better seen in Fig. 6), and the current distribution is anti-symmetric with respect to the equatorial plane. On the periphery of the polar cap there are thin current layers, as shown in red (upper) and blue (lower) oval structures in the right panel of Fig. 5. The current in these current layers forms loops connecting the two poles through the closed zone. Integrating over the polar cap, we find that the amount of current flowing to the other pole is about 20% of the current flowing on open field lines. Such closed current loops for orthogonal rotators are qualitatively consistent with predictions of the model by [24], although we find the amount of current shunting to the other pole to be smaller in our simulations. The total current on the open field lines (integrated by magnitude) is just 20% smaller for the orthogonal rotator than for the aligned rotator, suggesting that the current density for the orthogonal rotator exceeds the simple expectation of the speed of light times local GJ density on the polar cap. This current cannot be provided by charge-separated flow alone and requires abundant pair formation. The details of the current adjustment in such polar caps are still uncertain [35]. A thin current sheet outside the LC exists for all inclination angles; its structure asymptotically approaches the rotating split monopole solution outlined by Bogovalov [5]. If the current sheet outside the LC is connected to the star, it must be connected through a current sheet inside the LC, because the current flow in the corotating frame cannot cross magnetic field lines. In fact, the amount of current in the current sheet outside the LC that is connected to the star monotonically decreases with inclination angle (see Appendix B in [3]). This is related to the degradation of the current sheet inside the LC and the thickening of the Y-region for oblique rotators shown in Fig. 5. These features are unlikely to be caused by numerical resistivity, and we have tested that the thickness of the Y-region and the strong current layers inside the LC is not sensitive to numerical resolution. For the orthogonal rotator, the current sheet outside the LC is totally disconnected from the star. Therefore, the oval structures in the right panel of Fig. 5 are most likely the current loops that connect the two poles, rather than current sheets connecting to the outer magnetosphere. This strongly contrasts with the case of the aligned rotator, where the current sheet inside the LC unambiguously exists and connects to the equatorial current sheet outside the LC. While there are definitely strong currents flowing on the periphery of the open field lines for all other inclinations seen from Fig. 5, determining whether their thickness is finite or infinitesimal would require further study, so calling them “strong current layers” rather than “current sheets” is probably more correct.


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From Fig. 6 we see that the polar cap of the FF field encloses the current flowing into and out of the pulsar. For simplicity we defined the polar cap as the locus of field lines that extend to the light cylinder, although more precisely it should be the field lines that extend out to the Y-point. The polar current switches from flowing into the NS at α = 0◦ , to equal halves of oppositely-directed current at α = 90◦ . The peak of the current density slightly lags the zero phase (i.e., the phase of the magnetic pole) due to pulsar rotation. For aligned rotator, the rim of the polar cap corresponds to the footprint of the current sheet, as expected. As α increases, the strong current thickens on one side (lower side in Fig. 6), and weakens on the other side. The thickened part may no longer count as a current sheet, as it gradually occupies half of the polar cap to become the main contributor of the polar current at α = 90◦ . The weakened side gradually shifts to the outside of the polar cap (at α = 90◦ ), and forms the current loop in the closed field lines as seen in the rightmost panel of Fig. 5. The current sheet covers a circle on the polar cap for the aligned rotator. For oblique rotators, the region covered by the current sheet on the polar cap reduces to an arc covering the upper part of the polar cap in Figure 6. The extent of the arc-like region shrinks with inclination angle α, consistent with the reduction of star-connecting current in the current sheet outside the LC. In the mean time, some current in the arc-like region on the polar cap becomes connected to the other pole, forming current loops. This is associated with the thickening of the Y-region discussed in the previous subsection. The loop current is zero for the aligned rotator, and increases to about 20% of the total polar current for the orthogonal rotator. As can be seen, the 3D magnetospheric solution is extremely rich in physics that may have potential observational signatures. Extracting useful information from intrinsically 3D data sets is nontrivial, but this work is currently underway.

4 Implications of the magnetospheric solutions With force-free solutions of the magnetosphere available, we can start asking questions about the assumptions that went into the model, and begin adding extra physics that may have consequences for explaining the observations. In a sense, the forcefree solution provides the scaffold onto which the fully functioning and radiating magnetospheric machine has to be attached.

4.1 Consequences for spin down Having a reliable spin down formula allows better estimation of the magnetic field ˙ 1/2 (1 + sin2 α)−1/2 G. When compared to the strength of pulsars: B0 = 2.6 × 1019(PP) p canonical vacuum perdiction of Bvac = 3.2 × 1019 (P P˙ G the maximal difference is up to a factor of 1.7, which seems relatively unimportant. However, in some cases where the inclination angle of a pulsar is constrained, one could be tempted to use

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the vacuum formula including the angular factor Bvac1 = Bvac sin−1 α. In this case one can infer fields much larger than is warranted, especially for small inclination angles. Another immediate consequence of the spin down formula is that pulsars with large inclination angles should lose more energy than nearly aligned rotators. Therefore, we would expect oblique rotators to spin down faster, and be first to cross the death line in the P − P˙ diagram [13]. That would leave more aligned than oblique pulsars near the death line 3 . To the extent that the inclination angle can be inferred from calculating the pulsed fraction of the radio beam, observationally there indeed seems to be an excess of pulsars which have smaller inclination angles near the death line [34].

4.2 High energy emission Significant amount of research has been invested in explaining the high energy emission from pulsars (e.g., [11, 48, 17, 26]). The models that seem to work best in obtaining widely separated double emission peaks invoke the production of gamma rays in the region associated with the boundary between the closed and open field lines. This works on geometrical grounds, because the photons from different heights and rotation phases can arrive to the observer in phase due to relativistic aberration and light travel time effects (caustics). Most models attribute the production mechanism to an accelerating structure (“a gap”) that exists in the same region. Depending on the range of heights involved in the accelerator, the gaps are called the “slot gap” or the “outer gap” (polar gap may also be important for observations of primary gamma rays in the polar cap cascade). The physics of the gaps as proposed now relies on charge starvation, either because the pairs are underproduced in slot gap region due to geometry of the pair formation front, or because the sign of GJ density reverses with distance (the “null surface”). In force-free solutions the plasma is assumed abundant and there are no special points that would appear to cause violent acceleration. In particular, the “null surface” has no particular significance, as the net charge can change sign in a dense plasma rather easily. What is striking, however, is that the region at the boundary with last closed field lines, is exactly the region where strong current sheets flow in the magnetosphere (fig. 4). Therefore, it is tempting to suggest that we are dealing with the physics of the current sheet; however, whether this interpretation can work in practice requires additional study. In [2, 3] we studied the geometry of the emission zone in the force-free magnetosphere that could lead to the formation of double-peaked light curves4 . The differences in the geometry of the force-free field and the vacuum Deutsch field are not important close to the star, but increase further out, particularly near and beyond the light cylinder. However, as the shape of the polar cap is determined by the be3

The effect discussed in [13] also took into account the modification of the spin down due to the growth of vacuum gaps with age. 4 Also see chapter by X. Bai in this volume.


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havior of the field lines near the LC, even the emission close to the star is likely to be significantly affected by the new field geometry (e.g., compare vacuum polar cap and force-free polar cap in Fig. 6). In order to keep the investigation more general, in [2, 3] the emission was assigned uniformly per unit length of the field line along the whole field line, so that the peaks of the emission are associated with caustics rather than a particular region that is selected to emit more. The photons were emitted parallel to the field lines in the corotating frame and then binned on the sky map accounting for the relativistic effects, such as light aberration and time delay. The resulting sky maps showed that the same magnetospheric locations as invoked for the vacuum field geometry, namely the slot gap and the outer gap regions, did not seem to produce reliable double peaks in the force-free field. This was attributed to the larger polar cap shape in the force-free field and to the different geometry of the field lines near the LC, which affected the geometry of the null charge surface in the outer gap model. The slot gap model in vacuum geometry assigns the emission to an annulus congruent to the last open field lines that extends in radius from the stellar surface to ∼ 0.7RL. The outer gap model extends out from the intersection of the null charge surface with a similar annulus, so the height of the emission depends on the field line. In working with force-free field, we chose to include emission from all field lines in an annulus (since there is no special meaning to the null charge surface) tracing the field lines beyond the light cylinder (typically out to 1.5 RL ).

Fig. 7 Geometry of the emitting flux tube in force-free field for α = 60◦ . a) and b) 3D view of the flux tube. The rings mark intervals of 0.25 RL along each field line; c) location of field lines from the northern hemisphere on the sky map; d) same from both poles; e) sky map intensity.

The geometry of the emitting flux tube and the resulting sky map is shown in Fig. 7. The sky map in 7e shows the intensity of the emission as a function of pulsar phase for different observer viewing angles ξobs . The light curve for a given observer is then a horizontal cut through this plot. Two peaks are generally obtained and their separation can vary up to half a rotation period. This is in agreement with

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the properties of gamma-ray pulsars observed by Fermi. The high intensity regions on the sky map are formed by caustics, as can be seen from the overlap of emission from different heights along field lines in 7c,d. Most of the caustic formation occurs in the outer magnetosphere, at and beyond RL . This can be understood from the fact that force-free field lines start to resemble the rotating split monopole solution beyond the light cylinder, and the shape of the field line in the form of Archemedean spiral is highly conducive to the formation of caustics. Indeed, a relativistic particle rotating with the star and sliding along such a spiral would move on a straight line in the inertial space. Its emission from different radii will thus arrive at the observer simultaneously, and cause a strong caustic. In the vacuum field, particularly in the slot gap (or “two-pole caustic”) model, the caustics are formed due to very different chance overlaps of the emission from different field lines (e.g., see [2]).

a)

b)

Fig. 8 Geometry of the preferred flux tube that produces double-peaked emission in the forcefree magnetosphere with magnetic inclination α = 60◦ . Overplotted is the volume rendering of the strength of the current, dominated by the equatorial current sheet. Two phases of rotation are shown in panels a) and b).

To better illustrate the emitting region preferred in the force-free field, consider the 3D view of the magnetosphere in Fig. 8. White lines mark the preferred field line bundle that gives the double-peaked profiles. We also overplot the volume rendering of the current density, which peaks in the current sheet beyond the light cylinder. It is clear the the white lines trace very well the shape of the current sheet. Incidentally, the bulk of the emission that results in caustics is also accumulated beyond the light cylinder. The reason why these field lines give double peaks is relatively simple: any flux tube that becomes split-monpolar will produce caustics on the sky map that would look like rings surrounding each pole. The caustics from the field lines that start at the north and south magnetic poles merge only for the field lines that meet and follow each other near the current sheet. Thus, the force-free magnetosphere prefers the emission near the last open field lines close to the edge of the polar cap. The actual emission on these lines arises near and beyond the light cylinder close to


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the current sheet. Due to its association with the current sheet, we called this model the ”Separatrix Layer” model. The process responsible for high-energy emission in the force-free magnetosphere is still unclear. In the vacuum field, accelerating gaps filled with vacuum electric fields are postulated near the edge of the polar flux tube, and the emission is typically attributed to radiation-reaction limited curvature radiation of highly relativistic beams. The acceleration and radiation process in the force-free field requires a different approach. Based on geometry, the emission seems to be associated with the current sheet, so it is natural to invoke reconnection in the sheet as a means of both heating and accelerating the plasma. Since the plasma in the current sheet is likely to be much denser than the GJ density typically assumed in gaps, radiationreaction limited curvature radiation may be replaced by synchrotron radiation from the hot streaming plasma in the sheet. Recently, Gruzinov [22] suggested that there are regions in the magnetosphere where the current is necessarily “spacelike,” i.e., there is no frame where the current can be represented as the advection of charge density. This means that the current must be provided by the relative drift between the species, which may result in streaming instabilities and dissipation. The current sheet outside R L is indeed spacelike. Further advances in this modeling require improved force-free or MHD models that can accommodate finite resistivity 5 . This is now being pursued.

4.3 Reconnection and time-dependence Reconnection must be an integral part of the way magnetosphere works. This is clear just from the fact that as the pulsar slows down and the light cylinder recedes, the Y point probably moves out as well. In order to do this, some open field lines have to get converted into closed ones [12, 13], so reconnection must proceed at least on the spindown time scale [14]. Most likely, reconnection proceeds much faster, and the magnetosphere is constantly adjusting to the stresses at the light cylinder. This is evidenced in time-dependent force-free [55] and MHD [9] simulations, where the Y-point can oscillate near the light cylinder, resulting in periodic emission of small plasmoids. The amplitude and frequency of these oscillations depends on resistivity, which is not faithfully modeled in the simulations; however, the dynamical response of the magnetosphere is realistic. This implies that there could be quasiperiodic behavior of the magnetosphere controlled by the magnetospheric crossing time and the reconnection rate. It is natural to suggest that such breathing is ultimately responsible for the drifting subpulse phenomena, although no comprehensive model based on this currently exists. Another consequence of magnetospheric reconnection is the modification of the pulsar braking index. Note, that all force-free models ultimately yield spin down ¨ Ω) ˙ 2 = 3. Most of the reliably power going as Ω4 , so a braking index is n ≡ ΩΩ/( 5

For a particularly promising prescription for resistive force-free model see [22, 23].

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measured braking indexes are below 3 [33]. If the Y point and the light cylinder are allowed to move not in unison, then from n = 3 + 2∂ ln(1 + RY /R L )/∂Ω [9, 13] we get n < 3 for cases where the Y-point does not recede as fast as the light cylinder. Alternative explanations for n < 3 involve inertial effects or the evolution of the magnetic field with pulsar age [7, 49].

4.4 Current structure and origin A large area of research that is now open to reinvestigation concerns the origin and mechanics of current and plasma production in the magnetosphere. The force-free models provide the strength and shape of the conduction current that the magnetospheric plasma has to carry in order to support the stresses at the light cylinder and provide the spin down. How these currents are actually produced and extracted is a question that force-free theory cannot address. To zeroth order, the shape of the current as a function of flux surface coordinate for an aligned rotator is well approximated by the Michel’s split-monopole current [39]: I(Ψ) = R−1 L Ψ(2 − Ψ/Ψopen ) (up to ∼ 20% corrections due to the distributed return current at the edge of the polar cap), or in terms of the GJ current density, j = jGJ (1 − Ψ/Ψopen ), where Ψopen is the flux through the polar cap. This implies that the current significantly varies over the polar cap. On the other hand, most models of the electrostatics of polar accelerating gaps, which create a space-charge limited flow, approach typical values of j = ηGJ c, which are constant over the size of the polar cap. This is because ηGJ does not vary significantly over a small polar cap size, and relativistic outflows are readily produced in the large starvation electric fields near the surface. Herein lies a problem, because the gap seems to be unable to produce the current that is needed by the magnetosphere. This will lead to time dependence as the magnetosphere adjusts to the wrong current, and sends Alfven waves back to the gap. This contradiction probably is a consequence of overdetermining the structure of the gap by only considering the local electrostatics, without the influence of charges in the return current layer. Allowing more freedom to the flow such as counterstreaming electron distributions or time-dependent virtual cathode oscillations [32] could help as well. Another outcome was also entertained [59], where a force-free magnetospheric solution was found that corresponded to the constant current over the pole. The price was to relax the angular velocity of field lines, so the magnetosphere rotated differentially. Another alternative is to question the assumption that the charges are necessarily moving relativistically. Beloborodov [3] found that a space charge limited flow with j < jGJ could be generated in a 1D model of the polar cap, when a current is imposed (presumably by the magnetosphere) and in this case the charges move nonrelativistically. This solution, if it can also work in 2D, has an interesting consequence: the aligned rotator (which has j ≤ jGJ ) everywhere on the polar cap, will not accelerate plasma to high enough energy to radiate gamma rays and spark pair formation. This would be inconsistent with the force-free dense plasma picture, and, more importantly, is unlikely to lead to a viable current outflow higher up in the


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magnetosphere, where the flow has to cross the null surface. More work is clearly needed to understand the “chicken and the egg” question of the plasma supply. In contrast, the force-free current in the oblique rotator is larger than the local GJ current. For finite inclinations, the local GJ density and current drop as cos α. Yet, the current required by the oblique force-free models is of the same order as the GJ current of the aligned rotator. Although in principle, if the plasma is dense enough, super-GJ currents should not difficult to set up, one wonders if this is a generic configuration, or there would be some pulsars that are charge-starved and therefore, would spin down differently. The issue of the magnitude of the current is the fundamental difference between the time-dependent force-free solutions[55], and the analytic solutions of 3D force-free equations constructed by Beskin, Gurevich and Istomin [24, 5, 25], who explicitly require the conduction current in the oblique rotator to be limited by the local GJ current density. This leads to the suppression of the spindown power with inclination as cos2 α, quite the opposite result from eq. (4)! Which one is closer to the truth may depend on what can be produced in the polar gap. Also, since the oblique analytic solutions in [24] cannot be continued beyond the light cylinder, it is not clear whether they can be directly compared with the force-free simulations, which have no significant issues on the light cylinder.

4.5 Differential rotation The force-free models are a good first approximation if the potential drops in the various gaps are small compared to the available vacuum polar cap potential. Even if the gap potential is significant but there is a pair formation front beyond some height above the polar cap, the gaps can still be accommodated into the force-free formalism. The field lines above the gap are equipotentials, and hence rotate with the same angular velocity; however, this angular velocity is different from the stellar rotation Ω, because of the potential drop in the gap. Assuming a small vertical extent of the gap, such configurations can then be simulated by specifying different angular velocities on the surface of the star corresponding to open and closed lines. The effect on the spin down is to reduce the power of the aligned rotator as Laligned = µ2 Ω4 /c3 (1 − Ωdeath /Ω), where Ωdeath is the frequency of the star where the available potential can no longer generate the pairs [13]. So, if a nearly aligned pulsar approaches the death line, its trajectory on the P− P˙ diagram will curve downward, which can help to explain the shape of the P − P˙ diagram without requiring magnetic field decay. One can attempt to heuristically generalize this formula to the oblique rotator as L = µ2 Ω4 /c3 [(1 − Ωdeath /Ω) + ξ(Ωdeath /Ω) sin2 (α)]. Here, the first term in brackets is responsible for the aligned part, and ξ(Ωdeath /Ω) is a slowly varying function that goes from 1 for the healthy young pulsars (Ω ≫ Ωdeath ), to 2/3 for the “dead” pulsars, that have no plasma and must spin down as vacuum rotators. Such modification of the spin down law can help to explain recent observations of transient pulsars [30]. In PSR B1931+24, the torque in the “on” state, when the pulsar is shining and can be interpreted as filled with plasma, exceeds the torque in the

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“off” state by a factor of 1.5. It is clear that if one compares the original plasma spin down expression (4) with the vacuum spin down, the prediction is that the torque ratio has to be larger than 3 for any inclination angle, contradicting the observations. The modified law above does find solutions, but an extra parameter (Ωdeath ) is introduced. One has to also question whether the pulsar really turns off to a complete vacuum, or some residual plasma, perhaps in the closed zone, modifies the vacuum spin down. This can be studied with an oblique force-free simulation with a gap. Alternatively, if the research on polar current production finds that the current is limited to local GJ current, one would have to reconsider the spin down law [25]. Overall, the discovery of transient pulsars holds great promise in constraining the physics of the magnetosphere. For the first time, we have an actual handle on the bulk of the energy flow, and the evolution of the currents in the magnetosphere when the plasma supply is varied6 .

4.6 Conclusion The field of pulsar magnetospheres is now undergoing an exciting transformation, where a calculable standard model is being formulated. The shape and general properties of the plasma-filled magnetosphere are now known, and this opens the possibility of addressing old questions of plasma supply and current formation in a globally self-consistent way. Particularly exciting is the indication of connection between the high energy emission and the strong equatorial current sheet at and beyond the light cylinder. The fact that this region may be active makes energetic sense, as this is the ”wire” that carries most of the return current associated with the spin down energy loss. In order to dissipate large fractions of spin down energy (10-20% are inferred for older gamma-ray emitting pulsars by Fermi observations), a “resistor” in the circuit is needed, and the current sheet is well positioned to act as such a resistor. The actual physics of this resistivity and the ensuing particle energization and acceleration are currently uncertain, but modeling the phase-resolved gamma-ray spectra provided by Fermi will provide good handles on these processes. Important advances are also poised to happen on the theoretical front, with more elaborate relativistic MHD simulations and kinetic studies of the physics of relativistic reconnection coming online soon.

References 1. 2. 3. 3. 6

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A huge unanswered question is what actually triggers the state transition in the transient pulsars!


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Modeling of γ-ray Pulsar Light Curves from Force-Free Magnetosphere Xue-Ning Bai & Anatoly Spitkovsky

Abstract The Fermi LAT has recently discovered dozens of new gamma-ray pulsars, and is destined to revolutionize our knowledge of pulsar science. The gammaray pulsar light curves carry important information about pulsar magnetospheric structure, which has commonly been modeled as a vacuum dipole. We briefly review theoretical models of gamma-ray pulsar light curves and point out their uncertainties due to the usage of vacuum field. We present the first results of pulsar high-energy light curve modeling using the more realistic force-free (FF) field taken from timedependent FF simulations. With the FF field, we find the conventional slot-gap (twopole caustic) and outer-gap models are no longer able to produce the commonly observed double-peak light curves. The most geometrically favored gamma-ray emission zone lies in a thin layer near the edge of the open flux tube. Emission from this “separatrix layer” generally produces two sharp peaks in the light curve, which are formed near and beyond the light cylinder. We show that most features and statistics from the currently available gamma-ray pulsar light curves can be well reproduced and explained in this framework. The location of this emission zone strongly suggests its association with the current sheet, thus calling for more detailed study of current sheet physics and particle acceleration.

Gamma-ray pulsars (GRPs) are the most energetic objects in the pulsar population. Their high-energy emission carries important information about pulsar magnetospheric structure, particle acceleration mechanisms, and plasma physics in strong magnetic fields. Seven GRPs were known before the launch of the Fermi Gammaray Space Telescope (Fermi). With unprecedented sensitivity, Fermi has recently discovered more than 40 new GRPs, including 16 previously unknown pulsars from blind search (see [1] and references therein). The GRP population contains both normal and millisecond pulsars (MSPs). Despite the large diversity in surface magnetic Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ-08544, USA. e-mail: [email protected],[email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_12, © Springer-Verlag Berlin Heidelberg 2011

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field strength and rotation period, all these GRPs possess strong magnetic field at the light cylinder (LC) radius RLC ≡ c/Ω, where Ω is the pulsar’s angular frequency. The gamma-ray light curves from GRPs also show large diversity, but the majority of them are double-peaked with wide separation and have substantial bridge emission between the two peaks. When radio emission is detected, the first gamma-ray peak typically lags the radio pulse by a small fraction (δ) of the rotation period. Gamma-ray emission from GRPs are believed to originate from “gap” regions in the pulsar magnetosphere. Particles are accelerated in the gaps due to strong parallel electric field and produce curvature, synchrotron and inverse Compton radiation. Conventional models for pulsar gamma-ray emission include the polar cap model [8], the slot-gap model (SG, or two-pole caustic model, TPC) [2, 9, 12], the outergap model (OG) [16, 16, 7], and the annular gap model [15]. These models largely work on geometric grounds and differ in the assumed location of the emission zones (i.e., gaps). In particular, the TPC model assumes the emission zone to be located in a thin layer in the periphery of the last open field lines (LOFLs) extending from the neutron star (NS) surface to some cutoff radius inside the LC, while the emission zone in the OG model resides in the open field line region near the LOFLs extending from the null charge surface (NCS) to the LC. These two models are generally more favored because they have more extended emission zones and have been very successful in reproducing double-peak light curves. Most calculations of the GRP light curves from these models approximate the pulsar magnetosphere by a vacuum dipole field (either static or retarded dipole). However, pulsar magnetosphere is filled with plasma [10]. The plasma is essentially force-free (FF), with ρE + j × B/c = 0, where ρ and j are charge and current densities. Recently, [17] obtained the full 3D magnetospheric structure using timedependent FF simulations. The simulations self-consistently take into account the effect of conducting plasma, and provide more realistic approximations to the pulsar magnetosphere. The resulting FF field structure differs substantially from the vacuum field structure due to the strong poloidal current and the returning current sheet (see the Chapter by Spitkovsky). Such deviation raises the question of the robustness of the GRP light curve modeling using the vacuum dipole field. The basic procedure for light curve calculation can be summarized as follows. 1. Trace magnetic field lines to find the LOFLs (which are field lines that touch the LC tangentially), and record the locus of the LOFLs on the polar cap. 2. Define the open volume coordinate (rov , φm ) on the polar cap, where φm is the LOFL is the magnetic colatitude normalized to magnetic azimuth and rov = θm /θm that of the LOFLs. Each (rov , φm ) combination specifies one field line. 3. Assign the emission zone with prescribed range of rov and (inner and outer) spatial cutoff radii. Uniform emissivity along field line is commonly assumed. 4. Trace magnetic field lines in the emission zone, assume photons are emitted along the direction of the field lines in the corotating frame, and project the emitted photons to the sky with correction for aberration and time delay effects.1 1

The treatment of aberration in much of the literature was not self-consistent, see [3] for detailed discussion and correction.

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5. Bin the photons on the sky map (φ, ξobs ), where φ and ξobs correspond to rotation phase and observer’s viewing angle respectively. The light curve is obtained by cutting the sky map at fixed ξobs . Typical sky maps produced by the vacuum TPC and OG models contain sharp and bright arc regions which lead to peaks in the model light curves (see [3]). These arcs are called “caustics”, whose formation is due to the fortuitous overlap of radiation on the sky map from different regions of the magnetosphere. Mathematically, it means that the Jacobian determinant of the map from the emission zone to the sky coordinates approaches zero. Therefore, the formation of caustics (hence the peaks in the light curves) is very sensitive to the magnetic field geometry and the location of the emission zone. Indeed, by considering two types of vacuum fields (static and retarded dipole fields), and two different shapes of the polar caps (circular and polar cap obtained by tracing LOFLs), [3] found that the appearance of the sky maps are very different in the four combinations. Such differences reflect large uncertainties in the light curve modeling using the vacuum field, calling for re-investigation of the GRP emission models using the more realistic FF field. Bai & Spitkovsky [4] presented the first results of GRP light curve modeling using the FF field from simulations by [17]. They found that the TPC model fails to produce the double-peak pulse profiles, mostly because the size of the polar cap in FF magnetosphere is larger than the vacuum field polar cap, which suppresses caustic formation in the inner magnetosphere. The OG model can produce only one peak in most magnetic and viewing geometries, because a large fraction of open field lines do not cross the NCS. By exploring a wide range of different emission zone locations, they found that the most geometrically favored emission zone lies in a thin layer on the open field lines just inside the separatrix that bounds the open flux tube. Based on the geometric location, this emission zone is termed as the “separatrix layer” (SL), which generally corresponds to rov = 0.9 − 0.95. Figure 1 demonstrates how the SL model works in FF field geometry. Clearly, two bright and narrow caustics are formed on the sky map, which can naturally produce widely-separated double-peak pulse profiles under a wide range of viewing angles, as illustrated in panels (d) and (e). The origin of the caustics can be traced from panel (b): there is strong clustering of rings (mapped from panel (a), see the Figure caption) at the position of the caustics. Therefore, beyond a certain distance s0 along these field lines from the NS, emission from a single field line arrives to the observer simultaneously, which strongly enhances the local sky map brightness. Comparing with panel (a) suggests that s0 ≈ 0.75 − 1.0RLC. Therefore, caustics form in the outer magnetosphere, near and beyond the LC. The father the emission zone extends, the stronger the caustics are (hence the sharper the gamma-ray peaks are). This effect is termed as “sky map stagnation” (SMS). SMS is closely related to the fact that the FF field asymptotically approaches the split monopole solution [5], and is a robust effect for all open field lines (rov < 1). Nevertheless, only field lines with rov close to 1 produce sky maps similar to Figure 1. Field lines from smaller rov tend to produce four rather than two peaks. This fact strongly constrains the geometrically favored location of the emission zone to be in the SL.

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Fig. 1 Illustration of the SL model using FF field with magnetic inclination angle α = 60◦ . Panel (a) shows the emission zone geometry plotted as individual field lines (from the north magnetic pole) traced from the NS surface to cylindrical radius R = 1.2RLC . These field lines are projected to the sky map in panel (b). To guide the eye, different symbols are plotted along four field lines in both panels which clarify the line correspondence between the two panels. Furthermore, six rings (in black dots) are plotted across the field lines in panel (a) (the innermost ring is hardly visible) together with their projections in panel (b). Points on each ring are located at fixed distance, s, from the NS surface, measured along the field lines. Different rings are evenly separated, with ∆s = 0.25RLC . Panel (c) shows the brightness of the sky map (from both magnetic poles). Color scale is linear, and black arcs indicate strong caustics. Two sample light curves from ξobs = 45◦ and ξobs = 80◦ are shown in panels (d) and (e) respectively.

An atlas of GRP light curves from the SL model is presented in [4] (see their Figure 9), from which robust predictions on the temporal locations of the two peaks can be made regardless of input physics. The phase lag of the first peak relative to the radio peak ranges from δ = 0.14 to 0.4, and the separation between the two peaks ranges from zero (i.e., one peak) to ∆ = 0.5. Smaller phase lag typically corresponds to larger peak separation, and vice versa (which is also apparent in Figure 1). Statistically, the SL model predicts that majority of the light curves should have widely-separated double peaks, pulsars with smaller peak separation are less common, and pulsars with only one peak are possible but rare. Another consequence of the SL model is that smaller peak separation usually indicates stronger bridge emission between the peaks. All these predictions are consistent with the Fermi GRP sample [1]. Moreover, the fact that a large fraction of MSPs detected by Fermi are single peaked (and double-peaked with small separation) suggests that MSPs tend to have small magnetic inclination angle, based on the SL model. Being a geometric model, the physical origin of the SL emission remains to be explored. However, the location of the SL closely traces the Y-point (or “Y-ring” in 3D) and the equatorial current sheet beyond the LC. Strong dissipation and reconnection is expected in such regions [11], leading to particle acceleration and gamma-ray emission [14]. It may also be related to the stripped wind model by [13].

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Detailed theory on the physics of the Y-ring and current sheet has to be constructed to test these scenarios and uncover the origin of the SL emission.

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A Tale of Two Current Sheets Jonathan Arons

Abstract I outline a new model of particle acceleration in the current sheet separating the closed from the open field lines in the force-free model of pulsar magnetospheres, based on reconnection at the light cylinder and “auroral” acceleration occurring in the return current channel that connects the light cylinder to the neutron star surface. I discuss recent studies of Pulsar Wind Nebulae, which find that pair outflow rates in excess of those predicted by existing theories of pair creation occur, and use those results to point out that dissipation of the magnetic field in a pulsar’s wind upstream of the termination shock is restored to life as a viable model for the solution of the “σ” problem as a consequence of the lower wind 4-velocity implied by the larger mass loading. †

1 Follow The Energy Rotation Powered Pulsars (RPPs) provide the first and most definitive example of compact astrophysical systems which draw the power for their observed emissions from the extraction of rotational energy from gravitationally bound objects through the action of macroscopic electromagnetic fields. They have motivated models for similar energy extraction from disks around other gravitating bodies, such as black holes (e.g. Rees [46], Begelman et al. [10]). As objects of study, the RPPs have a virtue lacking in the black hole systems: timing of the precisely measured pulse periods, uniquely interpretable as the rotation periods of the underlying neutron stars, Jonathan Arons Department of Astronomy, Department of Physics, Space Sciences Laboratory and Theoretical Astrophysics Center, University of California, Berkeley e-mail: [email protected] (The title goes with apologies to Charles Dickens) †

Collaborators, none of whom should be held responsible for the content of this paper: D. Alsop, E. Amato, D. Backer, P. Chang, N. Bucciantini, B. Gaensler, Y. Gallant, V. Kaspi, A.B. Langdon, C. Max, E. Quataert, A. Spitkovsky, M. Tavani, A. Timokhin N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_13, © Springer-Verlag Berlin Heidelberg 2011

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provide measurements of the total energy budget free of all astrophysical uncertainties, other than the factor of ∼ 2 uncertainty in neutron stars’ moments of inertia, arising from the unecertainties in the equation of state of dense matter. The measured rate of rotational energy loss, P˙ E˙ R = −IΩ∗ Ω˙ ∗ = 4πI 3 , (1) P tells us the total energy budget for these systems, without our having to understand anything about the photon emissions from these systems - which is both a blessing and a curse - a blessing, because in contrast to other relativstic astrophysical systems, we know the energy budget, without having to unravel the partition between flow kinetic energy, large scale Poynting flux, thermal energy and radiative losses - a curse, since the energy loss is radiatively silent, thus supplying little information as to the details of the energy outflow, leaving the mechanics of the machine mysterious. Nevertheless, progress has been made. The Pulsar Wind Nebulae (PWNe) act as catch basins for the rotational energy lost. Observations of these systems Gaensler & Slane [24], using radio (including millimeter), X-ray, gamma ray and occasionally infrared telescopes1 , have made clear that RPPs deliver their energy to the outside world in the form of highly relativistic, magnetized outflows - stellar winds that are exaggerated versions of the solar wind - which must be electromagnetically driven by the magnetic pressure of the wound up magnetic field. The strength of that field is estimated by using the theory of magnetic braking of the neutron stars’ spin, which suggests Ω˙ = −KΩn , Ω = 2π/P,

(2)

P = rotation period, applied to the observed rotations periods and spindown rates ˙ 2. P˙ = −2πΩ/Ω The earliest model applied vacuum electrodynamics to a rotating sphere endowed with a magnetic dipole moment µ centered at the stars’ centers and tipped with respect to the rotation axis by an angle i. That theory yields the spindown luminosity E˙ R = KΩ4 , K = (2/3)µ2 sin2 i/c3 [e.g. [41, 43]] thus n = 3 in this model. Vacuum theory was motivated by the large gravitational forces at the surfaces, suggesting no plasma more than a meter or so above the star, but immediately Deutsch’s much earlier observation [[22]], made in the context of magnetic A stars, that in vacuum large electric fields parallel to B would overwhelm gravity and pull charged particles out from the star until the vacuum electric field would be altered, reducing E · B down to zero, was recovered [25] and extended with the suggestion that the charged particles would feed a curious charge separated wind, p with a total electric current I = cΦmag , Φmag = total magnetospheric potential = E˙ R /c. That wind could carry 1

Most PWNe lie in the galactic plane, therefore are relatively inaccessible to optical techniques, and are even less accessible to UV telescopes. Near and far infrared observations are extremely useful in unraveling the physics of the relativistic outflows [16], but have been much less in evidence than the high energy studies.

A Tale of Two Current Sheets

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away the rotational energy of even the aligned rotator, in a Poynting flux dominated flow - the electromagnetic energy density would vastly exceed the kinetic energy density (and pressure) of the outflow, in the initially conceived model - the particle flux in that scheme is only cΦ/e = 2.3 × 1030(I45 P˙ 15 /P3 )1/2 elementary charges/s, −15 , the “Goldreich-Julian” current. ˙ I45 = I/1045 cgs, P˙ 15 = P/10

Fig. 1 Observed RPP periods and period derivatives, from [33]. The line bounding the pulsar population corresponds to the magnetospheric voltage Φ = 1012 V, clearly marks a boundary beyond which pulsar emission is unlikely. Simple estimates of pair creation suggests this source of plasma should occur only for voltage larger than this value, which underpins the idea that pair creation is esential for radio emission [[51]]. The change in slope of this “death line” al short period, small P˙ indicates more sophistication in the pair creation physics, and/or in the association of pairs with radio emission, than is incorporated in the simplest models, a conclusion also apparent from the variety of quantitative problems with this widely accepted hypothesis [31, 39].

The charge separated model has several really serious theoretical difficulties, but perhaps of greater importance is that the observations of young PWNe have made clear that the particle outflows are many orders of magnitude larger than the Goldreich-Julian current, thus motivating MHD models, where E · B = 0 is assumed from the start. Pair creation occurring somewhere within the magnetospheres (first suggested by [51]) is thought to be the origin of the required dense plasma, although a quantitative model that yields the high mass loss rates observed is still

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lacking [Bucciantini et al. [16] and references therein]. In recent years, solutions for the MHD structure of the magnetosphere in the appropriate force-free limit have been obtained (numerically - the attempts of analytically minded theorists to guess the answer to the rather formidable free boundary/eigenfunction problem posed by the steady state version of the model, uniformly failed over 30 years of attempts), first for the aligned rotator [[19, 26, 35, 52]], then for the full 3D oblique rotator [[50, 32]]. As far as the P, P˙ diagram goes, the main result from these investigations is the innocuous looking conclusion in expression (3). K = k(1 + sin2 i)

Ω3 µ2 , k = 1 ± 0.1. c3

(3)

Physically, the most important result has been the identification of the current sheets separating the closed from the open regions of the magnetosphere, extending into the wind beyond the magnetosphere, whose last closed flux surface ends just touching the light cylinder whose cylindrical radius is ̟ = c/Ω. That such a current sheet should be present has been suspected from the early days of RPP research [e.g., [40]]. The error in k reflects the uncertainties in the numerical treatment of the problem, many of which are associated with how the current sheet is represented in the numerical schemes. Figure 2 shows a slice through the 3d force-free magnetosphere of the 60◦ rotator, from Spitkovsky’s (2006) results. Observationally, expression (3) shows that the vacuum rotator’s “braking index” n = 3 is preserved in full force-free MHD, which contradicts the observed values in the small number of stars where n has been determined [37], a contradiction which has led to a variety of suggestions ranging from evolution of the magnetic moment µ or the obliquity i [12] to effects of reconnection on the rate of conversion of open magnetic flux to closed [20], as the star spins down and the closed zone expands at the expense of the amount of open magnetic flux. That reconnection might affect the braking index is readily derived from the fact that the torque really depends on the magnitude of the open magnetic flux.The amount of open flux depends on the size of the closed zone, which ends at RY . If RY /R L < 1, the torque increases because of more open field lines and larger Poynting flux than is the case for a magnetosphere closing at r = R L . [15] show that the braking index is ∂ ln 1 + RRYL ΩΩ¨ n≡ = 3+2 ; (4) ˙2 ∂ ln Ω Ω thus, If RY /R L decreases with decreasing Ω, then n < 3. Reconnection usually is unsteady - figure 3 shows the blobs (“plasmoids”) ejected from the Y-line at the base of the current sheet in the relativistic wind of the aligned rotator. The speculation is that spindown slightly biases these reconnection events so that on the much longer spindown timescale, the net open flux slowly converts to closed. These current fluctuations might be associated with the timing “noise” [2, 18] identified long ago with torque fluctuations (e.g., Helfand et al. [30], Scott et al. [47]), although recent analysis of longer data sets [38] in long period pulsars has called the noise interpretation into question.


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Fig. 2 Field lines and current density of the oblique force-free rotator, i = 60◦ , from Spitkovsky (2006), seen in a cut in the Ω, µ plane. The last closed field lines end at a Y-point (a Y-line, in 3D) at distance RY from the neutron star. The current sheet encloses and separates the closed from the open field regions of the magnetosphere, and the separate branches merge in the wind zone, where the folded sheet continues to separate the oppositely directed fields of the striped wind. The arrows and “Gap” labels locate sites where vacuum gaps have been postulated, in test particle models of accelerators that lead to gamma ray emission and pair creation. None of these gaps appear in a current sheet accelerator based on the force-free magnetosphere model.

In itself, the force-free model does not provide mechanisms for photon emission. But it has a variety of implications, which are slowly being addressed. • The model specifies the polar flux tube size and shape - it is noncircular with a polar cap center displaced from the magnetic axis, even when the magnetic field is the simplest, that of a star centered, point dipole [9]. This has consequences for radio polarization structure, and for polar cap areas and dipole offsets inferred from soft X-ray emission from polar caps [13], thought to be heated by magnetospheric particle bombardment [3, 53, 29]. These theoretical improvements of the polar cap model have yet to be noticed and incorporated in phenomenological models of the observations used by data analysts; such incorporation might yield interesting tests of the force-free model. • The force free model quantitatively specifies the return currents required to prevent the star from charging up, as the polar flow extracts charge from the star.

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Fig. 3 Plasmoids formed at the base of the current sheet of the relativistic aligned rotator, where the sheet crosses the light cylinder, from a relativistic MHD simulation of a newly born neutron star’s magnetosphere [15]. The dissipation that allows reconnection to occur is numerical. They move out radially at the local Alfven speed vA ≈ c, and recur on the magnetospheric Alfven transit time ∼ P/π

The results for the oblique rotator are partly in accord with long held expectations, that return current exists in a thin (“auroral”) sheet bounding the polar flux tube (e.g. [25, 40]), consistent with the open circuited model [25] - current closure occurs far away, in the nebula/interstellar medium beyond the wind termination shock or perhaps in the outer wind, plus qualitatively new features: a) part of the return current surrounding the polar flux tube is spatially distributed, even in the aligned rotator; b) in the oblique rotator, this part of the current system is not a return current at all, but couple the two polar regions together [9] - in the orthogonal rotator (i = 90◦ ), the auroral component of the current is entirely in the polar coupling flow, with the volume current out of each half of the polar cap having equal amount and opposite sign, also consistent with early expectations (e.g. Scharlemann et. al. [48]) - the orthogonal rotator automatically balances it’s charge loss. The radiative consequences of these features are as yet unexplored - for example, the spatially distributed part of he return current might be a good candidate for the site of “conal” component of pulsar radio emission,


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an idea which requires non-force modeling of the current flow and identification of a workable emission process within that current flow model2 before one can relate the theoretical force free current distributions to the observations in a testable manner (although easier kinematic comparisons are certainly possible). • The location of the return current layer having been determined, the hypothesis that the return current layer is the site of the beamed particle accelerator that gives rise to the pulsed gamma rays observed by the FERMI and earlier orbiting gamma ray telescopes (see [45] in these proceedings for a recent review) can now be investigated in the context of a self consistent magnetopspheric structure that allows a quantitative evaluation of the beaming characteristics implied by the radiating current sheet concept - see [9] for a kinematical study of the radiating current sheet idea. Making progress on a physical model for radiation from the current layers can most expeditiously take advantage of the facts that a) pulsed gamma ray emission, when observed, is the largest photon output from rotation powered pulsars, but b) generally has less luminosity than the spin-down luminosity of these stars. Figure 4 illustrates this fact, which summarizes the results from the LAT instrument as of Spring 2010: Thus the energy invested in particle acceleration is a small fraction of the enegy stored in Poynting fluxes, for radiation reaction limited acceleration, so that the force free model can be considered as a good zeroth order magnetospheric description. √ ˙ The voltage limitation prediction Lgamma ∝ Φmag ∝ E is the same as Lgamma ∝ “particle current” = particle flux = Goldreich-Julian flux in unidirectional beam models of the polar electric current flow [28] only if the accelerator carries a fixed fraction of the total electric current that enters into the spin-down torque, indepen˙ In the traditional slot or outer gap models, pair creation establishes the dent of P, P. limitation of the accelerator to a thin sheet either in the outer magnetosphere [17] or back in the polar cap [4] - in such models, the gap width w∗ of a model which successfully reproduces the sharply peaked light curves, projected onto the neutron star following the field the poloidal field lines, is necessarily small compared to the polar cap size, and varies with the pulsars’ magnetic moment and spin parameters. This is not an issue for a model based on the currents flowing in the return current layer, which necessarily carries the whole magnetospheric return current and include a substantial fraction in a thin current sheet, for most obliquities of the magnetic moment with respect to the rotation axis. That magnetospheric current sheets, with particle densities within the sheets high compared to the Goldreich-Julian value, can sustain large parallel electric fields is well known in planetary magnetopsheres - such sheets are the accelerator sites of the particle beams that stimulate the aurora observed in the upper atmospheres of the Earth, Jupiter and Saturn, for example3 An elementary illustration of this possibility 2

Some earlier ideas on this subject relating to field aligned acceleration and gamma ray emission can be found in [5, 27], for example. 3 For a review of such phenomena, see [42]. Of particular significance to pulsars is the fact that the field aligned currents that power narrow auroral arcs consist of precipitating electron

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Laccel/Lspindown 0). The return current in the current sheet consists of a precipitating electron beam, launched from the diffusion region around the Y-line and possibly augmented by high altitude pair creation within the current sheet, with the charges in the precipitating beam extracted by reconnection flow from the pair plasma flowing from the polar cap into the wind, plus a counterstreaming ion beam extracted electrostatically from the stellar atmosphere. In obtuse geometry (ion polar current, Ω · µ < 0), positrons precipitate from the Y-line and counterstreaming electrons are extracted from the atmosphere. For clarity, the part of the return current not contained in the current sheet is omitted, even though this part of the current system is of increasing significance as i → 90◦ . Lower Panel, right: Possible structure of the Y-line region, with the termination of the closed zone to the left and the merger of the winds from the opposite polar caps to the right. The “guide field” Bφ also reverses across the mid-plane of the flow, along with the poloidal open field. As reconnection occurs, some of the ouflowing plasma (speed cβ, β ≈ 1) deflects toward the singular, unmagnetized “diffusion” region around the Y-line with speed vrec ∼ 0.1vAlfven = 0.1c. The figure represents a steady (in the co-rotating frame) flow model - in reality, the reconnection is likely to be bursty, as in Figure 3, with formation of sporadic X-lines.

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unstable. Since ω p,beam can be comparable to the relativistic cyclotron frequency in the outer magnetosphere, the growing waves can excite finite Larmor gyration of the particles in the current channel, thus producing incoherent emission through hard X-rays - gamma rays are possible, under some circumstances. These X-rays are an alternative to soft photons from the star, as targets for γ − γ pair production. If the lower frequency waves can escape the plasma, they are a direct source of coherent emission, perhaps of interest to modeling giant radio pulses, which appear to come from the outer magnetosphere. A more detailed description of the model will appear elsewhere.

2 Follow the Mass Pulsar Wind Nebulae (PWNe) demonstrate that pulsars loss rest mass at a rate large compared to the fiducial electrodynamic particle loss rate cΦmag /e [for a review, see [24]]. The only known explanation is pair creation in the pulsars’ magnetospheres. In many nebulae, the X-ray emitting particles rapidly lose energy to synchrotron radiation. Then the nebulae are particle and energy calorimeters, allowing direct inference of the pair multiplicity in the wind, of TeV to PeV pairs. The measured injection rates, up to ∼ 1038.5 pairs/s, compare well to the predictions of existing pair creation models [e.g. [31]], yielding multiplicities up to ∼ 104 . However, PWNe are also radio synchrotron emitters, radiation that samples much lower energy populations (100 MeV to 10 GeV), whose radiative efficiency is much less than their X-ray emitting cousins. The result is a much larger population of pairs, whose radiative lifetime exceeds that of the nebulae. The most efficient hypothesis is that these particles come from the embedded pulsars also, an idea supported by spectral continuity and by exotica, such as the observation of radio “wisps” near the Crab pulsars [11]. Applying simple evolutionary models allows one to infer time averaged injection rates. Recent evaluations by [16] and [49] yield lower limits for multiplicities κ± all in excess of 105 and upper limits for wind 4-velocities ˙ 2 = eΦmag /2κ± m± c2 all less than 105 in a number of nebulae. The Γwind = E˙ R / Mc data are the best for the younger systems, although even for these, the lack of far infrared data inhibits the analysis.

PWN Name Φmag (PV) Age (yr) κ¯ ± Crab 100 955 106 3C58 15 2100 104.7 B1509 120 1570 105.3 Kes 75 22 650 105 W44 1 20.3 × 103 105 K2/3 Kookaburra 5.5 13 × 103 105 HESS J1640-465 3.5 104 106

Γwind 5 × 104 3 × 104 1 × 104 7 × 104 104 104 103.6


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The inferred multiplicity excesses are a puzzle for pair creation theory, perhaps resolvable by appealing to magnetic anomalies near the neutron stars’ surfaces, the simplest being an offset of the dipole center from the stellar center, which strengthens the magnetic field at one pole [e.g., [7]]. The increase this gives to the magnetic opacity can be greatly enhanced if the magnetic axis is also tipped with respect to the radial direction, since then gravitational bending of photon orbits with respect to the B field direction much increases the magnetic opacity for pair creation. Such phenomenological modifications of the low altitude magnetic field must respect the observation that radio beaming morphology is consistent with the magnetic field being that of a star centered dipole quite close to the star [44, 36]. This problem warrants quantitative investigation. The large inferred multiplicities imply the wind 4-velocities (Γwind to be small compared to the much quoted value of 106 inferred by [34] in their model of the Crab Nebula’s optical and harder emission. The large mass loading and the inferred low wind four velocity has a large impact on the much storied “σ problem” of pulsar winds. In ideal MHD, the ratio σ of magnetic energy to kinetic energy in the wind is conserved outside the fast magnetosonic radius (since for a cold flow the wind does not substantially accelerate outside this surface) and is large - even with the increased mass loading found from recent nebular studies, σ is always well in excess of several hundred. Nevertheless the wind behaves at its termination shock as if σ is small - MHD models of the nebulae suggest σ at th termination shock is on the order of 0.02 in the Crab Nebula [e.g [23]] and similar values are plausible in other systems. [21] suggested that because the wind of an oblique rotator has the magnetically striped structure shown in Figure 6, magnetic dissipation of the corrugated B field, generically of a resistive nature propelled by instabilities of the current flow in the current sheet separating the stripes4 might destroy the magnetic field of the wind interior to the termination shock, thus converting a high σ flow into an effectively unmagnetized plasma. If the current sheets separating the magnetic stripes are to merge with a speed v s < c as measured in the proper frame of the flow, before they reach the termination shock located at distance RT S from the neutron star, the merger 2 time in the PWN frame T merge = πΓwind (R L /v s ) must be less than the flow time to √ √ the termination shock RT S /c, therefore Γwind < (RT S /πR L)(v s /c) = (Crab) v s /c must be satisfied if Coroniti’s model is to be viable. This inequality is satisfied for multiplicities above 105 , which does appear to be the case for the young PWNe recently analyzed. Possible mechanisms that can lead to the necessary dissipation are drift-kink instability of the current sheet, considered as if it were a flat sheet [54] and an interesting Weibel-like instability due to interaction between the sheets [8]. Most interesting, the dissipation of the curent sheets in the inner wind, while responsible for only a small fraction of the magnetic destruction, may have sufficient luminosity to allow detection of VHE and UHE emission. A much more elaborate paper de4

This wrinkled current sheet, frozen into the wind, is the second current sheet of this paper’s title, but really it is the continuation of the sheet separating the closed and open zones interior to the light cylinder, as is apparent in Figure 5.

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scribing these results is in preparation.

a)

d)

c)

b)

e)

f)

Fig. 6 a) Magnetic Geometry of a Force-Free Rotator for r < 2RL , for i = 60◦ , from Spitkovsky (2006). The rapid transition to inclined split monopole field geometry for r > RL is apparent. b) Geometry of the current sheet from the split monopole model for i = 60◦ , r > RL . For clarity, only one of the two spirally wound current sheets is shown. As i → 90◦ , the sheets almost completely enclose the star; for r ≫ RL , the spirals are tightly wrapped (Br ≪ Bφ ) and the current sheet surfaces closely approximate nested spheres. c) One sheet for i = 30◦ , shown for clarity. d) Meridional cross section of the current sheet for i = 60◦ . e) Equatorial cross section snapshot of the current sheet, showing the two arm spiral form. The arrows show the local directions of the magnetic field; the dots and crosses show the direction of the current flow. Panels b)-e) were constructed using Bogovalov’s [14] analytic model of the asymptotic wind. f) Current sheet from a 2D PIC simulation of the inner wind, from unpublished work by Spitkovsky (used by permission),

Acknowledgements The work described here has been supported by NSF grant AST-0507813, NASA grants NNG06GJI08G and NNX09AU05G and DOE grant DE-FC02-06ER41453.


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The high-energy emission from the pulsar striped wind Jérôme Pétri

Abstract Since the launch of the Fermi satellite, the number of gamma-ray pulsars increased by almost one order of magnitude. These objects show pulsed emission up to tens of GeV and the associated light-curves have frequently a double-pulse structure. We study this pulsed emission by considering the striped wind model. By numerical integration of the time-dependent inverse Compton emissivity in the current sheets, we compute the phase-dependent spectral variability of this radiation. Several light curves and spectra are presented. Our model is able to explain some of the high-energy (10 MeV-10 GeV) spectral features of several gamma-ray pulsars, like Geminga and Vela.

1 Introduction The high-energy, pulsed emission from rotating magnetized neutron stars is usually explained in the framework of either the polar cap or the outer gap models. In both of these models, the radiation is produced within the light cylinder. An alternative site for the production of pulsed radiation has been investigated [6] based on the idea of a striped pulsar wind, originally introduced by [3] and [7]. In this picture emission originates outside the light cylinder and relativistic beaming effects are responsible for the phase coherence of the radiation. It has already been shown that this model can satisfactorily fit the optical polarization data from the Crab pulsar [8].

Observatoire Astronomique de Strasbourg, 11 rue de l’Université, 67000 Strasbourg, France, email: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_14, © Springer-Verlag Berlin Heidelberg 2011

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2 The striped wind model We use an explicit asymptotic solution for the large-scale field structure related to the oblique split monopole [2]. The model used to compute the high-energy pulse shape and the phase-resolved spectrum arising from this solution is presented in [9]. The current sheets sustaining the magnetic polarity reversal arising in this solution are responsible for the pulsed emission. Because of the ideal MHD assumption, this surface is frozen into the plasma and therefore moves radially outwards at a constant speed V. Strictly speaking, the current sheets are infinitely thin. However, as was already done in the study of the synchrotron polarization of the pulsed emission [8] we release this prescription. Our model involves some geometrical properties related to the magnetic field structure and some dynamical properties related to the emitting particles. Furthermore, in order to compute the light curves and the corresponding spectra, we need to know the emissivity of the wind due to inverse Compton scattering. The geometry is described by the angle of inclination of the magnetic moment with respect to the rotation axis, χ, and the inclination of the line of sight, ζ. Moreover, the wind is expanding radially outwards at a constant velocity V close to the speed of light denoted by c. The innermost regions of the pulsar magnetosphere is believed to be a site of high-energy pair production feeding the wind with ultra-relativistic pairs. For these emitting particles, we adopt an isotropic distribution function in momentum space in the comoving frame of the wind. It is given by a power law in energy, with a sharp low and high-energy cut-off, γmin and γmax respectively, such that the particle number density at time t and position r with energy between γ and γ + dγ is ne (γ, r, t) dγ = Ke (r, t) γ−p dγ

(1)

with γmin ≤ γ ≤ γmax and Ke (r, t) is related to the number density of emitting particles in the current sheet. Moreover, the radial motion of the wind at a fixed speed imposes an overall 1/r2 dependence on this quantity, due to conservation of particle number. However, adiabatic losses in the current sheets due to pressure work will cool down this distribution function in such a way that Ke decreases with an additional factor 1/r2/3(p+2), see [5]. Furthermore, we assume the emission commences when the wind crosses the surface defined by r = r0 ≫ rL . We assume an isotropic distribution of mono-energetic target photons ε with density nγ (ε) in the observer frame. The total emissivity is denoted by jobs . Knowing ic the inverse Compton emissivity, the light curves are obtained by integration over the whole wind region. This wind is assumed to extend from a radius r0 to an outer radius rs which can be interpreted as the location of the termination shock. Therefore, the inverse Compton radiation at a fixed observer time t is given by Z rsZ πZ Iicobs (t) = r0

0

0

2π

2 jobs ic (r, tret ) r sin θ dr dθ dϕ

(2)

The high-energy emission from the pulsar striped wind

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Fig. 1 Gamma-ray light curve above 100 MeV of Geminga, on the left and Vela, on the right, fitted with the inverse Compton emission from the striped wind.

The retarded time is expressed as tret = t − ||R0 − r||/c ≈ t − R0 /c + n· r/c. The approximation is valid if the observer, located at R0 , is very far away from the radiating system, R0 ≫ rs . Eq.(2) is integrated numerically for several frequencies from far below the low-energy cut-off to far above the high-energy cut-off. We are therefore able to predict the phase resolved spectral variability and the pulse shape simultaneously.

3 Application to γ-ray pulsars We apply the aforementioned model to inverse Compton scattering of either lowenergy photons from the cosmic microwave background or from the thermal stellar black body radiation. The former photon field is employed for Geminga whereas the latter for Vela. For the Geminga pulsar, in our best fit, we choose an inclination of the magnetic moment with respect to the rotation axis of χ = 60o . In order to obtain a phase separation of 0.5 between the two pulses, we have to adopt an inclination of the line of sight ζ = 90o . The Lorentz factor of the wind is Γ = 10. Results for the lightcurve above 100 MeV and the definition of the different phase intervals is shown in Fig. 2. The rising and falling shape of both pulses are well fitted by our model. The corresponding spectral variability is reproduced with satisfactory accuracy except for the OP phase for which the intensity is overestimated, see Fig. 2 [9]. For the Vela pulsar, in our best fit, we choose an inclination χ = 60o and ζ = 76o . The Lorentz factor of the wind is Γ = 16. Results for the light-curve above 100 MeV and the definition of the different phase intervals is shown in Fig. 2. The spectra within the two pulses, P1/2, IP1, LW2 and TW1 are well reproduced as well as the cut off energy around a few GeV, Fig. 2. The other phases still need some intensity level readjustment [10]. In the striped wind model, the pulsed high-energy emission from pulsars arises from regions well outside the light-cylinder. By computing the inverse Compton emission on the CMB or stellar thermal black body photons, we were able to fit the EGRET data of the light-curves and spectra for several gamma-ray pulsars such as

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Vela and Geminga. The new gamma-ray pulsar catalog from Fermi-LAT will help to constrain the physics of this wind [1].

References 1. Abdo, A. A, 2009, arXiv/astro-ph:0910.1608A 2. Bogovalov, S. V. 1999, A&A, 349, 1017 3. Coroniti, F. V. 1990, ApJ, 349, 538 4. Fierro, J. M., Michelson, P. F., Nolan, P. L., & Thompson, D. J. 1998, ApJ, 494, 734 5. Kirk, J. G. 1994, in Saas-Fee Advanced Course 24: Plasma Astrophysics, 225 6. Kirk, J. G., Skjæraasen, O., & Gallant, Y. A. 2002, A&A, 388, L29 7. Michel, F. C. 1994, ApJ, 431, 397 8. Pétri, J. & Kirk, J. G. 2005, ApJL, 627, L37 9. Pétri, J. 2009, A&A, 503, 13 10. Pétri, J. 2010, A&A, submitted

Gamma-rays from millisecond pulsars in Globular Clusters Włodek Bednarek

Abstract Globular clusters (GCs) with their ages of the order of several billion years contain many final products of evolution of stars such as: neutron stars, white dwarfs and probably also black holes. These compact objects can be at present responsible for the acceleration of particles to relativistic energies. Therefore, γ-ray emission is expected from GCs as a result of radiation processes occurring either in the inner magnetosperes of millisecond pulsars or in the vicinity of accreting neutron stars and white dwarfs or as a result of interaction of particles leaving the compact objects with the strong radiation field within the GC. Recently, GeV γ-ray emission has been detected from several GCs by the new satellite observatory Fermi. Also Cherenkov telescopes reported interesting upper limits at the TeV energies which start to constrain the content of GCs. We review the results of these γ-ray observations in the context of recent scenarios for their origin.

1 Introduction Globular Clusters are huge concentrations of old stars with masses of the order of the Solar mass or lower. These 105 − 106 stars are contained within a spherical volume of a few parsec. About ∼ 150 of the known clusters have been observed creating a spherical halo around the Galaxy. They are at typical distances of ∼ 10 kpc from the Sun (e.g. Harris 1996). GCs also contain remnants of evolution of stars with masses M∗ > 1M⊙ , which can be responsible for acceleration of particles to high energies. In fact, more than a hundred of millisecond pulsars (MSPs) have been discovered within globular clusters (e.g. Camilo & Rasio 2005) and large fraction of objects belonging to GCs are X-ray emitters. These sources are identified with the Cataclysmic Variables (accreting White Dwarfs) or Low Mass X-ray Binaries (LMXBs), i.e. accreting neutron stars in the binary systems. Due to the presence of these compact Department of Astrophysics, University of Łód´z, ul. Pomorska 149/153, 90-236 Łód´z, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_15, © Springer-Verlag Berlin Heidelberg 2011

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objects, GCs have been suspected to be sources of non-thermal processes which can turn to the production of high energy radiation. However, only recently GCs have been detected in high energy γ-rays (HE: E>100 MeV) by the Fermi-LAT telescope (Abdo et al. 2010a). In this paper we review the state of the knowledge on the observations and modelling of these oldest structures in the Galaxy.

2 The stellar content of Globular Clusters A large number of solar type stars in a small volume create a very well defined background radiation field (the mass to luminosity ratio in GCs is close to ∼ 2, e.g. van den Bosch et al. 2006). The observed luminosity of the globular clusters, LGC , and the density profile for the distribution of the stars inside it (Michie 1963a,b,c,d),   1, R < Rc    2 (R /R) , Rc < R < Rh D(R) =  c    (R R )2 /R4 , R < R < R , c h

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allows us to calculate the energy density of stellar photons inside the cluster (Bednarek & Sitarek 2007), q 2 − 3 6R3 R − 2R2 18R c t t c LGC U rad = , (2) q 2 cRt 6( 6Rt R3c − 2R2c

where Rc is the core radius, √ Rt is the tidal radius, and the half mass radius is related to those both by Rh = 2Rc Rt /3. For typical parameters, Rc = 0.5 pc, Rt = 50 pc, and LGC = 105 L⊙ = 3 × 1038 erg s−1 , we obtain Urad ≈ 300 eV cm−3 . The energy density of this stellar radiation field clearly dominates over the energy density of the Cosmic Microwave background Radiation (CMBR), UCMBR = 0.25 eV cm−3 . However, the photon number densities of the stellar and CMBR are comparable. The radiation field inside GC can be defined as a function of distance to its center by normalizing the density profile of the distribution of stars inside GC to the total number of stars contained in the GC such as N⋆tot = 105 M⊙ . The number of stars as a function of the distance is then N⋆ (R) = AD(R)dR (where A = N⋆tot /[2Rc − 2R2c /(3Rh ) − R2c R2h /(3R3t )] ≈ N⋆tot /(2Rc )). As a first approximation can be assumed that in average stars inside GC has parameters similar to the Sun, i.e. the surface temperature 6000 K and the radius 7 × 1010 cm. The density of stellar photons at a specific distance from the center of GC is calculated by integration over the whole distribution of stars inside the GC. These density profiles for stars and stellar radiation inside the GC are shown in Fig. 1. Thus, GCs belongs to the rare class of sources in which the soft radiation field within the cluster is very well defined. This is very important since it limits the number of free parameters when modelling high energy radiation in these objects.

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Fig. 1 The density of stars (a) and density of stellar photons (b) as a function of distance R from the center of a typical globular cluster with the mass 105 M⊙ , the core radius Rc = 0.5 pc, the half mass radius Rh = 4 pc, and the tidal radius Rt = 50 pc (from Bednarek & Sitarek 2007).

3 Compact objects within Globular Clusters Due to their ages, GCs contain large population of compact objects which are the final products of the evolution of stars with masses > 1M⊙ . The white dwarfs (Cataclysmic variables) and neutron stars (LMXBs and MSPs) has been detected in many globular clusters. In contrary to isolated compact objects in the Galaxy, the evolution of compact objects within the GCs is strongly influenced by their frequent encounters with normal stars. They turn to the formation of compact binary systems. Therefore, a number of the X-ray sources related to such binary systems has been observed (see below). Here we briefly discuss these compact binaries (or their remnants) within the GCs.

3.1 Millisecond pulsars About 140 millisecond pulsars (MSPs) have been discovered in radio observations in 26 GCs (for summary see Freire 2009). They are believed to be the result of spun-up to millisecond periods of old neutron stars which accumulate the angular momentum with the matter accreting from the companion star (Alpar et al. 1982). Some of these MSPs are isolated at present due to complete evaporation-destruction of the companion star. The largest population of MSPs has been detected in 47 Tuc (23 MSPs) and Ter 5 (33 MSPs). However, many more are expected based on simulations of their formation in stellar encounters which should occur very frequently in GCs. For instance Ter 5 may contain of the order of ∼ 200 MSPs (Fruchter & Goss 2000, Kong et al. 2010). In fact, there should exist a link between stellar encounter rate in GC and the number of MSPs and LMXBs (Pooley 2003, Abdo et al. 2010). The stellar encounter rate is estimated based in the known core stellar

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density and core radius for each particular GC (Verbunt & Hut 1987). In this way it is possible to predict the MSP population. It has been recently argued (Hui et al. 2010) that the population of MSPs in GCs have different X-ray emission properties from the MSPs in the Galactic field (note however Becker et al. 2010 for counter opinions). It is not clear whether proprieties of MSPs observed at other photon energies (e.g. in γ-rays) do not differ significantly as well.

3.2 Cataclysmic Variables and LMXBs First X-ray observations of GCs (Uhuru and OSO − 7 satellites) reported a relatively large number of luminous low mass X-ray binaries (LMXBs) per unit mass within GCs with respect to those observed in the Galactic field (Clark 1975, Katz 1975). The observed emission was variable with power as high as L x > 1035 erg s−1 . More sensitive instruments a population of low-luminosity X-ray sources with luminosities L x ∼ 1031 − 1033 erg s−1 within GCs has been reported by the more sensitive instruments such as Einstein and ROSAT (Hertz & Grindlay 1983, Verbunt 2001). However, only recently a firm identification has been possible thanks to deep observations with the Chandra telescope, which was able to resolve ∼1400 X-rays sources. Many of these sources have been identified with the LMXBs and Cataclysmic Variables. The number of LMXBs within specific GC shows clear correlation with the encounter rate (Pooley et al. 2003). Similar correlation has been also discovered between the number of Cataclysmic Variables within specific GC and the encounter rate (Pooley & Hut 2006). Recently, Pooley (2010) proposed that the correlation between the number of X-ray sources within specific GC and the encounter rate has different slope for the normal and core collapsed GCs. Such effect is consistent with predictions of simulations of different types of GCs (see Fregeau 2008). In conclusion, not only the amount of MSPs within the GCs are correlated with the encounter rates but also the amount of LMXBs and Cataclysmic Variables show such correlations.

3.3 Intermediate mass black holes ? It has been suspected on theoretical grounds that in the central regions of the core collapsed GCs intermediate mass black holes (IMBHs, WBH ∼ 103 M⊙ ) should exist. Observational arguments for the existence of a black hole with mass ∼ 3 × 103 M⊙ in M 15 has been reported by Gerssen et al. (2002). On the other hand, observations of radio emission from a supposed accreting IMBHs in Tuc 47 and NGC 6397 put upper limits on the black hole mass equal to a few hundred M⊙ (De Rijcke et al. 2006). Similar upper limits of same order of magnitude have been reported on the masses of IMBHs in Galactic GCs. Note that only recently, the evidence of the existence of the intermediate black hole (∼ 500M⊙) inside another galaxy has been reported by


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Farrell et al. (2009). IMBHs in GCs can not certainly be strong persistent emitters since such sources are not observed in the Galactic GCs. However, transient activity, e.g. as a result of capturing-disruption of a star from the globular cluster, may happen rarely and can not be excluded at present.

4 Non-thermal emission from Globular Clusters Here we review the results of observations of GCs which indicate the existence of relativistic particles. The presence of such particles is explicitly proved by detection of GeV γ-ray emission from GCs. The existence of relativistic electrons of diffusive nature within the globular cluster (or near the compact objects inside GCs) can be also envisaged through the detection of non-thermal lower energy radiation, e.g. in the form of diffusive radio or X-ray emission.

4.1 Low energy radiation First reports on the extended non-thermal X-ray emission appeared in the results from the Einstein and ROSAT observatories (e.g. Hartwick et al. 1982, Krockenberger & Grindlay 1995). This emission has been identified in many cases as a result of the acceleration of particles of heating of gas in the interaction of GCs with the gas in Galactic halo. More recently, extended X-ray emission has also been reported from the direction of 6 GCs using Chandra data (Okada et al. 2007). However, most of these X-ray sources appeared not to be related with the GCs but rather with the background clusters of galaxies. Other analyses of Chandra data such the one reported by Hui et al. (2009) show X-ray emission from 10 GCs and identifies most of this emission with compact sources. Recently, Eger et al. (2010) observes diffuse X-ray emission from Ter 5 well described by a hard power spectrum. We conclude that up to now there are not clear reports on the discovery of nonthermal diffusive X-ray emission from GCs. It looks that most of the reports can be interpreted as the X-ray emission from the compact sources within the GCs or the X-ray emission from the background clusters of galaxies.

4.2 Gamma-rays High energy γ-ray emission (HE: E>100 MeV, VHE: E>100 GeV) from a population of GCs has been discovered only recently. The prediction of very high energy γ-ray emission from GCs is on the level which gives a realistic chance for detection by the next generation of Cherenkov telescopes (HESS II, MAGIC II). The production of VHE γ-rays by leptons accelerated in the vicinity of MSPs seems to be

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quite certain. However, the level of this emission is difficult to estimate based on the present stage of knowledge since it depends on the number of MSPs and the diffusion of relativistic particles within the cluster. Its discovery may have to wait for the construction the next generation of instruments such as CTA. 4.2.1 GeV emission The first upper limits on the GeV γ-ray emission were derived based on the EGRET and COMPTEL observations on the board of Compton GRO (Michelson et al. 1994, Manandhar et al. 1996, O’Flaherty et al. 1995). First clear detections of two globular clusters, Tuc 47 and Ter 5, were claimed based on the data collected by the Fermi-LAT detector (Abdo et al. 2009a, Kong et al. 2010). The analysis of 13 GCs allowed to associate 8 γ-ray sources in the directions of known GCs (see Table I in Abdo et al. 2010a). The γ-ray spectra of these GCs are incredibly similar (see Fig. 2 in Abdo et al. 2010a). They are characterised by differential spectral index in the range 0.7 ÷ 1.4, showing the maximum of the emission at a few GeV and energy of the exponential cut-offs have been estimated in the range 1.0 ÷ 2.6 GeV. The γ-ray power of specific GCs can differ by an order of magnitude. It seems not to be directly related to the mass of the cluster. Moreover, γ-ray spectra from GCs have very similar features to the average spectrum of MSPs in the Galactic field (see Tables in Abdo et at 2009b). 4.2.2 TeV emission GCs became interesting targets also for the Cherenkov telescopes at TeV energies. First upper limits have been reported based on the observations of two GCs, M 13 and M 15, by the Whipple Collaboration (Hall et al. 2003, Le Bohec et al. 2003). Recently, new much more sensitive instruments have also reported upper limits from directions of some GCs. For example, the MAGIC Collaboration (Anderhub et al. 2009) observed M 13 for more than 20 hours and reported an upper limit at energies Eγ > 140 GeV, shown in Fig. 2. This limit already starts to constrain the population of the MSPs within this GC based on the model developed by Bednarek & Sitarek (2007). The HESS Collaboration (Aharonian et al. 2009) reported the upper limit for Tuc 47 at energies > 800 GeV which is on the level of predictions of the models by Bednarek & Sitarek (2007) and Venter et al. (2009), see Fig. (2). Also the VERITAS Collaboration (McCutcheon et al. 2009), observed 3 GCs, M 5, M 13 and M 15, reporting the upper limits above 600 GeV on the level of 0.6%, 2.2%, and 1.6% of the Crab Units, respectively. These last limits allow to constrain the population of MSPs within GCs on the level of 30-50, assuming that the energy conversion efficiency from the MSPs to relativistic electrons is equal to 1%. Such observations should be continued with the enlarged MAGIC and HESS telescope systems. They will be able to search for the γ-ray signal clearly in the sub-TeV energies.


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Fig. 2 Upper limits on the TeV γ-ray emission from two globular clusters: Tuc 47 (left figure, thick solid curve, from Aharonian et al. 2009, reproduced by permission of the A&A) and M 13 (right figure, arrows, from Anderhub et al. 2009, reproduced by permission of the AAS). The additional curves show the predictions of the models by Bednarek & Sitarek (2007) and Venter, de Jager & Clapson (2009).

5 Models for gamma-ray emission Due to general similarities between radiation processes occurring in the inner magnetospheres of the millisecond and classical pulsars, these first have been also suspected to be sources of pulsed γ-rays. However, the rotational energy loss rate of the MSPs is typically orders of magnitudes lower than classical pulsars. Therefore, only the closest MSPs might be potentially detected. In fact, already the EGRET detector was able to see a hint of a signal from one of such objects, PSR J0218+4232 (Kuiper et al. 2004). Recently, the Fermi-LAT team reported detection of γ-ray emission from several MSPs in the Galactic field (Abdo et al. 2009b). Thus, confirming general theoretical predictions concerning γ-ray emission from these sources (e.g. Bulik et al. (2000), Luo et al. 2000, Harding et al. 2005, Venter & de Jager 2005). Since globular clusters contain many MSPs, their cumulative γ-ray emission might be also above the sensitivity of γ-ray telescopes. A few estimates of the γ-ray fluxes from MSPs in globular clusters have appeared before launching the Fermi Observatory. Harding et al. (2005), based on the pair starved polar cap model, predicted the γ-ray fluxes from Tuc 47 near the upper limits from the EGRET. Venter & de Jager (2008), applying the modern version of the polar cap model (general relativistic effects included), also predicted γ-ray spectra clearly above the sensitivity of the Fermi-LAT telescope. A significant part of MSPs, detected in globular clusters, are within binary systems. MSP winds can interact with the winds of companion stars creating shocks which can accelerate electrons (e.g. Klu´zniak et al. 1988, Phinney et al. 1988, Arons & Tavani 1993). The X-rays from MSPs magnetospheres can illuminate the companion star heating it to significantly larger temperatures than expected from pure nuclear burning (e.g. Bednarek & Pabich 2010). Relativistic electrons interact with

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Table 1 The γ-ray luminosities from several globular clusters detected by the Fermi-LAT telescope. Also the expected number of millisecond pulsars estimated based on the observed γ-ray luminosity, efficiency of energy conversion from the pulsars to γ-rays and the average spin-down power of pulsars (from Abdo et al. 2010a, reproduced by permission of the AAS).

this enhanced stellar radiation producing γ-rays. Some of these MSPs can be completely surrounded by the stellar winds creating the so called ”hidden” MSPs (Tavani 1991). Such MSPs in compact binary systems can in principle also contribute to the γ-ray emission observed from the globular clusters. Another scenario for GeV γ-ray emission can be envisaged in the case of accreting, fast rotating neutron stars and possibly also white dwarfs (see recent model by Bednarek 2009). In the case of slowly rotating neutron stars, the matter from the companion star can penetrate deep into the inner NS magnetosphere. It is stopped at some distance from the NS surface as a result of the interaction with rotating magnetic field. A turbulent transition region is created. Electrons can be accelerated in such a turbulent region to E e > GeV energies. They interact with the thermal radiation from the NS surface (and/or the accretion disk) producing GeV γ-rays.

5.1 Interpretation of the observed GeV γ-ray emission General features of the γ-ray spectra observed by Fermi-LAT from GCs (spectral indices, cut-offs) are incredibly similar to the spectra detected by this same telescope from the population of MSPs observed in the galactic field and from the classical pulsars (Abdo et al. 2009b). Therefore, it seems obvious that the main contribution to the GC γ-ray emission is a cumulative emission from the inner magnetospheres of the whole population of MSPs. In fact, such general γ-ray emission from MSPs fits quite well to the earlier predictions made based on the polar cap model (Harding et al. 2005, Venter & de Jager 2008). However, there are at present some doubts concerning the validity of the polar cap model as a likely scenario for the γ-ray emission from the pulsar inner magnetospheres. Recent observations of the pulsed


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Fig. 3 From top to bottom: a) γ-ray (0.1-300 GeV, 40 bins), b) X-ray (0.55-4.5 keV, 22 bins) and c) radio (1336 MHz) pulse profiles of PSR J0613−0200. The error bars represent a 1 σ deviation. The background level is indicated by the dashed line. The analysis revealed that X1 and the radio structure are aligned and of similar widths, which suggests that part of the X-ray radiation (thermal component) and the radio emission are produced in the same region.

γ-ray spectrum from the Crab pulsar at energies above ∼ 10 GeV (Aliu et al. 2008, Abdo et al. 2010b) are clearly inconsistent with the γ-ray production region close to the stellar surface. Similar features of the γ-ray emission from the classical and the millisecond pulsars suggest that they are working under similar mechanism probably located farther from neutron star surface but closer to the light cylinder radius.

5.2 TeV γ-ray emission from MSP winds and shocks The possibility of the TeV γ-ray emission from GCs has been at first discussed by Bednarek & Sitarek (2007). Here we follow the general scenario for γ-ray production within GCs proposed in this paper. It is assumed that leptons are accelerated in the millisecond pulsar winds, shocks created by such winds (as a result of collisions with the stellar winds or between themselves), or they are injected from the inner pulsar magnetospheres. These energetic leptons diffuse through the volume of the GC interact at the same time with its soft radiation content, i.e with the optical photons from stellar population and the CMBR. We assume that the diffusion process of electrons is determined only by the magnetic field strength within GC. The simplest diffusion model is applied assuming Bohm diffusion coefficient, Ddif = RL c/3, where RL is the Larmor radius of leptons, and c is the velocity of light. Due to the lack of detailed knowledge on the spectral features of leptons injected by the MSPs, a few different models for electrons are considered with the limitations expected from the comparison with classical pulsar population.

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5.2.1 Relativistic leptons from MSPs The spectra of leptons injected from the MSPs into the surrounding is simply an enigma. Recent detections of GeV γ-ray emission from MSPs in the Galactic field allow to estimate the energy conversion efficiency from the rotating pulsar to the γ-rays. It is on the average of the order of ηγ ∼ 0.1 (see Abdo et al. 2009b). The observed γ-ray luminosities of GCs and ηγ (assuming that MSPs in GCs and Galactic field are similar) allows us to estimate the total energy loss rate of MSPs in obs specific GC on LMSP rot ≈ Lγ /ηγ . The relativistic leptons leaving the light cylinder radius take a part, ηe , of LMSP rot . This power can be also related to the magnetization parameter of the pulsar wind at the light cylinder radius of the pulsar, σLC . These coefficients have been estimated in the case of classical pulsars based on the various models, e.g. σLC ∼ 104 (Cheng et al. 1986), ηe ∼ ηγ ∼ 0.1 (Harding et al. 2002), or ηe ∼ 0.01 (Venter & de Jager 2008). Based on these values we can only say that the power in relativistic electrons leaving the light cylinder radius can be of the obs −4 obs order, Le ∼ LMSP rot /σMSP ≈ Lγ /(ηγ σMSP ) ∼ (10 ÷ 1) × Lγ . These leptons can be additionally re-accelerated in the pulsar wind zone and/or the pulsar wind shock. Therefore, the above estimate on the power of injected leptons should be considered as the lower limit. The power in relativistic leptons accelerated above the light cylinder radius could be in principle estimated based on the value of the magnetization parameter of the pulsar wind, which is the ratio of the energy density of the magnetic field to the energy density of leptons in the wind. Unfortunately, we can not estimate this value for the MSP population due to the lack of observational constraints. Therefore, we base on the analysis done for the classical pulsars keeping in mind that the processes in their magnetospheres seem to be identical to those in MSPs. From modelling of two well known pulsars and their nebulae, the magnetization parameter at the pulsar wind shock has been estimated to be σ 100 MeV) was obtained during the 2.5 yr period of observations (July 2007 - October 2009) which, combined with AGILE effective area, gives our observations a good photon harvest from this pulsar. Simultaneous radio observations of PSR 1622−4950 with the Parkes radiotelescope in Australia are ongoing since the epoch of AGILE’s launch. Strong timing noise was present and it was accounted for using the f itwaves technique developed in the framework of the TEMPO2 radio timing software (Hobbs et al. 2004, 2006). Using the radio ephemeris provided by the Parkes telescope, we performed the folding of the γ-ray lightcurve including the wave terms (Pellizzoni et al. 2009a). An optimized analysis followed, aimed at cross-checking and maximization of the significance of the detection, including an energy-dependent events extraction angle around source position based on the instrument point-spread-function (PSF). The chi-squared (χ2 )-test applied to the 10 bin lightcurve at E > 30 MeV gave a detection significance of σ = 4.8. The unbinned Zn2 -test gave a significance of σ = 5.0 with n = 2 harmonics. The difference between the radio and γ-ray ephemerides was ∆Pradio,γ = 10−9 s, at a level lower than the error in the parameter, showing perfect agreement among radio and γ-ray ephemerides as expected, further supporting our detection and AGILE timing calibration. We observed PSR 1622−4950 in three energy bands: 30–100 MeV, 100–500 MeV and above 500 MeV. We did not detect pulsed emission at a significance σ ≥ 2 for

AGILE observations of PSR B1509-58

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E > 500 MeV. The γ-ray lightcurves of PSR 1622−4950 for different energy bands are shown in Fig. 1. The AGILE E > 30 MeV lightcurve shows two peaks at phases φ1 = 0.39 ± 0.02 and φ2 = 0.94 ± 0.03 with respect to the single radio peak, here put at phase 0. The phases are calculated using a Gaussian fit to the peaks, yielding a FWHM of 0.29(6) for the first peak and of 0.13(7) for the second peak, where we quote in parentheses (here and throughout the paper) the 1σ error on the last digit. The first peak is coincident in phase with COMPTEL’s peak (Kuiper et al. 1999). In its highest energy band (10–30 MeV) COMPTEL showed the indication of a second peak (even though the modulation had low significance, 2.1σ). This second peak is coincident in phase with AGILE’s second peak (Fig. 1). AGILE thus confirms the previously marginal detection of a second peak. Based on our exposure we derived the γ-ray flux from the number of pulsed counts. The pulsed fluxes in the three AGILE energy bands were Fγ = 10(4) × 10−7 ph cm−2 s−1 in the 30–100 MeV band, Fγ = 2.1(5) × 10−7 ph cm−2 s−1 in the 100–500 MeV band and a 1σ upper limit Fγ < 8 × 10−8 ph cm−2 s−1 for E > 500 MeV. Fig. 2 shows the SED of PSR 1622−4950 based on AGILE’s and COMPTEL’s observed fluxes. COMPTEL observations suggested a spectral break between 10 and 30 MeV. AGILE pulsed flux at energies E > 30 MeV confirms the presence of a soft spectral break, but the detection of significant emission at E > 100 MeV hints to a cutoff at slightly higher energies. As shown in Fig. 2, we modeled the observed fluxes with a power-law plus cutoff fit using the Minuit minimization package (James et al. 1975): F(E) = k × E −α exp[−(E/Ec )β ], with three free parameters: the normalization k, the spectral index α, the cutoff energy Ec and allowing β to assume values of 1 and 2. No acceptable χ2 values were obtained for β = 2, while for an β = 1 we found χ2ν = 3.2 for ν = 2 degrees of freedom, corresponding to a null hypothesis probability of 0.05. The best values thus obtained for the parameters of the fit were: k = 1.0(2) × 10−4, α = 1.87(9), Ec = 81(20) MeV.

3 Discussion The bulk of the spin-powered pulsar flux is usually emitted in the MeV-GeV energy band with spectral breaks at ≤ 10 GeV (e.g. Abdo et al. 2010). PSR 1622−4950 has the softest spectrum observed among γ-ray pulsars, with a sub-GeV cutoff at E ≈ 80 MeV. When PSR 1622−4950 was detected in soft γ-rays but not significantly at E > 30 MeV, it was proposed that the mechanism responsible for this low-energy spectral break might be photon splitting (Harding et al. 1997). The photon splitting (Adler et al. 1970) is an exotic third-order quantum electro-dynamics process expected when the magnetic field approaches or exceeds the critical value defined as Bcr = m2e c3 /(e¯h) = 4.413 × 1013 G. In very high magnetic fields the formation of pair cascades can be altered by the process of photon splitting: γ → γγ.

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In the case of PSR 1622−4950 a polar cap model with photon splitting would be able to explain the soft γ-ray emission and the low energy spectral cutoff, now quantified by AGILE observations. Based on the observed cutoff, which is related to the photons’ saturation escape energy, we can derive constraints on the magnetic field strength at emission, in the framework of photon splitting: sat ǫesc ≃ 0.077(B′ sin θkB,0 )−6/5

B′

(1)

where ǫesc is the photon saturation escape energy, = B/Bcr and θkB,0 is the angle between the photon momentum and the magnetic field vectors at the surface and is here assumed to be very small: θkB,0 ≤ 0.57◦ (Harding et al. 1997). Using the observed cutoff (E = 80 MeV) we find that B′ ≥ 0.3, which implies an emission altitude ≤ 1.3R NS , which is the height where also pair production could ensue. This altitude of emission is in perfect agreement with the polar cap models (see Daugherty & Harding 1996). The scenario proposed by Harding et al. (1997) is strengthened by its prediction that PSR B0656+14 should have a cutoff with an intermediate value between PSR 1622−4950 and the other γ-ray pulsars. Additionally, PSR 1622−4950 (Kuiper et al. 1999, Crawford et al. 2001) and PSR B0656+14 (De Luca et al. 2005, Weltevrede et al. 2010) show evidence of an aligned geometry, which could imply polar cap emission. The polar cap model as an emission mechanism is debated. From the theoretical point of view, the angular momentum is not conserved in polar cap emission (Cohen & Treves 1972, Holloway 1977, Treves et al. 2010). And a preferential explanation of the observed γ-ray lightcurves with high altitude cascades comes from the recent results by Fermi (Abdo et al. 2010). In the case of PSR 1622−4950, the derived γ-ray luminosity from the flux at E > 1 MeV, considering a 1 sr beam sweep, is Lγ = 5.7+0.1 × 1035 erg/s. The convertion efficiency of the rotational energy loss −0.5 (E˙ ≈ 1.8 × 1037 erg s−1 , see §1) into γ-ray luminosity is 0.03. If the γ-ray luminosity cannot account for most of the rotational energy loss, then the angular momentum conservation objection becomes less cogent for this pulsar. Alternatively, an interpretation of PSR 1622−4950 emission can be sought in the frame of the three dimensional outer gap model (Zhang & Cheng 2000). According to their model, hard X-rays and low energy γ-rays are both produced by synchrotron self-Compton radiation of secondary e+ e− pairs of the outer gap. Therefore, as observed, the phase offset of hard X-rays and low energy γ-rays with respect to the radio pulse is the same, with the possibility of a small lag due to the thickness of the emission region. According to their estimates a magnetic inclination angle α ≈ 60o and a viewing angle ζ ≈ 75o are required to reproduce the observed lightcurve. Finally, using the simulations of Watters et al. 2009), the observed lightcurve from AGILE is best reproduced if α ≈ 35◦ and ζ ≈ 90◦ , in the framework of the two pole caustic model (Zyks & Rudak 2003). The values of α and ζ required by the Zhang & Cheng model are not in good agreement with the corresponding values obtained with radio measurements. In fact, Crawford et al. (2001) observe that α must be < 60◦ at the 3σ level. The prediction obtained by the simulations of Watters et al. better agrees with the radio polarization

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observations. In fact, Crawford et al. also propose that, if the restriction is imposed that ζ > 70◦ (Melatos 1997), then α > 30◦ at the 3σ level. For these values, however, the Melatos model for the spin down of an oblique rotator predicts a braking index n > 2.86, slightly inconsistent with the observed value (n = 2.839(3)). Therefore, at present the geometry privileged by the state of the art measurements is best compatible with polar cap models. Acknowledgements M.P. thanks A. Treves for useful discussion and comments. AGILE is funded by the Italian Space Agency (ASI), with programmatic participation by the Italian Institutes of Astrophysics (INAF) and Nuclear Physics (INFN). The Parkes radiotelescope is funded by the Commonwealth Government as part of the ATNF, managed by CSIRO.

Fig. 1 Phase-aligned γ-ray light-curves of PSR 1622−4950 with radio peak at phase 0. From the top: AGILE > 100 MeV, 20 bins, 7.5 ms resolution; AGILE < 100 MeV, 10 bins, 15 ms resolution; COMPTEL 10–30 MeV and COMPTEL 0.75–30 MeV (from Kuiper et al. (1999).

References 22. Abdo, A. A. et al. 2010, ApJS, 187, 460 22. Adler, S. L., et al. 1970, PhRevL, 25, 1061 22. Cohen, R. H. & Treves, A. 1972, A&A, 20, 305

Fig. 2 SED of PSR 1622−4950 (solid line) obtained from a fit of pulsed fluxes from soft to hard γ-rays. The circular points represent COMPTEL observations. The square points represent AGILE pulsed flux at 30 < E < 100 MeV and 100 < E < 500 MeV. The horizontal bar represents AGILE upper limit above 500 MeV.

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22. Crawford, F., Manchester, R. N., & Kaspi, V. M. 2001, AJ, 122, 2001 22. Daugherty, J. K. & Harding, A. K. 1996, ApJ, 458, 278 22. De Luca, A., Caraveo, P. A., Mereghetti, S., Negroni, M., & Bignami, G. F. 2005, ApJ, 623, 1051 22. Dyks, J. & Rudak, B. 2003, ApJ, 598, 1201 22. Harding, A. K., Baring, M. G., & Gonthier, P. L. 1997, ApJ, 476, 246 22. Hobbs, G., Lyne, A. G., Kramer, M., Martin, C. E., & Jordan, C. 2004, MNRAS, 353, 1311 22. Hobbs, G. B., Edwards, R. T., & Manchester, R. N. 2006, MNRAS, 369, 655 22. Holloway, N. J. 1977, MNRAS, 181, 9P 22. James, F. & Roos, M. 1975, Computer Physics Communications, 10, 343 22. Kuiper, et al. 1999, A&A, 351, 119 22. Manchester, R. N., Tuohy, I. R., & Damico, N. 1982, ApJL, 262, L31 22. Melatos, A. 1997, MNRAS, 288, 1049 22. Pellizzoni et al. 2009a, ApJ, 691, 1618 22. Pellizzoni, A. et al. 2009b, ApJL, 695, L115 22. Tavani, M. et al. 2009, A&A, 502, 995 22. Treves, A., Pilia, M. & Lopez, M. 2010, A&A, submitted 22. Watters, K. P., Romani, R. W., Weltevrede, P., & Johnston, S. 2009, ApJ, 695, 1289 22. Weltevrede, P. et al. 2010, ApJ, 708, 1426 22. Zhang, L. & Cheng, K. S. 2000, A&A, 363, 575

Understanding the fundamental parameters of millisecond pulsars Benoit Pancrazi

Abstract How the high energy emission from millisecond pulsars (MSPs) is generated is currently unclear. It has been proposed that the acceleration of charged particles and the radiation of high energy photons can occur in the neutron star vicinity (polar cap model), along the last open field line (slot gap model) and/or further into the magnetosphere, in a region close to the light cylinder (outer gap model). Different signatures are expected for these models that can be identified through spectral and timing analysis. For this purpose, we have explored the XMM-Newton datasets of five millisecond pulsars that have not previously been observed in X-rays. Thanks to the accurate timing analysis of this sample, we compare for the first time radio, X-ray and γ-ray absolute pulse profiles of these faint X-ray sources. This study combined with spectral analysis allows us to make constraints on the size and location of the emission regions in each energy domain. Furthermore, the orientation as well as the mass and radius of the neutron star can be estimated through modelling of the brightest MSP X-ray pulse profiles. We present the latest models that account for the thermal emission produced by a heated polar cap on the surface of a rapidly rotating neutron star, and show how we can use them to constrain the equation of state of the neutron star dense matter.

1 Introduction Millisecond pulsars (MSPs) are rapidly rotating neutron stars that are known to emit mainly in radio. However, observations in other energy domains carried out in recent decades show substantial evidence for an emission in X-rays and/or in γ-rays [11, 1]. How this high energy radiation is generated is still unclear. It is thought that the acceleration of charged particles (e± ) to extreme relativistic energies Benoit Pancrazi Centre d’Etude Spatiale des Rayonnements, CNRS/UPS, 9 avenue du Colonel Roche, 31028 Toulouse Cedex 04, France, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_19, © Springer-Verlag Berlin Heidelberg 2011

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could occur in regions of magnetospheric charge depletion (gaps), where a very high electric potential exists. Three main models based on different acceleration region geometries and locations have been proposed : the polar cap (PC), the slot gap (SG) and the outer gap (OG) models [7, 2, 5]. Whether one or a combination of these models can account for the high energy emission from MSPs is still an open question. Using absolute timing in the radio, X-rays and γ-rays, we can evaluate the width, shape and phase shift of the pulsed emission in each energy domain, and draw conclusions on the size and location of the emitting regions. Furthermore, the nature of the emission can be constrained using phase resolved spectroscopy. It has been shown that the X-ray emission coming from rotation powered pulsars consists of thermal and non-thermal components [6]. Thermal radiation is expected to arise from heating of the PC by backflowing e± , as non-thermal emission could be due to synchrotron emission at high altitude. Furthermore, the low surface magnetic fields of MSPs imply that the accelerating field (Ek ) is unscreened over most if not all of the PC, and e± will consequently continue to accelerate and radiate to high altitudes. In this context, high-energy emission could also be produced by Inverse Compton Scattering (ICS) of thermal X-rays by primary e± , or by resonant cyclotron absorption of radio photons at high altitude followed by spontaneous synchrotron radiation [8]. ICS pair fronts have also been shown to be very important for heating the PC and producing detectable thermal X-rays [7]. Moreover, pulsar-driven synchrotron nebulae or the interaction of pulsar winds with a close companion star can play a significant role in the X-ray emission coming from MSPs. So far, ten detections of MSPs in X-rays associated with spectra and timing solutions have been reported [11]. The enlargement of this sample is of crucial importance if we want to discriminate between the competing high energy models. Thus the present study is a significant step forward. Taking advantage of the large collecting area and high timing accuracy of XMM-Newton, it is becoming possible to perform reliable spectral and timing analysis of faint MSPs in X-rays. Recently, Fermi Large Area Telescope (LAT) observations revealed a pulsed emission in γ-rays coming from MSPs [1]. It has been shown that γ-ray MSPs are divided into two sub-classes, either described by pair-starved PC (PSPC) or by SG/OG models [10]. In this study, an empirical model which assumes that the radio emission consists of a core beam centred on the magnetic axis, and one or more surrounding hollow cone beams was also developed. These hypotheses combined with absolute timing analysis will allow us to improve our knowledge of MSPs. Finally, important information can be obtained through modelling of the X-ray pulse profile, when the emission is dominated by thermal radiation [3]. The model considers a relativistic rotating neutron star with two identical hot spots located at the magnetic poles, and accounts for gravitational light bending, aberration, Doppler boosting and propagation time delays in a nonrotating Schwarzschild metric. Radiative transfer processes are also included in the context of an unmagnetized (B < 109 G), optically thick H atmosphere. By fitting parameters such as viewing angle or magnetic inclination, it is possible to constrain the mass to radius ratio of the brightest MSPs, and therefore the equation of state of neutron star matter.

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2 Observations and data analysis PSR J0613−0200, PSR J1911−1114, PSR J2129−5721, PSR J1600−3053 and PSR J1853+1303 were observed in X-rays with XMM-Newton. We processed the data and extracted the events using standard techniques (see [9]). We used the task barycen and the coordinates given by radio observations to convert times of arrival (TOAs) measured in the local satellite frame to Barycentric Dynamical Time (TDB). The γ-ray data were taken during the first year survey of the Fermi LAT. To derive γ-ray pulse profiles, we selected events above 100 MeV within a region of interest (ROI) of 1◦ or 0.5◦ , depending on the Galactic latitude of the MSP, using the task gtselect of the Fermi Science Tools1 . TOAs were converted to TDB with gtbary. For both X-ray and γ-ray timing analysis, the TEMPO22 package was used to convert barycentred TOAs into phase values with the ephemerides provided by the the Nançay or Parkes radio telescopes. We compare the phase alignment of the absolute pulse profiles by fitting the main fluctuations using the software QDP/PLT3 . The extraction of γ-ray spectra was done by considering ROI of angular width 10◦ , and modelling the nearby strong pointlike sources as well as the diffuse Galactic plus extra-Galactic γ-ray emission using gtlike. We fitted the spectrum of the MSP with an exponential cutoff power law of the form N0 (E/100 MeV)−Γ e−E/Ec where N0 is the normalisation factor and E c , the cutoff energy.

3 Discussion and conclusion The X-ray timing analysis of PSR J0613−0200 (Figure 1) reveals a main peak (X1 ) aligned and of similar width to the radio peak which is expected to be produced in a region close to the PC, as stated above. X1 is therefore consistent with thermal emission coming from the PC of the pulsar. Interestingly, the similar widths of X1 and the radio peak suggest that the extensions of the emitting regions are of comparable size. This conclusion is strengthened by the spectral analysis which revealed that it was possible to fit the soft X-ray spectrum with a thermal component, when using the γ-ray fitting parameters to constrain the non-thermal X-ray radiation. Furthermore, it has been shown that the best model fits to the γ-ray lightcurve are likely to be given by magnetospheric models (SG/OG) [10], which is consistent with a phase shift between the main γ-ray and the radio peaks. For both PSR J1911−1114 and PSR J2129−5721, the X-ray pulse profiles show two main fluctuations, one that is aligned and of similar width to the radio peak, and a second one that could result from the emission coming from the antipodal heated PC of the pulsar. As for PSR J0613−0200, the X-ray spectral analysis revealed possible further support for thermal emission coming from the PC. 1 2 3

http://fermi.gsfc.nasa.gov/ssc/data/analysis/ http://www.atnf.csiro.au/research/pulsar/tempo2 http://heasarc.gsfc.nasa.gov/docs/software/ftools/others/qdp/qdp.html

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Fig. 1 From top to bottom: a) γ-ray (0.1-300 GeV, 40 bins), b) X-ray (0.55-4.5 keV, 22 bins) and c) radio (1336 MHz) pulse profiles of PSR J0613−0200. The error bars represent a 1 σ deviation. The background level is indicated by the dashed line. The analysis revealed that X1 and the radio structure are aligned and of similar widths, which suggests that part of the X-ray radiation (thermal component) and the radio emission are produced in the same region.

Evidence for pulsations in the X-ray emission coming from PSR J1600−3053 and PSR J1853+1303 were found, although these MSPs appear to be very faint Xray sources. Amongst our sample, PSR J1600−3053 is the only one for which radio and X-ray pulse profiles show a shift in phase. The current models accounting for thermal emission in X-rays [3] are limited by the spin period P of the considered neutron star, as the effect of rotation-induced oblateness becomes important when P . 3 ms [4]. We have included this in a model based on [3], and used the constraints that can be made on the viewing geometry from the modelling of the γ-ray lightcurves. Thus, we will be able to make much tighter constraints on the neutron star equation of state for MSPs showing predominantly thermal X-ray spectra, and for which X-ray pulsations have been detected such as PSR J0437−4715 or PSR J2124−3358.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Abdo, A. A., et al. (Fermi LAT Collaboration) 2009, Science, 325, 848 Arons, J., Scharlemann, E. T. 1979, ApJ, 231, 854 Bogdanov, S., Rybicki, G. B., Grindlay, J. E. 2007, ApJ, 670, 668 Cadeau, C., et al. 2007, ApJ, 654, 458 Cheng, K. S., Ho, C., Ruderman, M. 1986, ApJ, 300, 500 Cheng, K. S., Zhang, L. 1998, ApJ, 515, 337 Harding, A. K., Muslimov, A. G. 2002, ApJ, 568, 862 Harding, A. K., Usov, V. V., Muslimov, A. G. 2005, ApJ, 622, 531 Pancrazi, B., et al. in prep. Venter, C., Harding, A. K., Guillemot, L. 2009, arXiv, 0911.0872 Webb, N. A., et al. 2004, A&A, 419, 269

Pulsars as gravitational wave detectors George Hobbs

Abstract Pulsar timing array projects are carrying out high precision observations of millisecond pulsars with the aim of detecting ultra-low frequency (∼ 10−9 to 10−8 Hz) gravitational waves. We show how unambiguous detections of such waves can be obtained by identifying a signal that is correlated between the timing of different pulsars. Here we describe the ongoing observing projects, the expected sources of gravitational waves, the processing of the data and the implications of current results.

1 Introduction The first strong evidence for the existence of gravitational waves (GWs) was obtained by measuring the orbital period decay in the PSR B1913+16 binary pulsar system [25, 59, 62]. Various ground- and space-based detectors have been developed with the aim of making a direct detection of GW signals. Unfortunately, to date, no such detection has been made. Millisecond pulsars are amazingly stable rotators. In many cases a simple model for the pulsar spin-down can be used to predict pulse times-of-arrival (TOAs) with an accuracy and precision of < 1µs over many years of observation. The pulsar timing technique relies on this stability to obtain precise measurements of a pulsar’s spin, astrometric and orbital parameters. However, in some cases the pulse TOAs are not exactly as predicted, suggesting that the model and analysis procedure do not parameterise all of the physical effects that are affecting the pulse emission, propagation and detection. As the effects of GWs are not included in the analysis, the existence of any such waves will induce deviations between the actual and predicted TOAs (commonly known as the ‘timing residuals’). Here we describe how these George Hobbs CSIRO Australia Telescope National Facility, PO Box 76 Epping NSW 1710, Australia, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_20, © Springer-Verlag Berlin Heidelberg 2011

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signals may be unambiguously confirmed as being caused by GWs and provide upper bounds on their amplitude. In §2 we provide a basic explanation of how pulsar data sets may be used in the search for GWs, §3 describes current data sets and highlights some aspects of the data that need careful consideration when the data are processed, §4 lists potential sources of GWs, §5 describes how data sets may be accessed and §6 highlights future possibilities.

2 Using pulsars to search for GWs Pulsar observations lead to measurements of TOAs at an observatory. The tempo2 software package [10, 23] can be used to convert these TOAs to a time of emission by 1) transforming the TOAs to the Solar System barycentre, 2) determining excess propagation delays caused by the interstellar medium and, for binary systems, 3) transforming to the pulsar frame. The derived time of emission can then be compared with a pulsar model to form the timing residuals. The induced pulsar timing residuals caused by a GW signal were first calculated at the end of the 1970s [9, 52]. This early work showed that a GW signal causes a fluctuation in the observed pulse frequency, δν/ν, which induces pulsar timing residuals at time t from the initial observation as Z t δν(t) R(t) = − dt. (1) ν 0 The Dopper shift can be shown to have the form (e.g. [17]) δν p = H i j (heij − hi j ) ν

(2) p

where heij is the GW strain at the Earth at the time of observation, hi j the strain at the pulsar when the electromagnetic pulse was emitted and H i j is a geometrical term that depends upon the angle between the Earth, pulsar and GW source. The GW strains evaluated at the positions of multiple pulsars will be uncorrelated, whereas the component at the Earth will lead to a correlated signal in the timing residuals of all pulsars. Hobbs et al. (2009 [21]) demonstrated how pulsar TOAs affected by GWs can be simulated using the tempo2 software package. Since the intrinsic pulsar pulse period, spin-down, orbital motion and various astrometric parameters are a priori unknown, they need to be determined from the pulsar timing data. Initial estimates of the pulsar parameters are used to form pre-fit timing residuals. A least-squares fitting procedure is subsequently used to fit an analytical model to obtain improved pulsar parameters and “post-fit” timing residuals (see [23]). In Figure 1 we plot preand post-fit timing residuals for a simulated pulsar in the presence of GWs from 1)

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Fig. 1 Simulations of pre-fit (left column) and post-fit (right column) timing residuals. The first row simulates a non-evolving, black-hole binary system defined by A+ = AX = 5 × 10−14 and ω = 1 × 10−7 . The second row contains a simulation of the predicted timing residuals from the evolving source 3C66B (see Section 4). The third row contains a GW burst with memory source leading to a change in rotational frequency ∆ν = 1 × 10−12 Hz and the bottom row is a realisation of a GW background defined by α = −2/3 and A = 10−14 .

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Fig. 2 The expected correlation in the timing residuals of pairs of pulsars as a function of angular separation for an isotropic GW background (solid line). The points correspond to simulated pulsar data sets in the presence of a GW background with power-law index α = +3/2 and amplitude A = 0.01; Figure from Hobbs et al. (2009, [21]).

a single, non evolving binary black-hole system, 2) an evolving binary black-hole system, 3) a burst GW source and 4) an isotropic stochastic background of GWs. It is not possible to determine the exact origin of the timing residuals for a single pulsar data set. Any observed residuals may have been caused by, for example, irregularities in terrestrial time standards [48], errors in the planetary ephemeris, irregular spin-down of the pulsar [19], calibration effects (e.g. [66]) or GWs. These effects can only be distinguished by searching for correlations in the timing residuals of multiple pulsars. For instance, residuals caused by the irregular spin-down of one pulsar will be uncorrelated with the residuals observed for a different pulsar. Irregularities in terrestrial time standards will lead to correlated residuals for all pulsars (this is only true for data sets which have the same data span; see Section 3). For an isotropic, stochastic GW background, the GW strain at each pulsar will be uncorrelated, but the GW strain at the Earth provides a common signal. The common signal for such a background was determined by Hellings & Downs (1983) and is reproduced in Figure 2. More recently it has been shown that approximately 20 pulsars are necessary, timed with an rms timing residual of ∼100 ns or better over five years with observations every week, in order to make a significant detection of a possible GW background signal [28]. Pulsar timing experiments are sensitive to GW signals in the ultra-low frequency band (f ∼ 10−9 to 10−8 Hz) as individual pulsars are typically only observed once every few weeks, have maximum data spans of years to decades and require the


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Fig. 3 Characteristic strain sensitivity for existing and proposed GW detectors as a function of GW frequency. Predicted signal levels from various astrophysical GW backgrounds are shown. The current limit is that published by Jenet et al. (2006). The ‘PPTA limit’ is a predicted limit if the PPTA project achieves its design sensitivity. The SKA limit is a prediction of the sensitivity of the planned Square Kilometre Array telescope.

fitting of a pulsar timing model. The pulsar timing method is therefore complementary to other GW detection methods such as the Laser Interferometer Space Antenna (LISA)1 and ground based interferometer systems (such as the Laser Interferometer Gravitational Wave Observatory, LIGO2 ), which are sensitive to high frequency GWs. In Figure 3 we plot the sensitivity of the pulsar timing experiments, LISA and LIGO as well as some expected GW sources.3 Pulsar timing projects that aim to obtain data sets on the most stable millisecond pulsars with the aim of searching for correlated timing residuals are known as pulsar ‘timing arrays’. The first attempts to undertake such projects are described by Romani (1989) and Foster & Backer (1990).

1

http://lisa.nasa.gov http://www.ligo.caltech.edu/advLIGO/ 3 Various authors e.g. [35, 44] have indicated that it may be possible to limit the existence of GWs with even lower frequencies (10−12 to 10−8 Hz) where the minimum sensitive GW frequency is determined by the distance to the pulsar. However, the methods required to achieve this sensitivity are different to those described in this paper. We also note that a few other methods exist that can limit the ultra-low frequency GW background. One example is reported by Gwinn et al. (1997) who obtained an upper bound on the background amplitude by analysing limits on proper motions of quasars. 2

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3 Current data sets The International Pulsar Timing Array (IPTA) project has the main aim of detecting GW signals using pulsar observations and is a collaboration between three separate projects. The European project (EPTA [13]) currently obtains data using the Effelsberg, Jodrell Bank, Nançay and Westerbork telescopes (a new telescope in Sardinia is currently under construction and, when commissioned, will be used as part of the EPTA). The North American project (NANOGrav [27]) uses the Arecibo and Green Bank telescopes and the Parkes project (PPTA; e.g. [22, 39, 68]) uses the Parkes radio telescope in Australia. In total approximately 37 different pulsars are being observed by these projects4 (see [18]). Some of the most precise timing residuals have been obtained for the brightest millisecond pulsar, PSR J0437−4715. The rms timing residuals over ∼ 1 yr obtained with the Parkes telescope at an observing frequency close to 3 GHz is ∼60 ns and some individual TOA uncertainties are ∼30 ns. Achieving such low rms timing residuals relies on removing the effects of dispersion measure variations [74], precisely calibrating the data [67] and determining many post-Keplerian binary parameters [70]. However, over longer data spans clear irregularities are observed in the timing residuals (see Figure 4; R. Manchester, private communication). These residuals differ from those published by Verbiest et al. (2008) as 1) new data have been added between the years 2006 and 2010 and 2) the time offsets between different backend systems at the observatory have been measured and subsequently not included in the fitting procedures. The cause of the observed variations is not currently known. Pulsars exhibit two main types of timing irregularity: ‘glitches’ in which the pulsar’s rotation rate suddenly increases before undergoing a period of relaxation and ‘timing noise’ which consists of low-frequency features in the timing residuals. Hobbs et al. (2010) analysed a sample 366 pulsars and showed that the timing noise, in general, consisted of quasi-periodic oscillations with periodicities of years to decades. However, the “amount” of timing noise decreases with characteristic age and millisecond pulsars, which are used in timing array experiments, are typically extremely stable. In a few cases, timing noise and glitches are clearly seen in the residuals for millisecond pulsars. For instance, the timing residuals for PSR J1939+2134 have long been known (e.g. [33]) to be dominated by timing noise. The first glitch in a millisecond pulsar was found in PSR B1821−24 which is located in the globular cluster M28 [6]. The glitch was shown to follow the main characteristics of glitches seen in the slower pulsars. Verbiest et al. (2009) studied the timing stability for 20 millisecond pulsars included in the PPTA project, over time scales up to 10 yr. Apart from PSR J1939+2134 it was concluded that the timing of most of the other pulsars is stable enough for GW detection on decadal time scales. 4

The exact number of pulsars varies as new pulsars are discovered and added to the IPTA sample. Radio pulsar surveys are being carried out (Keith et al., submitted to MNRAS,[7]) and the Fermi gamma-ray spacecraft, has recently discovered numerous previously unidentified gammaray sources. Many of these have now been shown to be millisecond pulsars (P. Ray, these proceedings) some of which are likely soon to be included in the IPTA.


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Fig. 4 The timing residuals for PSR J0437−4715 over 14 years.

The basic method to detect a GW background signal in pulsar data is to search for correlated timing residuals between different pairs of pulsars. However, we note that these correlations only hold in the case where all pulsar data sets are processed using the same fitting procedure and have the same data span. In Figure 5 post-fit timing residuals are shown that include simulated clock irregularities. Even though the same signal has been added to each data set, the residuals are not highly correlated because of the differing data spans and the model fits that have been carried out. The following need to be taken into account when attempting to detect or limit GW signals in pulsar timing data: • Pulsar timing residuals are irregularly sampled, have large gaps and different pulsars have different sampling and data spans. • The uncertainty on each TOA for a given pulsar can vary by an order-ofmagnitude because of interstellar scintillation, different observing durations for different observations and when combining data sets obtained from different observatories. For an unknown reason it is often found that the TOA uncertainties are under- or over-estimated (by factors of ∼2). • Timing residuals are always related to a pulsar timing model for which various fits have been carried out to determine the pulsar’s spin, astrometric and orbital parameters. • Arbitrary offsets can exist between TOAs measured with different instruments or at different observatories. • The timing residuals may be affected by timing noise or glitch events.

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Fig. 5 Post-fit timing residuals for three simulated pulsars. Each pulsar data set consists of white noise plus a clock irregularity that is the same for each pulsar. The post-fit residuals are not correlated because of model fitting and because each data set has a different data span.

4 Potential sources of gravitational waves Theoretical models predict that pulsar timing experiments are sensitive to individual, periodic sources of GWs, burst sources and a background of GWs. This section describes the various possible sources that have been discussed in the literature.

4.1 Single sources GWs are generated by the acceleration of massive objects. For a two-body orbital system the GW frequency is twice the orbital frequency implying that supermassive binary black-hole systems can produce GW signals that are strong enough, and are in the correct frequency regime, to be detectable by pulsar timing experiments. An estimate of the timing residual for a massive black-hole binary system can be obtained from [27]:


t ∼ 10ns

1Gpc d

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!

M 109 M⊙

!5/3

10−7 Hz f

!1/3

(3)

where d is the distance to the black-hole binary which has a total mass of M/(1 + z) and emits GWs at frequency f . Sesana, Vecchio & Volonteri (2009) showed that it is likely that the maximum timing residuals induced by such a system will be in the ∼ 5 − 50 ns range. Any such source is likely to be from a massive system (with a chirp mass Mc > 5×108 M⊙ ) and at a redshift between 0.2 < z < 1.5. More recently Sesana & Vecchio (2010) showed for a “fiducial” timing array project containing 100 pulsars uniformly distributed in the sky that, if a source is detected with a signal to noise ratio of 10, the source position could be determined to within ∼ 40 deg2 with a fractional error on the signal amplitude around 30% and the source inclination and polarisation angles could be recovered to within ∼ 0.3 rad. Unfortunately there has not yet been any clear detection of a supermassive binary black hole system where the black holes are close enough, and massive enough, for the system to be emitting detectable GW emission. Rodriguez et al. (2006) discovered a system in the radio galaxy 0402+379, which has a projected separation between the two black holes of just 7.3 pc. However, this is still too wide to be emitting detectable GWs. Sudou et al. (2003) reported the possible detection of a supermassive black hole binary in the radio galaxy 3C 66B and provided the orbital parameters for the postulated system. Jenet et al. (2004) showed that such a system should have produced detectable GW emission and managed to rule out its existence with high confidence. Lommen & Backer (2001) unsuccessfully searched for GW emission from Sagittarius A∗ which had also been suggested to be part of a binary system. Sillanpaa et al. (1996) have identified a candidate supermassive black hole binary system in the blazar OJ287 with member masses of 1.3 × 108 M⊙ and 1.8 × 1010 M⊙ . However, Yardley et al. (2010) showed that this system will require the sensitivity of future telescopes (such as the Square Kilometre Array, SKA) for detection. Searches for more supermassive binary black hole candidates are ongoing. Wen, Liu & Han (2009) selected 1209 pairs of galaxies from the Sloan Digital Sky Survey and searched for features indicative of merging events. More recently Burke-Spolaor (submitted to MNRAS) used archival VLBI data to search 3114 radio-luminous active galactic nuclear for binary supermassive black holes. Only one such source (the same as that previously discovered by Rodriguez et al. 2006) was detected. Wen et al. (submitted to ApJ) described the basic methods in which existing pulsar timing observations can be used to place constraints on the coalescence rate of binary supermassive black holes in the Universe. Yardley et al. (2010) determined the sensitivity of the Verbiest et al. (2008, 2009) data sets to individual GW sources and obtained a sky-averaged constraint on the merger rate of nearby (z < 0.6) blackhole binaries in the early phases of coalescence with a chirp mass of 1010 M⊙ of less than one merger every seven years. This work is summarised in Figure 6 which plots the current sensitivity to single sources and predicted future sensitivity (with the Square Kilometre Array, SKA, telescope).

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Fig. 6 Figure from Yardley et al. (2010) showing the sensitivity of current and future GW observatories to individual, periodic GW sources as a function of the GW frequency.

4.2 Burst sources Sources of detectable burst GW emission include 1) the formation of supermassive black holes which leads to a day-long burst of radiation [63], 2) highly eccentric supermassive black hole binaries [12], 3) close encounters of massive objects [34] and 4) cosmic string cusps [8]. Pshirkov & Tuntsov (2010) constrained the cosmological density of cosmic string loops using photometry and from pulsar timing showing that the pulsar timing data provides the most stringent constraints on the abundance of light strings. Seto (2009), Pollney & Reisswig (2010), van Haasteren & Levin (2010) and Pshirkov, Baskaran & Postnov (2010) all considered GW bursts “with memory”. In general such events consist of a rise in the GW field, followed by an oscillatory behaviour for a few cycles and finally convergence to a non-zero value. The permanent change is known as the burst’s “memory”. Such events can occur during close encounters of massive bodies on hyperbolic trajectories or in an asymmetric supernova. Pshirkov, Baskaran & Postnov (2010) showed that one such event could be detected from distances of up to 1 Gpc (for the case of equal mass supermassive binary black hole systems of M = 108 M⊙ ). A similar event can occur if the line of sight to a pulsar passes a cosmic string (Pshirkov & Tuntsov 2010). Such an event would instantaneously change the apparent frequency, ν, of the pulsar by a small amount ∆ν in the same way as that of a GW burst with memory although the


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Fig. 7 Upper bounds from Jenet et al. (2006) for stochastic backgrounds with various values of the GW spectral exponent α (solid line). The dotted lines indicate regions predicted by various GW background models. The dashed line indicates potential future limits from the PPTA project. The star symbol provides the upper bound given by Kaspi, Taylor & Ryba (1994). Figure from Jenet et al. (2006).

memory phenomenon would apply to all observed pulsars whereas this line-of-sight effect is specific to an individual pulsar. Amaro-Seoane et al. (2010) discussed the possibility that supermassive black holes do not coalesce before the merger with a third galaxy. This leads to orbits with high eccentricity leading to an intense burst of GWs. They showed that, for reasonable supermassive black-hole evolution models, a few bursts will induce timing residuals > 1 ns, however, if pulsar timing were sensitive at the nanosecond level, most of these bursts would be undetectable because of confusion with the GW background. A detection of a burst source using pulsar timing would provide the ability to localise the position of the source with the hope of identifying an electromagnetic counterpart. The angular resolution of a given timing array experiment depends upon the number of pulsars in the array, the timing precision and the distribution of the pulsars on the sky.

4.3 Stochastic background A stochastic background of GWs is expected from the early phases of coalescence for supermassive black holes [47, 26, 72, 11, 53], cosmic strings or relic GWs from the big bang [38]. In most models, the GW strain spectrum, hc ( f ), is represented by a power-law in the GW frequency, f ,

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hc ( f ) = A

f yr−1

!α

(4)

where the spectral exponent, α = −2/3, −1 and −7/6 for likely GW backgrounds caused by coalescing black hole binaries, cosmic strings and relic GWs respectively. The energy density of the background per unit logarithmic frequency interval can be written as 2 π2 2 ΩGW ( f ) = f hc ( f )2 (5) 3 H02 where H0 is the Hubble constant. Various predictions suggest that A ∼ 5 × 10−16 − −10−14 [72, 55]. Post-fit timing residuals over a time span ∼ 5 yr may reach ∼ 100 ns for such values of A implying that this such a background may be detectable with only small improvements in the data sets. It is therefore likely that such a background will be the first gravitational wave signal detected. Sesana, Vecchio & Colacino (2008) showed that the expected form of the stochastic background is not simply hc ∝ f −2/3 , but the frequency dependence becomes steeper above ∼ 10−8 Hz. They showed that the major contributors to the background come from massive > 108 M⊙ binary black hole systems that are relatively nearby (z < 2). In contrast to backgrounds formed from supermassive black-hole binary systems, Saito & Yokoyama (2009) showed that the formation of intermediate-mass (∼600 M⊙ ) black holes at the end of the inflationary era will lead to a potentially detectable background of GWs. Current pulsar upper bounds already limit the process for the formation of such black holes. Both “kinks” and “cusps” on cosmic string loops can also contribute to a background of GWs. Olmez, Mandic & Siemens (2010) showed that both phenomena contribute at the same order to the background. The most recent constraints, and their implications, on the cosmic string tension using pulsar timing experiments have been provided by Battye & Moss (2010). A background of GW radiation from the early universe is also expected, if detected, to provide a unique view of the physics of the very early universe (e.g. [15]). Boyle & Buonanno (2007) showed that combinations of cosmic microwave background experiments and GW detection experiments lead to strong constraints on the existence and properties of various energy components that may have dominated the universe at the end of the inflationary era. One of the first limits on a GW background was placed by Stinebring et al. (1990). Kaspi, Taylor & Ryba (1994) used observations of PSRs J1857+0943 and J1939+2134 from the Arecibo observatory to provide an upper bound on the GW background. Their data sets were made publically available allowing other algorithms to be applied to their data sets [40, 29]. Jenet et al. (2006) developed a method that took into account all the effects of fitting a pulsar timing model to data sets of different data spans and applied the technique to carefully selected PPTA data sets as the technique can only be applied to data sets that are statistically “white”. Van Haasteren et al. (2008) developed a Bayesian algorithm which has been applied to EPTA data sets [13]. Anholm et al. (2009) developed an independent method which currently does not address some issues relating to real pulsar data. Work is ongoing


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to develop a method that correctly detects the GW background or limits its amplitude and can easily be applied to the IPTA data sets. The most stringent limits published to date on the amplitude of a background caused by these various phenomena were obtained using observations from the PPTA project combined with archival data from the Arecibo telescope [29]. These upper bounds on A are shown in Figure 7. These results were shown to 1) constrain the merger rate of supermassive black hole binary systems at high redshift, 2) rule out some relationships between the black hole mass and the galactic halo mass, 3) constrain the rate of expansion in the inflationary era and 4) provide an upper bound on the dimensionless tension of a cosmic string background.

5 Accessing pulsar data sets The IPTA pulsar data sets contain some of the most precisely measured observations yet made of radio pulsars. These data sets can be used to search for GW sources and for numerous other purposes. Details of the only currently publically available data sets are provided in Kaspi, Taylor & Ryba (1994). Hobbs et al. (2009) provided a sample of simulated data sets for comparison of GW detection algorithms that are available for download. In the near future it is expected that all observations from Parkes Observatory (after an embargo period of 18 months) will be available for download providing access to most PPTA data. A few data sets relating to the PPTA project are also available as part of the PULSE@Parkes outreach project[20, 24]. The tempo2 package provides a few “plugin” packages and routines suitable for GW analysis: • GWsim.h: a library that implements the mathematics described by Hobbs et al. (2009). The routines in this library can be used to create new tempo2 plugins easily. • fake: plugin that simulates pulsar TOAs given a timing model. • GWsingle: plugin that simulates a single non-evolving GW source and produces a file of site-arrival-times that can be used for subsequent processing. • GWevolve: plugin that simulates a single evolving GW source. • GWbkgrd: plugin that simulates a background of GW sources. A new plugin is currently under development that will either provide limits on the amplitude of the GW background or give the significance of any detection by searching for correlations in the timing residuals of multiple pulsars.

6 The future It is likely that the signature of a GW background will be discovered in IPTA data sets shortly. However, any such initial “detection” will only have a low significance

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(e.g. σ ∼ 2 to 3). How this significance will increase with time will depend upon the intrinsic pulsar timing noise, the amplitude and spectral exponent of the background, whether new pulsars are discovered and whether observing systems are improved. A very high significance detection, enabling detailed studies of the astrophysical objects that form the background and the physics of the GWs themselves (e.g. [36]), will require large numbers of pulsars to be observed with high precision. Various new telescopes are being developed that should detect a large number of new pulsars or be able to observe pulsars with high precision (e.g. the Australian Square Kilometre Array Pathfinder [31, 32], MeerKAT [4] and FAST [41]). These telescopes are pathfinders to the Square Kilometre Array which should be fully operational by 2024. This telescope should revolutionise pulsar and GW astronomy by allowing almost all pulsars in our Galaxy to be detected and GW detection using pulsar observations should become commonplace.

7 Conclusion Pulsar timing experiments can detect gravitational wave signals. The most likely detectable source is an isotropic, stochastic background from a large number of coalescing supermassive binary black hole systems. It is possible that a detection of such a background could be made with existing data, but it will require a further 5-10 yr to have a definitive, highly significant detection. It is expected that GW astronomy using pulsars will become a standard astronomical tool during the Square Kilometre Array era when the background will be analysed in detail and individual binary black-hole systems and burst GW sources will be detectable. Acknowledgements This work is undertaken as part of the Parkes Pulsar Timing Array project, which is a collaboration between CSIRO Astronomy and Space Science, Swinburne University, the University of Texas, Brownsville and the University of California, San Diego. The Parkes radio telescope is part of the Australia Telescope, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. GH thanks D. Yardley, J. Verbiest, R. Manchester and A. Sesana for comments on early drafts of this text.

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Magnetar outbursts: an observational review Nanda Rea & Paolo Esposito

Abstract Transient outbursts from magnetars have shown to be a key property of their emission, and one of the main way to discover new sources of this class. From the discovery of the first transient event around 2003, we now count about a dozen of outbursts, which increased the number of these strongly magnetic neutron stars by a third in six years. Magnetars’ outbursts might involve their multi-band emission resulting in an increased activity from radio to hard X-ray, usually with a soft Xray flux increasing by a factor of 10–1000 with respect to the quiescent level. A connected X-ray spectral evolution is also often observed, with a spectral softening during the outburst decay. The flux decay times vary a lot from source to source, ranging from a few weeks to several years, as also the decay law which can be exponential-like, a power-law or even multiple power-laws can be required to model the flux decrease. We review here on the latest observational results on the multiband emission of magnetars, and summarize one by one all the transient events which could be studied to date from these sources.

1 Author’s preface The magnetar field have been recently boosted by the discovery of transients magnetars, and more in general by their possible role in GRB and gravitational wave researches. However, probably ”because” of the rapid development of the field , there is still a large confusion in the literature on when a source can be labelled as a magnetar candidate, and what exactly this word means: is the super-critical dipolar magNanda Rea Institut de Ciences de l’Espai (CSIC-IEEC), Campus UAB, Facultat de Ciencies, Torre C5-parell 2a planta, Bellaterra (Barcelona), Spain; e-mail: [email protected] Paolo Esposito Osservatorio Astronomico di Cagliari, Localitá Poggio dei Pini, strada 54, 09012, Capoterra, Italy; e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_21, © Springer-Verlag Berlin Heidelberg 2011

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netic field which defines a magnetar? Is the bursting behavior? Is the low rotational power with respect to their X-ray luminosity? Is the blackbody plus power-law Xray spectrum? Is the erratic radio pulsed behavior? When do we define a source an Anomalous X-ray Pulsar (AXP) or a Soft Gamma Repeater (SGR)? Apparently in the recent literature, even groups working in the magnetar field since decades are not fully in agreement with their exact definition (see the archetypical example of the AXP 1E 1547−5408= SGR 1550-5418= PSR J1550-5418 which has been discovered only 2 years ago and it already has three names, or PSR J1846−0258 which showed all the typical magnetar-like activity but it is still labelled as a rotational powered pulsar since as such it was first discovered). On the other hand, most of the questions above can be answered with a counter-example, it is then indeed becoming very difficult to give a definite and unique answer on when we can call a source an AXP, an SGR, or a magnetar in general. With this preface we aim at warning non-expert readers on the assumption and conceptual choices we will make in this review. In particular, this is a pure observational review, mainly foscussed on transients. We will then enter very little in the theoretical interpretations. We will not discuss about X-ray bursts or flares, but only the magnetar outbursts. Furthermore, a part from the historical section, we will consider hereafter AXPs and SGRs as the same class of sources, calling them ”magnetar candidates”. We apologize in advance if from time to time we drop the ”candidate” label in the text, but this is only due to the page limitation, while we do consider the magnetar as one of the most viable explanation to date, but possibly not the final solution, at least in its current form. We will include PSR 1622−4950 and PSR J1846−0258 in the magnetar list, given the discovery of their magnetarslike behavior, which clearly shows that (at least occasionally) they cannot be only rotational powered. This review is structured as follow: a brief historical overview followed by the description of the multi-band emission of magnetars (with detailed numbers reported in the two tables rather than in the text). Then, we report one by one on all magnetars’ outburst observed to date.

2 A bit of history Neutron stars (NSs) are the debris of the supernova explosion of massive stars, the existence of which was first theoretically predicted around 1930 [12, 1] and then observed for the first time more than 30 years later [55]. We now know many different flavours of these compact objects, and many open questions are still waiting for an answer after decades of studies. The NS world is mainly populated by the radio pulsars and the binary pulsars (thousands of objects), however in the last decades also extreme and puzzling small sub-classes of NSs were discovered: Anomalous X-ray Pulsars (AXPs), Soft Gamma Repeaters (SGRs), Rotating Radio Transients (RRATs), X-ray Dim Isolated Neutron Stars (XDINs), and Central Compact Objects (CCOs). The large amount of different acronyms might already show how diverse is

Magnetar outbursts: an observational review

249

Fig. 1 Diagram of the P– P˙ of all isolated pulsars known to date. Stars represents all sources which showed magnetar activity: in red all SGRs and AXPs, and in magenta PSR J1846−0258 and PSR 1622−4950.

the neutron star class, and on the other hand, how far we are from a unified scenario. In particular, despite being presumably governed by a single equation of state, the NS zoo manifest itself as a puzzling multicoloured class, whose bewildering variety of observational properties is still largely unexplained. These objects are amongst the most intriguing populations in modern high-energy astrophysics and in physics in general. In fact, besides being interesting themselves in terms of studying the NS equation of state and the physical processes and mechanisms involved in their emission, they are precious places to test gravitational and particle physics, relativistic plasma theories, as well as strange quark states of matter and physics of atoms and molecules embedded in extremely high magnetic fields (impossible to be reproduced on Earth). The focus of this review is the outburst emission of strongly magnetized NSs, having magnetic fields close or stronger than the electron critical magnetic field of Bcrit = m2e c3 /e¯h ∼ 4.4 × 1013 Gauss, at which the cyclotron energy of an electron reaches the electron rest mass energy.

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3 General observational characteristics Before presenting these ultra-magnetic objects, it is instructive to indicate how the magnetic field of isolated pulsars is estimated. Assuming that the spin-down torque is due to magnetic dipole radiation, the surface magnetic field can be estimated from ˙ for each pulsar: the measured pulsar spin period P and its derivative P, ˙ 1/2 Gauss Bsurface = (3 I c3 P˙ P/2π2 R6 )1/2 ∼ 3 × 1019(PP) (where P is in units of seconds, and I ∼ 1045 g cm2 and R6 cm are the assumed neutron star moment of inertia and radius). Presently there are almost 1800 spindown powered radio pulsars known, with periods from about 1.5 ms to 8 s [87], and on average they have magnetic fields of ∼ 1012 Gauss. However, beside the magnetar candidates which are the topic of this review, there are also a handful of radio pulsars and other newly discovered type of pulsars having super critical magnetic fields ( > Bcrit ): namely the high–B pulsars, a few XDINSs and RRATs. We will not report on those in this review, however we want to point out that they might represent somehow quiescent or evolved magnetars . The “magnetars” are a small group of X–ray pulsars (16 objects with spin periods between 2–12 s) the emission of which is very hardly explained by any of the common scenario for the radio pulsar or the X-ray binary pulsar populations [91]. In fact, the very strong X–ray emission of these objects is too high and variable to be fed by the rotational energy alone (as in the radio pulsars), and no evidence for a companion star has been found so far in favour of any accretion process (as in the X–ray binary systems). Moreover, roughly assuming them being magnetic dipole radiator, their inferred magnetic fields appear to be as high as B ∼ 1014 − 1015 Gauss, definitely larger than the quantum electron critical magnetic field limit Bcrit . On the other hand, the indication for possible proton resonant cyclotron lines in the X–ray emission of two of these objects, whether confirmed, supports this estimate [113, 60]. Because of these high B fields, magnetars emission is thought to be powered by the decay and the instability of these strong fields [39, 129] but despite valuable recent theories [128, 3] a complete physical interpretation of all different aspects of their emission is still missing. Very interestingly, the magnetars are also characterised by catastrophic and peculiar X-ray bursting, flaring and outbursting events where luminosities of the order of 1046 erg s−1 are reached. In Tab. 1-3 we list the magnetar’s main characteristics, and in the rest of this review we discuss one by one the multiband properties of these objects, finishing with reviewing their transient activity as known to date.

4 Multiband view of magnetars Until about 10 years ago, magnetars were thought to be emitting exclusively in the X-ray energy range, while having sporadic flares reaching the soft γ-ray energies. It was only recently that the availability of new instruments, as well as a progressively


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Table 1 Accurate positions and timing characteristics of magnetars. Magnetars

RA (J2000)

Dec (J2000)

P (s)

P˙ −12 (s/s)

B14 (G)

db (kpc)

1E 2259+586 4U 0142+614 1RXS J1708−4009 1E 1048.1−5937 1E 1841−045 CXOU J0100−7211 CXOU J1647−4552 XTE J1810−197 1E 1547−5408 SGR 1806−20 SGR 1900+14 SGR 0526−66 SGR 1627−41 SGR 0501+4516 SGR 0418+5729 SGR 1833−0832 PSR 1622−4950 PSR J1846−0258 AX J1844−0258a

23 01 08.29 01 46 22.44 17 08 46.87 10 50 07.14 18 41 19.34 01 00 43.14 16 47 10.2 18 09 51.08 15 50 54.11 18 08 39.33 19 07 14.33 05 26 00.89 16 35 51.84 05 01 6.78 04 18 33.86 18 33 44.38 16 22 44.8 18 46 24.94 18 44 54.68

+58 52 44.45 +61 45 03.3 -40 08 52.44 -59 53 21.4 -04 56 11.16 -72 11 33.8 -45 52 16.9 -19 43 51.74 -54 18 23.7 -20 24 39.94 +09 19 20.1 -66 04 36.3 -47 35 23.3 +45 16 34.0 +57 32 22.91 -08 31 07.71 -49 50 54.4 -02 58 30.1 -02 56 53.1

6.98 8.69 10.99 6.45 11.77 8.02 10.61 5.54 2.07 7.55 5.17 8.05 2.59 5.76 9.08 7.56 4.32 0.32 6.97

0.5 2.0 24* 50* 41 19 0.9* 10* 23 * 10* 100* 65 19 6.8 1033 erg s−1 ; [59, 63, 46]. Unfortunately, the initial phases of the outburst were missed and we do not know whether a bursting activity phase occurred in cohincidence with also for this source. During the latest 5 years it was extensively observed, covering a flux variability over a factor of about >60. Since the very first 2003 observations of XTEJ1810-197, carried out approximately one year after the onset of the outburst, it was evident [46] that the source spectral shape (initally of two blackbodies with kT=0.29±0.03 keV and kT=0.70±0.02 keV) was significantly different from that serendipitously recorded by ROSAT in 1992 (one BB with kT∼160 eV [46]). Moreover, the source showed a 5.54 s pulsation with a pulsed fraction of nearly 45% during outburst, while an upper limit of 24% was inferred from the ROSAT data. In 2006 the source was discovered to be one of the most intense and polarised radio pulsar in our sky with single peak flux density reaching few Jy [9] On the one

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hand, this finding provided direct evidence that the radio pulsar emission can also be at work in magnetars, corroborating the analogy between the spectral properties of AXPs and RPs. On the other hand however, this finding strongly suggested that a better way to study these objects (when in a high state) is taking into account the whole emission properties of the source from the radio to the hard X-ray bands. Simultaneous X-ray and radio observations have been performed. These suggested that the Xray and radio emitting regions are likely coincident (or superimposed), the Xrays likely coming from a larger area. Moreover, during all these campaigns large radio flux (∼50%) and pulse shape variations have been detected which do not correlate with any change (at a few percent level) of the Xray timing and/or spectral parameters (Burgay et al. in preparation). This suggests that the Xray emission likely originates deep in the crust (or more in general, the radio and Xray mechanisms are not closely related). A variable infrared counterpart have been discovered for this object [63, 116], although no clear correlattion between the X-ray and infrared variability haver been confirmed [127].

5.2 1E 1547−5408 1E 1547–5408 was first proposed as a possible magnetar in the candidate supernova remnant G327.24–0.13 through X-ray observations [43] and subsequently recognized as a transient radio magnetar thanks to the discovery at radio frequencies of its spin period of ∼2.1 s [8] (later detected also in X-rays [53]). In recent years, 1E 1547–5408 has been one of the most active magnetars. A first outburst occurred during the Summer 2007, when Swift observations caught 1E 1547–5408 at an Xray flux level of ∼5 × 10−12 erg cm−2 s−1 , more than one order of magnitude brighter than in quiescence [53]. However, the early phases of this outburst were missed and no bursts were observed (possibly due to a sparse X-ray coverage). A new outburst started on 2008 October 3 [67, 105]. This time several bursts were detected by Swift and in the data taken immediately after the Swift trigger, 1E 1547– 5408 was found at a flux level of ∼6 × 10−11 erg cm−2 s−1 . Then the luminosity declined by 70% in three weeks, following a power-law fading trend with decay index ∼−0.2 [67]. During this period, the source displayed a complex timing and spectral variability [67, 105]. No further bursts were reported until 2009 January 22, when the source entered a new stretch of much stronger activity, with thousands of bright bursts detected by many instruments [96, 74, 121, 105]. A spectacular event connected with this giant outburst was the appearance around the source of multiple expanding X-ray rings due to scattering by different layers of interstellar dust of a particularly bright burst [134]. From the analysis of these structures, a distance to the source of ∼4


257

Fig. 4 Dynamic Spectral Profiles (DSPs). Each row corresponds to one XMM-Newton observation (epoch increases from top to bottom: 2008 August 23, 29, 31, September 02 and 30) of SGR 0501+4516(Rea et al. 2009). The three columns represent in the phase/energy plane the contour plots for the total (left), power-law (middle) and blackbody (right) νFν flux. The colour scale is in units of 0.01 keV(keV cm−2 s−1 keV−1 ).

kpc was proposed [134].1 Shortly after the onset of the outburst, pulsations were detected with INTEGRAL and Fermi up to ∼150 keV [80, 74] and the source topped a flux level of ∼8 × 10−11 erg cm−2 s−1 (see Fig. 3). The (ongoing) intensive X-ray monitoring of 1E 1547–5408 shows that the flux is slowly decaying with an overall power-law trend with index ∼−0.3 (Bernardini et al in preparation). 1

This value agrees with the distance suggested by the possible association of 1E 1547–5408 with the supernova remnant G327.24–0.13 [43]. A distance of 9 kpc was instead derived from the dispersion measure obtained from radio observations [8].

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As periods of activity and enhanced luminosity are the most promising to search for radio and optical/infrared emission from magnetars, the 2009 outburst of 1E 1547–5408 triggered several multiwavelength follow ups. Multiple radio observations were carried out at Parkes on 2009 January 22, 23 and 25. Pulsed emission from 1E 1547–5408 was detected at 3 GHz during a 1.2-hour-long observation on January 25, but, notably, not in the other two occasions [4]. Moreover, a relatively bright transient (near) infrared source (Ks ∼ 18.5 mag) was discovered with ESO/VLT within the radio positional uncertainty of the AXP and identified with its counterpart [72]. Deep infrared observations taken with ESO/VLT during the 2007 outburst revealed four objects consistent with the radio position of 1E 1547–5408 [100]; none of them, however, showed variability and the likely counterpart was not detectable at the time. This sets an upper limit of about 21 mag in the Ks band on the infrared emission of the AXP during the 2007 outburst.

5.3 AX J1844−0258 This source was discovered in a 1993 observation of the (not associated) supernova remnant Kes 75 during a search for pulsating sources [135, 47]. The observed flux was ∼4 × 10−12 erg cm−2 s−1 . The long period (7 s) together with the spectral properties and the lack of a companion suggested that AX J1845.0–0258 is an AXP. The source was observed again with ASCA in 1997 and 1999 and revealed only in the 1999 observation, at a ten times lower flux (which is consistent with the marginal 1997 non detection) [138]. Subsequent BeppoSAX, Chandra, and XMM-Newton observations revealed an X-ray source at a flux level similar to that observed from AX J1845.0–0258 in 1999 [63, 142]. The low flux precluded new measurements of pulsations and therefore there is no information about the rate of change of the spin period (for this reason the source is often indicate as a candidate AXP). If AX J1845.0–0258 is indeed an AXP, it is plausible that like other magnetars it has a transient behaviour and that the 1993 ASCA observation was carried out during (or shortly after) an outburst and then AX J1845.0–0258 settled into a low luminosity state. Moreover, Tam et al. [142] noticed that, given the large uncertainty on the ASCA position, it is not ruled out that the X-ray source observed by the other satellites is a field-source unrelated to the 7-s pulsar AX J1845.0–0258. If so, the upper limit on the flux that they obtained from a deep Chandra observation of the field of the candidate AXP points to a flux decrease of a factor 200 or more.

5.4 1E 2259+586 This 7s X-ray pulsar was discovered a few decades ago, and it was believed to be a very stable X-ray emitter and pulsator. However, in 2002, it emitted the first notable recorded case of flux variability from a magnetar [75]. Its active phase, with a factor


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of ∼10 persistent flux enhancement, was followed by the onset of a bursting activity phase during which the source displayed more than 80 short bursts [41, 145] . Furthermore, despite being the first case of an outburst from an otherwise persistent and quiet magnetar candidate, 1E 2259+586 was also the first connected X-ray and infrared outburst [125], and it showed a glitch during the enhanced activity, corroborating the idea of these outbursts being due to crustal stresses impareted by the unstable magnetic fields [75]. Furthermore, this magnetar lies in the Supernova Remnant G109.1-1.0 (CTB 109), being one of the few associations between magnetars and SNR which still holds [40] .

5.5 1E 1048.1−5937 The 6.4-s X-ray pulsar 1E 1048.1–5937 was serendipitously discovered by Einstein during observation of the Carina Nebula [122]. Immediately suggested to be highly variable,2 it was tentatively classified as a binary with a V ∼ 19 mag Be companion [122]. Subsequent observations however ruled out the candidate optical counterpart and 1E 1048.1–5937 was placed in the emerging (at the time) class of the anomalous X-ray pulsars [54, 137, 97]. During October/November 2001 a couple of SGR-like bursts – the firsts ever found in an AXP – were detected from 1E 1048.1–5937 with RXTE, virtually unifying the SGR and AXP classes [42]. 1E 1048.1–5937 is one of the most frequently observed magnetars and in the last decade in particular it has been extensively monitored with RXTE since, because of its unstable spin down, frequent RXTE observations are necessary in following the spin evolution [41]. The long-term light curve of 1E 1048.1–5937 shows two consecutive outbursts in the 2002–2004 and a third event in 2007 [123]. The late-2001 bursts marked the start of the first stretch of enhanced flux that persisted a few months [41]. The peak flux was ∼2 times the mean quiescent value (≈7 × 10−12 erg cm−2 s−1 ). Another larger (the peak flux reached ∼3 times the quiescent one) and longer-lived flux increase started in Spring 2002 and lasted into 2004. A third burst was observed from 1E 1048.1–5937 in June 2004, during the final phases of the outburst. Both events had a few-weeks-long rise time and much longer and gradual decays. These flux variations were accompanied by substantial timing irregularities (including glitches) which, however, do not correlate in an obvious way with the flux enhancements [41]. On the other hand, anti-correlation between pulsed fraction and flux and a correlation between spectral hardness and flux have been reported for this source [133, 123]. In March 2007 1E 1048.1–5937 entered a new outburst accompanied by a large spin-up glitch [28]. This time, the flux rose to the peak (slightly higher than that of the 2002–2004 outburst) in less than a week. Also a fourth burst was detected by

2

The flux variability of 1E 1048.1–5937 had been long debated and could be confirmed only twenty years later [99, 41].

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RXTE about a month after the outburst onset [28]. For a distance3 of 9 kpc [23], the total energy emitted has been estimated in roughly 4.8 × 1041 , 3.5 × 1042, and 4.3 × 1042 erg for the three outbursts in chronological order [28]. A candidate infrared counterpart to 1E 1048.1–5937 (Ks = 19.4 mag) was selected in 2001 with the Baade (Magellan I) telescope[141] and confirmed by subsequent observations of large variability (∼2 mag) [66, 22]. Changes in the infrared flux were initially suggested to be anti-correlated with those in the X-ray flux [22]. Recent observations however showed a behaviour inconsistent with this hypothesis, with infrared flux enhancements near those at X-rays, indicating that neither disposition holds all the time [123, 140]

5.6 CXOU J1647−4552 CXOU J0100−7211 was discovered when it underwent a large outburst in 2006 [102, 103], preceeded by a bright X-ray burst detected with the Swift observatory on 2006 September 21. This 10.6 s X-ray pulsar is located in the young cluster of massive stars, Westerlund 1 [102]. Several observations with multiple X-ray telescopes were performed following the burst detection, showing a the flux from this magnetar increased by a factor of ∼100 following the outburst. XMM-Newton observed the source just 4 days prior to the outburst, providing one of the few cases where the beginning of the outburst could be assessed with relative precision. Muno et al. [103] showed that the spectrum of CXOU J0100−7211 hardened significantly when the flux increased and that the pulse profile changed dramatically from a simple near-sinusoidal shape to a complex profile with three distinct peaks per cycle. A glitch as large as ∆ν/ν > 1.5 × 10−5 was detected in coincidence with the outburst ([68] but see also Woods et al. 2010).

5.7 4U 0142+614 4U 0142+614 is one of the brightest magnetar known to date, and it was first detected by Uhuru in 1978. However, mainly because of the presence of the accretionpowered binary pulsar RX J0146.9+6121 nearby, only in 1994 was an ∼8-s periodicity reported using EXOSAT data taken in 1984 [69]. Long-term spin-period variations were discovered thanks to a large RXTE campaign [42], leading to the measure of the period derivative P˙ ∼ 2 × 10−12s s−1 . Despite deep searches [69, 144], no evidence for orbital motion has been found, supporting the isolated NS scenario. Further observations [143, 70] revealed a soft (110 keV) X-ray spectrum typical of an AXP, best fitted by an absorbed blackbody (kT∼0.4 keV) plus a power-law (Γ ∼3.7). More recent Chandra [73, 110], XMMNewton [115] and Swift X-ray Tele3

We note that Gaensler et al. [39] propose an association between 1E 1048.1–5937 and the hydrogen shell GSH 288.3–0.5–28 at a much shorter distance of 2.7 kpc.


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scope (XRT) [118] observations have shown that 4U 0142+614 is a relatively stable X-ray emitter. In the last few years, two peculiar characteristics of 4U 0142+614, have been found in comparison with other AXPs: (i) an optical counterpart [56] dispaying 8-s pulsation with a 30 per cent pulsed fraction [76] and (ii) mid-infrared emission, tentatively interpreted as the signature of a non-accreting disc around the NS [142]. Furthermore, like in other magnetars, a hard X-ray emission up to 250 keV has been revealed [17, 44].

5.8 SGR 1806−20 SGR 1806–20 is arguably the most burst-prolific magnetar and showed several periods of bursting activity since the time of its discovery in 1979 [83, 84]. Its persistent X-ray counterpart was observed for the first time with the ASCA satellite in 1993 [104]. Subsequent observations with RXTE led to the discovery of coherent pulsations (the first time in an SGR) at P ≃ 7.5 s and a secular increase of the period at a rate of ∼8 × 10−11 s s−1 [78]. These values confirmed the debated neutron star nature of the SGRs and, since under the assumption of pure magnetic dipole braking they imply a surface magnetic field strength of 8 × 1014 G, provided strong support for the magnetar model, that was developed in the early 1990s [39, 108]. The source luminosity remained fairly constant for many years at ∼5 × 1035 erg −1 s (for a distance of 15 kpc [14, 90]), until both the burst rate and the X-ray persistent emission started increasing during 2003 and throughout 2004, when the luminosity approximately doubled with respect to the “historical” level [98, 146]. This period of intense activity culminated with a giant flare recorded on 2004 December 27 [58, 95, 109]. This giant flare was exceptionally intense (assuming isotropic luminosity ∼1047 erg were released) and produced strong disturbances in the Earth’s ionosphere [11, 61] and detectable effects on the geomagnetic field [88]. The initial flash was followed by a tail clearly modulated at the spin frequency of SGR 1806–20 that persisted for ∼380 s. Comparing this giant flare with those seen from SGR 0526–66 and SGR 1900+14, it is found that the energy in the pulsating tails of the three events was roughly of the same order (∼ 1044 erg), while the energy in the initial spike of SGR 1806–20 (a few 1046 erg) was at least two orders of magnitude higher than that of the other events. Observations with RXTE unveiled, for the first time in an isolated neutron star, rapid quasi-periodic oscillations in the pulsating tail of the flare, likely related to global seismic oscillations on the neutron star surface [64]. The flare was accompanied by the emission of relativistic particles which powered a synchrotron nebula (a “mini-plerion”) that faded in a few months [6, 38, 126, 34]. A similar “radio afterglow” was observed also following the giant flare from SGR 1900+14 [36] (in the case of the 1979 event from SGR 0526–66, no data at radio wavelengths were available). The small positional uncertainty of the radio observations permitted the identification of the infrared counterpart of the SGR [77, 62]. The fluxes observed in

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the infrared and gamma energy bands show a variability correlated with that observed in the 2–10 keV energy range [92]. After the giant flare, the persistent Xray flux of SGR 1806–20 started to decrease from its outburst level, and its X-ray spectrum to soften, but the source has remained moderately burst-active to to date [117, 92, 132, 146, 32]. During the Spring 2006 the source recovered its pre-outburst luminosity [92] and about five years after the flare (on 2009 September 7–8) the value measured with XMM-Newton was ∼ 3 × 1035 erg s−1 . A flux decrease have been observed also from its infrared counterpart [62, 112, 92].

5.9 SGR 1627−41 SGR 1627–41 was discovered in 1998, when about one hundred bursts in six weeks were observed by CGRO/BATSE and other high-energy instruments [147]. Soon after the discovery of the bursts, its soft X-ray counterpart was identified with BeppoSAX at a flux level of ∼ 7 × 10−12 erg cm−2 s−1 (unabsorbed, 2–10 keV), corresponding to a luminosity of ∼ 1035 erg s−1 for a distance to the source of 11 kpc [13]. In the following 10 years no further bursting activity was reported while various observations carried out with BeppoSAX, ASCA, Chandra, and XMM-Newton showed a spectral softening and a monotonic decrease in the luminosity, down to a level of ∼1033 erg s−1 [79, 93, 31]. The long-term fading of SGR 1627–41 was suddenly interrupted by its burst reactivation on 2008 May 28, when several bursts were detected by the Swift/BAT during a short period of activity (about one day) [31]. This episode was associated with an abrupt and temporary large enhancement of the persistent X-ray flux (a factor of about 100 above the last measurement, in February 2008 with XMM-Newton) and a marked spectral hardening [31]. In September 2008, a deep XMM-Newton observation yielded the first measure of the spin period of the source (2.6 s, making SGR 1627–41 the second fastest spinning magnetar after 1E 1547–5408) and, together with searches in Chandra archival data, of its spin-down rate (1.9 × 10−11 s s−1 ) [33, 27]. In fact, while the detection of strong SGR-like bursts from SGR 1627– 41 made it a bona fide member of the SGR class, these two strong pieces of evidence in favour of the identification were still missing. Follow-up observations at near infrared and radio wavelengths were carried out in response to the 2008 burst activation, but they failed to detect the source [16, 10]. In particular, the limit on the radio pulsed emission of SGR 1627–41 at 1.4 GHz obtained at Parkes on 2008 May 30 and June 1 was 0.5 mJy (for a sinusoidal pulse profile) [10].


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5.10 SGR 0501+4516 A new magnetar candidate, SGR 0501+4516 was discovered on 2008 August 22nd by the Swift Burst Alert Telescope (BAT), thanks to the detection of SGR-like bursts . The activation of this new SGR followed a very long quiescent interval: the all sky X-ray monitors which were operative during the last three decades never observed activity from the source. Tens of bursts were observed [96, 24, 131, 51] with fluxes exceeding the underlying continuum by a factor >105. The bursts reached a maximum luminosity of ∼ 1041 erg s−1 and had a durations of BQED ≃ 4.4 × 1013 Gauss on the surface and one (or more) order of magnitude higher in the interior [7, 8, 9, 10]. This picture is compatible with the magnetic fields of ∼1014 Gauss inferred for SGRs and AXPs from their period and period derivative according to the magnetic dipole radiation for˙ 0.5 G mula for a neutron star of 10 km radius, and 1.4 solar masses, B∼3.2×1019(PP) (e.g. [11]). In the magnetar model, the magnetic field is the dominant source of free energy (orders of magnitudes higher than the rotational energy of the star), powering the persistent emission through low-level seismic activity and heating of the stellar interior [145]. When magnetic stresses build up sufficiently to crack a patch of the neutron star crust, the resulting “crustquake” ejects hot plasma particles into the magnetosphere, which results in an SGR burst [8]. Alternatively, the short SGR bursts may arise from magnetic reconnection events in the stellar magnetosphere [12]. Giant flares likely result from a sudden reconfiguration of the star’s magnetic field that produces large fractures in the crust and propagates outwards through Alfvén waves of enormous power. The ∼0.2 s initial spike of giant flares marks the ejection of the

Bursts and Flares from Highly Magnetic Pulsars

6 0

180

4

190

200

210

10 2 0

80

(b)

1

1 peak

Power

6

Frequency (Hz)

8

(e)

4 2 0

100

100

Frequency (Hz)

80

100

DC level 8

80

6

60

(g)

4

40

2

20 80

(f)

2

(a)

st

peak

4

0

0.1 120

100

220

2

Power

(c)

8

Power

(d)

kcts/s

Power

6

nd

5

All phases kcts/s

8

281

50

100

150

200

250

Time (seconds)

300

0

80

100

Frequency (Hz)

Fig. 1 The ∼92 Hz oscillation as seen by the PCA during the 2004 December event from SGR 1806-20. (a) Spectrogram with 2 s time step and resolution. The contours represent Leahy powers from 3.2 to 3.7; (b) Light curve corresponding to the same time axis as panel (a). The time resolution is 0.75 s. The grey-shaded area indicates the time interval shown in panel (c); (c) Close–up of the grey area in panel (b). The different symbols mark the first peak (black circles), the second peak (stars) and the DC level (grey circles); (d) average power spectrum (at 0.5 Hz resolution) of the grey area in panel (b); (e) average power spectrum (at 1.33 Hz resolution) of the phase interval including the first peak as seen in panel (c); (f) same as (e) for the second peak; (g) same as (e) for the DC level (adapted from [15]).

largest part of the total event energy (up to ∼1047 ergs) as well as the onset of a relatively large surface fracture [13]. The ringing tail that follows results most likely from the part of the fireball that remains trapped in the stars magnetosphere. The energy release in the ringing tail yields a limit for the external field of magnetars ( >1014 Gauss) in agreement with the values inferred from spin-down dipole losses [8, 14]. The detection of deca-, hecto-, and kilo-Hertz Quasi Periodic Oscillations (QPOs) in the decaying phases (tails) of giant flares have been interpreted in terms of global seismic oscillations following the fracture formation [15, 16]. The superEddington fluxes observed in the tails of these events are thought to be possible because of the suppression of the electron scattering cross sections in the presence of very strong magnetic fields [5]. In the following we will focus on the results, outlined in the latest two sentences, and on the information that have been obtained in recent years by means of the study of the timing and spectral properties of the flaring activity of magnetars.

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GianLuca Israel and Simone Dall’Osso

2 SGRs Giant Flares and their magnetic fields In 2005 QPOs were discovered in the X-ray flux of the ringing tail of SGRs’ giant flares [15][; see Figure 1]. Different QPO modes were detected, some of which were excited simultaneously. The ringing tail of the December 2004 event from SGR 1806-20 displayed clear QPO signals at about 18, 30, 93, 150, 625 and 1840 Hz [17]. Similarly, QPOs around frequencies of 28, 54, 84 and 155 Hz were detected during the ringing tail of the 1998 giant flare of SGR 1900+14 [16], while hints for a signal at ∼43 Hz were found in the March 1979 event from SGR 0526-66 [18]. These QPOs show large variations of the amplitude with time and, especially, of the phase of the spin modulation in the giant flare’s tail. The similarity in some of the QPO modes and frequencies across different SGRs suggests that the production mechanism is the same. Indeed, giant flares are thought to be powered by catastrophic global reconfigurations of the magnetic field. As the field is anchored to the charged particles in the neutron star crust, it had long been suspected that giant flares might be closely related to starquakes [23, 8, 14, 13] strong enough to excite global seismic vibrations of the NS crust [24]. In the model of [8] the field twists and puts the crust under strain, but crustal rigidity prevents movement and reconnection. Stresses build up until the crust reaches its breaking strain and a flare is thus triggered. In the alternative model of [25] the crust deforms plastically as the field twists, and flares occur when the field reaches an instability point [82]. The colossal and rapid reconfiguration of the field can drive strong, global magneto-elastic vibrations in this case, even without crustal yielding. Indeed, the frequencies of the detected QPOs are in good agreement with models of torsional shear modes of neutron star crusts - in accordance with early theoretical suggestions. The models used to make these identifications were based on early calculations that assumed free slip of the solid crust over the fluid neutron star core [19, 20, 21, 22]. In the nice review by Watts (2006, [27]), it was however noted that neutron stars can sustain many types of oscillation restored by various different forces. Early calculations for neutron star models with a fluid core and a solid crust indicated that the modes most likely to be excited by a magnetar crustquake were the torsional shear oscillations of the crust, with a fundamental frequency at ≈ 30 Hz [28, 20, 21, 24]. These oscillations are primarily horizontal (as opposed to radial) and the crustal shear modulus provides their restoring force. Which harmonic would exactly be excited in this case depends on fracture properties (location, geometry, speed), and subsequent coupling and damping processes. These findings hold in themselves a great potentiality in using seismology to study the interior structure and composition of neutron stars. This would be a major breakthrough in the study of the nature of matter under conditions of extreme pressure. In fact, the frequencies of the fundamental n = 0 torsional shear modes deduced from the low-frequency QPOs in SGRs 1806-20 and 1900+14 are different, the latter source having a lower fundamental. This most likely reflects differences in the mass, radius or magnetic field strength of the two stars (mass and radius having a strong effect due to gravitational redshift). [16] analysed the differences in mass

Bursts and Flares from Highly Magnetic Pulsars SGR 1806-20 SGR 1900+14 18∗ 26∗ 30∗ 28 53 92∗ 84 150 155 625∗ 1840

283

Torsional shear mode identification

n = 0, l = 2 n = 0, l = 4 n = 0, l = 6 n = 0, l = 10 n = 0, l = 11 n=1 n=3

Table 1 Summary of QPO frequencies (in Hz) detected in the tails of the SGR 1806-20 and SGR 1900+14 giant flares. QPOs with asterisks have been detected in the datasets of both the Rossi X-ray Timing Experiment (RXTE) and RHESSI missions. The 150 Hz and 1840 Hz QPOs in the SGR 1806-20 flare have fractional amplitudes too low to be detected in RHESSI. The third column indicates the identification as torsional shear modes on the basis of models that do not include crust-core coupling. The mode identification given for the n = 0 modes is consistent with that given in [29]. l marks the different angular harmonic number. This differs very slightly from the identification given in previous papers, and reflects the use of (more accurate) spherical geometry in the more recent paper (from [27]).

and magnetic field that would be necessary to explain the different frequencies, for various different equations of state [30]. Estimates of the magnetic field derived from timing constrain the parameter space to rule out both very hard and very soft equations of state [31]. For intermediate equations of state reasonable results were obtained that support the finding that SGR 1806-20 has a stronger field than SGR 1900+14. Additionally, the possible identification of an n = 1 radial overtone is particularly exciting, as it might allow to estimate crust thickness. This is on its own an independent constraint on the nuclear equation of state. In the Newtonian perturbation calculations of [19], one can show that in the thin crust limit the ratio of first radial overtone to fundamental frequency is proportional to the ratio of crust thickness to stellar radius. Subsequent Newtonian perturbation calculations included a correction to the frequency for gravitational redshift; a factor which cancels when one takes the ratio of two frequencies. Strohmayer & Watts [16] used this fact to compute mode frequencies for realistic (non-thin) neutron star crust models in spherical geometry. Using the SGR 1806-20 observations, assuming a fundamental at 30 Hz and a first overtone at 625 Hz, this resulted in a crust thickness estimate of 0.1 – 0.13 times the stellar radius. Recent more detailed modelling is now refining this initial value. General relativistic mode calculations by [29] and [32], which take into account not only gravitational redshift but also the effect on crust thickness associated with relativistic models, have already resulted in revised estimates. Efforts to include crust/core coupling will doubtless lead to further changes [33, 34]. This is nonetheless the first time that there has been the possibility of making a direct measurement of crust thickness in a neutron star (for constraints on strange stars see [35]).

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2.1 The Cavallo-Fabian-Rees Variability Limit The QPO properties, in particular those of SGR 1806-20 at 625 and 1840 Hz, have been used to infer a lower limit on the magnetic field strength at the neutron star surface in a way which is model-independent and based on very simple assumptions [36]. This is based on the Cavallo-Fabian-Rees Variability Limit on the rate of change of the luminosity of any given source ([37, 38, 39], see also [40, 41]). The QPO rms amplitude reached a maximum of arms ∼ 18%. Approximating the QPOs with sinusoids, their highest luminosity derivative is ∆L/∆t = 23/2πLarms νQPO , with νQPO the QPO frequency. Here L ∼ 1041 ergs s−1 is the average luminosity in the relevant section of the ringing tail (for the likely source distance of 15 kpc). This gives ∆L/∆t ∼ 1043 and 6 × 1043 ergs s−2 for the 625 and 1840 Hz QPOs, respectively (the effect of beaming is taken into account). Moreover, the presence of spin pulsations during the giant flare tail indicates that the emission in the ringing tail originates from a region that remains stably anchored to the star’s magnetosphere, and thus that (relativistic) bulk motions are not present at this stage of the flare. Finally, the blackbody temperature and luminosity in the ringing tail translate into a lower limit on the size of the emitting region of about ∼ 30 km, i.e. significantly larger than the neutron star. On the other hand the black body-like spectral shape testifies that the emitting region is optically thick (or at least effectively thick), implying a scattering optical depth ≫ 1. The Cavallo-Fabian-Rees Variability Limit is based on the fact that the total energy released within ∆t due to a large luminosity variation ∆L is related to the total mass within the source dimension R by ∆L∆t = η

4π 3 R nm p c2 , 3

(1)

where n is the average baryon density, and η is the energy extraction efficiency. At the same time the time-scale ∆t must obviously exceed the time over which the photons escape from the source ∆t > Rc (1 + τT ) where τT = σT nR is the Thomson optical depth and σT the Thomson cross-section. This yields the limit ∆t >

3 σT ∆L 2π m p c4 η

(2)

which is independent of both R and n, or any combination thereof: only the dependence on ∆L, a directly observable quantity, is left. The Cavallo-Fabian-Rees, CFR, limit thus writes ∆L/∆t < η 2 × 1042erg s−2 . (3)


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The 625 and 1840 Hz QPO signals from SGR1806-20 exceed the CFR limit by about an order of magnitude1: the largest value found in the previous section is ∆L/∆t = 6 × 1043 erg s−2 , which is a whole factor 30/η larger than the CFR’s limit. Vietri et al. 2006 ([36]) demonstrated that, in this specific case, there is only one way to circumvent the CFR limit, i.e. the scattering cross-section may differ from Thomson’s because of the presence of a strong magnetic field B, exceeding the quantum value Bq = m2 c3 /(e¯h) = 4.4×1013G. In this case, the photon scattering cross section for the ordinary (O) and extraordinary (E) modes, and for the conversion of photons into the other state, are given by [42], when the dielectric tensor is dominated by vacuum polarization effects. In fact, for photons emitted in the extraordinary mode, the cross section is reduced, with respect to the Thomson value, by a factor ≈ (ǫBq /(me c2 B))2. Thus, to bring the observed value, △L/ △ t = 6 × 1043 erg s−1 , in agreement with Eq. 2, we just need to have (ǫBq /(me c2 B))2 ≤ η/30; here we take for ǫ the value ǫ ≈ 14 keV, which is the peak of the Planck distribution for the observed temperature T = 5 keV. So our conclusion is that the QPOs’ luminosity variation agrees with the CFR limit provided B ≥ 1.5Bq

0.1 η

!1/2

≈ 6.6 × 1013 G

(4)

as inferred at the surface of the observed black body with radius of 30 km. Given the rapid decrease of the dipole field (and a fortiori of the other multipoles) with distance from the star, the surface magnetic field must certainly satisfy B ≥ 1.8 × 1015 G

10 km Rns

!3

0.1 η

!1/2

.

(5)

The above result is strongly suggesting that two species of photons, those corresponding to ordinary (O) and extraordinary (E) polarized modes, are present in presence of a magnetic field with strength in excess of Bq . This is still debated and not easy to prove or disprove unambiguously. However, in the latest years, several indirect proofs have been collected all in favour of this scenario (see Section 3).

3 SGRs Intermediate Flares in the Swift era Burst activity in SGRs occurs sporadically and is quite diverse in behavior. Burst active phases of SGRs vary both in total energy released and duration, tending to be concentrated into relatively narrow intervals (weeks or months) separated by relatively long periods (years) of quiescence. Since its discovery in 1979, when bursts where detected three times in three days, SGR 1900+14 remained in quiescence until 1992, when a handful of bursts were again detected within a few days [43, 44]. 1

We note that also the slower ∼ 90 − 150 Hz QPOs signals in the giant flares’ tail of SGR1806-20 and SGR1900+14, exceed the CFR limit, though by a smaller factor.

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In 1998 the source entered an unprecedented level of activity during which more than 1000 burst were recorded within 9 months, and culminated with the ∼ 400 s long and rather intense 1998 August 27 giant flare event (∼ 4 × 1044 erg s−1 ). Burst activity was detected until 1999. Particularly interesting, are two events detected in May and September 1998, during which ”bunching” of short and long burst were detected [45, 46]. Finally, after almost two years of inactivity, on 2001 April 18, an intense and long (∼ 40 s) burst was detected from SGR 1900+14 [47]. The energy released by this flare (few × 1042 ergs) was less than that of the giant flare, though larger than that of the most common short SGR bursts. Consequently the flare was dubbed an “intermediate flare” [48]. Indeed, looking back at the burst history of SGR 1900+14, it was realized that a handful of similar events, characterized by a longer duration (few seconds–few tens of seconds) and a higher fluence than those characterizing short bursts, were present. These bursts were then grouped into the class of intermediate flares likely forming a continuum in terms of duration and fluences [49]. A number of broad-band spectroscopic studies of short and intermediate flares were carried out in the past by different missions. These found that, above 15– 20 keV spectra are usually well fitted by an optically-thin thermal bremsstrahlung (OTTB) with characteristic temperatures ranging from 20 to 40 keV [50]. Moreover, the study of the cumulative spectral properties of 100 bursts from SGR 1806−20 in the 5–200 keV energy range showed that the number of the photons in the spectrum of the detected bursts was remarkably stable in spite of the large intensity spread (a factor of 50) and that the low-energy (below 15 keV) data were inconsistent with the back-extrapolation of an OTTB model that provided a good fit to the high-energy portion of the spectrum [86, 52]. Qualitatively similar spectral properties were measured during a bright intermediate flare from SGR 1900+14 using HETE–2 data, which also showed that the OTTB model largely overestimated the flux at low energies (40 between short bursts and IFs), therefore largely improving the statistics over which the detailed analysis can be carried out. The impact of the increased statistics and time resolution is evident when comparing the Swift results with previous ones. On 2001 July 2, the HETE-2 instruments recorded a 3.5 s IF from SGR 1900+14 and a time resolved (∆t >30 ms) spectral analysis was carried out in the 2–100 keV range [49]. They found that the 2BB model fitted the spectra well, the higher temperature blackbody (BBhard ) evolving in a manner consistent with a shrinking emitting region, the lower temperature one (BBsoft ) showing a constant radius. They also suggested that, within the magnetar model, the 2BB model might be an approximation of a more complex multi-temperature spectrum. Figure 3 includes both the results obtained from the Swift and HETE-2 data: clearly, the Swift data fill in those regions on the kT -R2 plane, which remained unexplored with HETE-2. Several properties can be inferred: a) the Swift data populate, almost homogeneously, all temperatures between ∼2 and 12 keV, and the HETE-2 measurements (black diamonds in Figure 3) can be regarded as a subset of them; b) the distribution

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is such that a sharp edge between the populated regions and the rest of the kT -R2 plane is clearly present, with a cut-off (or sharp turn) in the distribution of RBBh at kT h ≈ 12–13 keV. This sharp edge provides an estimate of the typical size of the relevant emitting regions (by assuming a reference distance of 10 kpc; [57, 58]): 30– 200 km range for the BBs component and 3-30 km range for the BBh one. c) there is an additional turn in the BBh component size between 6 and 16 km, at approximately 10 keV (see Figure 3), and d) there is a strong correlation between kT and R2BB in the brightest phases of the IFs, corresponding to BB temperatures ≤ 10 keV. This correlation is consistent with a power-law with index of about −3 (while, were the luminosity the same for all events, the relationship expected for a BB component would be y=x−4, where x = kT and y = R2BB). The sharp edge in the distribution of the 2BB parameters suggests that a saturation effect occurs. In order to investigate this effect further, we divided the data points of the two BB components in two samples, below and above a bolometric luminosity of L = 3×1040 erg s−1 (see Figure 3). The luminosity threshold was chosen so as to roughly separate the peaks of the bursts and flares from the inter-burst/flare time intervals. We note that the HETE-2 data lie just above and below the flux threshold, but never reach the values corresponding to the peaks and tops of the Swift IFs. As we can see from right panel of Figure 3, as long as both BB component are below ∼ 3 × 1040 erg s−1 , their two luminosities are strongly correlated (L(BBhard) versus L(BBsoft) is well fitted by a power law with index 0.7±0.3 at 1σ c.l.). This correlation, which seems indicative of a physical link between the two BB components, was already noticed by Feroci and collaborators who analyzed the time-averaged spectral properties of 10 short bursts from SGR 1900+14 recorded by BeppoSAX in April 2001 (filled squares in Figure 3, right panel; [54]). It is apparent that the BeppoSAX measurements are fully consistent with those obtained with Swift and can be regarded as a subsample of the latter. On the other hand, this trend was not reported for the IF observed by HETE-2 in 2001 (empty diamonds in Figure 3, right panel; [49]). Intriguingly, the correlation no longer holds above ∼ 3 × 1040 erg s−1 for the Swift data. Above this value, the luminosity of the BBsoft component reaches a maximum in the (7–14)×1040 erg s−1 range, while that of the BBhard continues to increase up to ∼ 3 × 1041 erg s−1 . Clearly, this previously unknown behavior strengthens the idea of a saturation mechanism in the burst emission. In the following, we will concentrate on the information (mainly concerning the brightest part of IFs) which can be inferred from spectral analysis of IFs. i) the existence of two blackbody components, the harder one (kT h ∼ 7–11 keV) having a systematically smaller radius (RBBh ≤ 25 km) than the softer one (RBBs ∼ 25–100 km).

This first finding shows that different thermal components originate from different regions around the NS, ranging from its surface (at R < RNS ) to well up in the magnetosphere, at a height of several stellar radii. The maximum observed flare luminosity is ∼3×1041 erg s−1 , attained by the hard blackbody component at an effective temperature of ∼10 keV and radius of ∼15 km. Interestingly, this matches well the magnetic Eddington luminosity, LEdd,B , at that same radius, for a surface dipole field ≃8×1014 G (this value of the B-field is very close to that deduced from the spindown


289

106 L40BBs < 3

105

L40BBs > 3

10

L40BBh < 3 L40BBh > 3

1000

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R2BB (km2 @ 10 kpc)

104

100 10

I08 F04 O04

1

0.1

1 0.1 0.01

1

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5 kT (keV)

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1 L40(BBsoft)

10

Fig. 3 Swift BAT time-resolved spectral results obtained during the burst “storm” of 2006 March 29. Left panel: square of radii of the two blackbodies as a function of their temperatures for the whole ∼30 s BAT dataset. Red filled squares and dark green filled circles mark the BBsoft component for luminosities below and above 3×1040 erg s−1 , respectively. Violet filled triangles and blue filled stars are the same quantities as above for the BBhard component. Black diamonds marks the HETE measurements obtained for the 2001 IF ([49]=O04). We also plot two representative power-laws for R2 = kT α , with α equal −3 and −4 (the latter corresponding to the expected relation for a pure BB). Right panel: Time-resolved bolometric luminosity of the BBsoft versus that 40 α of the BBhard (in units of 1040 ). The solid line marks the power-law relation L40 soft = (Lhard ) with 40 α=0.70±0.03 (1σ c.l.) obtained by fitting points in the 0.01–3 Lsoft range. Filled squares represent the measurements for short bursts ([54]=F04; adapted from [56]=I08).

rate of SGR 1900+14), where (cfr. [5, 8]): LEdd,B (r) ≃ 2LEdd

" #4/3 !2/3 B 4/3 B R 40 ≈ 2 × 10 erg s−1 . BQED RNS 1012G

(6)

If radiation originated from a trapped hot fireball this would be in line with the theoretical expectation that the radiative efficiency of a magnetic confined fireball never exceeds (to within a small factor) the magnetic Eddington flux [8, 14]. In fact, ablation of matter from the NS surface would increase the scattering depth in a super-Eddington radiation field, thus providing a self-regulating mechanism. The radius and temperature that we inferred at maximum burst luminosity are also in good agreement with the prediction for the emission coming from a trapped fireball ([8], cfr. their discussion for the best fit temperature and radius in the case of SGR 1806−20). Most remarkably, the luminosity of the soft component can be larger than 1040 erg s−1 out to R∼100 km. For R>(30-40) km this value exceeds the magnetic Eddington luminosity at the corresponding radius (for a dipole field geometry). This suggests that magnetospheric confinement plays an active role at those distances, with magnetic stresses balancing radiation forces. If this were the case, the saturation of the soft component at ≃ 1041 erg s−1 would be related to the magnetic field strength at the relevant radii and its maximum ability to retain the trapped fireball

290


matter which is subject to very high radiation pressure. ii) the existence of a clear correlation between the luminosities of the two components up to ∼ 3 × 1040 erg s−1 , above which value the luminosity of softer blackbody shows signs of saturation, while that of the harder blackbody still grows up to a few times 1041 erg s−1 .

This second finding implies that, in the luminosity range 1040–1041 erg s−1 , the total radiation energy is divided almost equally between the two components. Combining the information of the two panels of Figures 3 we can see that, for a given luminosity ≤ 1041 erg s−1 , there are two separate emission regions: a smaller and hotter one, whose radiating area suggests emission from (part of) the NS surface with a relatively high effective temperature (10–12 keV), plus a second, possibly magnetospheric region, with significantly larger emitting area and lower effective temperature (3–7 keV). The hotter component attains the highest luminosities, i.e. > 1041 erg s−1 , as its radius grows slightly and the effective temperature decreases. On the other hand, the colder component is characterized by a minimum blackbody radius of ∼ 25 km and maximum temperature of ∼ 7 keV. A possible interpretation involves the different way in which photons with ordinary (O) or extraordinary (E) polarization mode (a property introduced by the presence of a birefringent medium, such as the magnetic field; [59]) propagate across the magnetosphere. Since the scattering cross section of E-mode photons is much reduced in presence of strong magnetic fields, E-mode photons have a scattering photosphere which is located much closer to the NS than that of O-mode photons. On the other hand, in supercritical magnetic field (B > BQED ), E-mode photons have a non-negligible probability of splitting (and switching to the O-mode). The probability is a strong function of energy, so that E-mode photons of high energy cannot travel far from their scattering photosphere before splitting into O-mode photons. On the other hand, O-mode photons will be entrained with streaming electrons and baryons and advected out to where their scattering optical depth becomes τ(O) ∼ 1 [8, 12]. As a consequence of Compton scattering (and, with lower efficiency, photon merging), a fraction of O-mode photons can also switch back to the E-mode. Therefore, the two modes are effectively coupled and are advected at comparable rates as long as mode switching is efficient: an approximately equal distribution of energy in the two modes is thus to be expected [8, 12]. This may suggest that the two observed spectral components reflect the population of photons in the two polarization modes and, thus, the regions from which they are emitted. We note that the minimum radius of the cold blackbody almost corresponds to the maximum radius of the hot component, the distribution of points in the R2 versus kT plane being continuous across this point. This suggests the existence of a narrow zone of separation between the two emission regions. In order to further characterize this zone, we studied the R2 versus kT distribution for each of the seven longest IFs and for one short burst (see Figure 4). Remarkably, the transition between the two BB components is more evident for the brightest flares (IF1 and IF7 in Figure 4) where the upper left edge of the parameter distribution of the hard component is confined to smaller radii (R ≤ 20 km) and correspondingly higher temperatures (kT ≥ 8 keV). The soft component seems less dependent on the flux than the hard

R2BB (km @ 10 kpc)


104

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IF1

IF2

IF3

IF4

IF5

IF6

IF7

SB

1000 100 10 1

R2BB (km @ 10 kpc)

0.1 104 1000 100 10 1

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0.1 104 1000 100 10 1

R2BB (km @ 10 kpc)

0.1 104 1000 100 10 1 0.1

2

5 10 kT (keV)

20 2

5 10 kT (keV)

20

Fig. 4 Same as Figure 3 but for each of the seven longest intermediate flares (IF1 to IF7) plus a short burst (SB; adapted from [56]).

one, its minimum size being of the order of ≥ 25-35 km in all IFs. Qualitatively, this behavior is in agreement with the above scenario. In fact, a larger brightness can be reached when the burst energy is trapped closer to the NS surface, where the stronger magnetic field allows a larger flux (of E-mode photons) to be released. Moreover, the sharp and narrow gap between the emitting regions of the two BBs, at a radius of (∼ 20–30 km), can be interpreted as the signature of the presence of an E-mode splitting photosphere; this represents the surface (at radius R = RQED ) below

292


which the magnetic field is supercritical (B ≥ BQED ), photon splitting is efficient and the two polarization modes can remain coupled. E-mode photons can stream freely to the observer from the splitting photosphere (at radius RQED ∼ 20–30 km), which then would naturally define a maximum size for the emission region of radiation in this polarization mode. On the other hand, O-mode photons could not originate from regions internal to the splitting photosphere, as their scattering optical depth is still much larger than unity within that volume. If this scenario is correct, it implies that the emission region of E-mode photons can range from the base of the trapped fireball (near the NS surface) to a slightly higher region in the magnetosphere, but well within the splitting photosphere. In this case, part of the internal energy of the coupled E and O-mode photons is lost in the E-mode photosphere due to (adiabatic) expansion from near the NS to the splitting photosphere. This degrades the original spectrum towards lower temperatures and larger radii, up to RQED . On the other hand, O-mode photons might either be released near the splitting photosphere or advected to much larger radii, depending on the value of their optical depth at that location (see [8]). iii) the existence of a correlation between temperature and blackbody radius, which holds for the most luminous parts of the flares (approximately for Ltot > 4 × 1040 erg s−1 ).

Finally, our third finding is the apparent correlation between the surface and temperature of the spectral components at different luminosities. This behavior does not have a clear interpretation. As shown in Figure 3, the top part of the data strip is −3 , where Σ is the radiating blackbody surface. Since well fit by a power-law Σ ∝ T BB 4 ΣT BB = L, this implies T BB ∝ L. Therefore, along lines of constant luminosity, the radiating surface would scale like T −4 , i.e. steeper than the data points (on the edge of the allowed region in the kT versus R2 plane). The ΣT 3 =const relation that implies a roughly constant number of emitted photons per unit time. At the highest luminosities (≥ 1041 erg s−1 ) of the flares, where the softer blackbody saturates, the observed correlation involves both components. It is tempting to attribute this to the fact that, in this luminosity range, Comptonization, and/or adiabatic losses play a dominant role in the formation of the emerging spectrum, both processes being characterized by conservation of the photon number (photon splitting should have only a minor impact). This is in agreement with the prediction by [8], that at effective temperatures less than ∼ 10 keV photon splitting would not be efficient in maintaining a pure Planck spectrum for both modes. However, if the photon chemical potential is sufficiently small compared to the photon temperature, deviations from a Planck spectrum are expected only at low energies, which we do not observe given they are masked by absorption [8, 12]. On the other hand, at luminosities ≤ 1041 erg s−1 , the two blackbodies approximately share the same luminosity, therefore the colder one emits a larger number of photons. This suggests that efficient photon number-changing processes (such as photon splitting or double Compton scattering) may play a key role in the formation of the spectrum. Indeed, we note that the photon number ratio is roughly the same as the temperature ratio in this case, since the luminosities are approximately equal. As this ratio peaks at around 2 and extends from 1.5 to 4, it appears to be


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qualitatively compatible with the combined effects of photon splitting and double Compton scattering (cfr. [12]). Finally, we briefly comment on the sharp turn in the hard component distribution at around kT∼10 keV and subsequent cut-off at ∼12÷14 keV which, together with the ΣT3 =const relation, are among the most distinctive properties of Figure 3 (left panel). Among others, these features clearly imply that no thermal component with characteristic temperature above the cut-off is detected, though the BAT energy interval extend up to at least 100keV. Within the discussed scenario it is tempting to account for the above properties in terms of photon splitting process and, in particular, its efficiency as a function of (mainly) flux and energy. In fact, the turn at kT∼10 keV marks the drift of the parameter distribution from the ΣT3 =const relation, identifying the passage between photon number-conservation (such as Comptonization) and photon number-changing (photon splitting) emitting processes. As reported by [8], the minimum temperature at which photon splitting is efficient in maintaining a nearly Planckian spectrum for E-mode photons, is ≃10 keV.

3.2 Further Observations: the case of SGR 0501+4516 and 1E 1547.0-5408 The results outlined in the previous section are certainly interesting, though they should be confirmed and tested through the study of similar events (IFs or bursts) with sufficient statistics detected both from the same source or from other magnetars. It is worth emphasizing that the data of the burst “storm” has been collected due to the specific Swift capabilities (unique among current high energy missions) of rapid slew of the satellite which ensure an on-axis source observation within 12 minutes from the initial trigger. Correspondingly, obtaining an additional dataset with similar high statistics is not an easy task. During 2008 three outbursts from three different magnetars were detected, namely SGR 1627−41 , SGR 0501+4516 and 1E 1547.0-5408. In all cases the outburst onsets were studied by Swift after the detection of one or more bursts from the sources in the BAT (for details see [35, 131, 63]). In all cases the statistics collected by BAT was not sufficient (both in terms of detected bursts and statistics within each burst) to allow a detailed time-resolved study of the spectral parameters during the bursts. However, in the case of SGR 0501+4516 more than 50 bursts were identified out of which 18 had enough counts to carry out a relatively detailed time-averaged spectral analysis ([60]; see Figure 5). Among the several different spectral models used, the cut-off powerlaw and the two-blackbody models provided the best fit in the 15–150 keV energy range. The cut-off powerlaw model fit yields a mean photon index Γ = 0.5±0.1 and a cut-off energy Ecut = 19±2 keV for the bursts [60]. The mean hard and soft blackbody temperatures are found to be kT = 12.8±0.7 keV and kT = 4.6±0.5 keV for the BBsoft and BBhard components, respectively. Moreover, they are anti-correlated with the square of the radii of the hard and soft emitting regions (RBBh and RBBs ) as R2BBh ∝ kT −5.8 and R2BBs ∝ kT −2.7 , respectively ([60];

294


100

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Soft kT

BB -2.7

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)

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ergs s )

Fig. 5 Left panel: square of the radii of the BB+BB model components as a function of their temperatures. The red circles and blue squares denote the soft and hard kT values, respectively. The soft kT values show an anti-correlation of ρ = −0.5, P = 0.06 with R2BBs , and the hard kT shows a strong anti-correlation of ρ = −0.7, P = 0.01 with R2BBh . Right panel: bolometric luminosity of the hard BB component (Lhard ) versus that of the soft BB component (Lsoft ) in units of 1039 ergs s−1 . The solid line is the powerlaw fit which gives the relation Lsoft = (Lhard )α where α = 0.6±0.1 (from [60]).

similarly to the case of SGR 1900+14). The soft and hard component temperatures with different indices support the idea of two distinct emitting regions with the hard component corresponding to a smaller radius and the soft component corresponding to a larger radius, which further corroborate the idea of the propagation of extraordinary (E) and ordinary (O) mode photons across the photosphere, as predicted in the magnetar model. However, by comparing datapoints in Figure 4 and 5, it is evident that the “saturation” effect was not reached during SGR 0501+4516 bursts, or at least not observable within the time-averaged spectra. The properties of a peculiar burst (bouble-peaked) observed from SGR 0501+4516 with the Fermi GBM have been studied by [64]. They show that a phenomenology similar to that of the Photospheric Radius Expansion (PRE) seen in some bright thermonuclear bursts on accreting neutron stars, is also possible during magnetar bursts. After having identified the factors necessary to generate double-peaked PRE events, [64] showed that the direct measurement of the magnetic Eddington limit (see Eq. 6) in a magnetar would constrain the magnetic field strength and the distance and might, in principle, enable a measurement of gravitational redshift. Though the confirmation of the presence of PRE events in magnetar requires more detailed radiative models for bursts, the properties of the peculiar burst observed from SGR 0501+4516 are in agreement with the predicted critical flux (by using the magnetic field strength inferred from timing and the distance suggested by its probable location in the Perseus arm of our Galaxy). It was only in January 2009 that a large outburst was detected from 1E 1547.05408 after only three months from the previous one (see [65, 66] for more details).


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106 105

10

1000

L40(BBhard)

R2BB (km @ n kpc)

104

100 10

1

0.1

1

0.01

0.1 0.01 10−3

1

2

5

10 kT (keV)

20

50

10−3 10−3

0.01

0.1 1 L40(BBsoft)

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Fig. 6 Similar to Figure 3 but for SGR 1900+14 and 1E 1547.0-5408 together. Radii and luminosities (the latter without uncertainties in order to better appreciate the comparison with the corresponding quantities inferred for SGR 1900+14) are normalized to the distances of 15 kpc for SGR 1900+14 and 4.5 kpc for 1E 1547.0-5408 (adapted from [65, 66]). Left panel: grey points refer to SGR 1900+14, while those in blue and violet mark the hard and soft blackbody components of 1E 1547.0-5408, respectively. Right panel: grey points refer to SGR 1900+14.

1E 1547.0-5408 is very peculiar magnetar, first discovered in 1980 with the Einstein X−ray satellite [67], but studied in detail for the first time only in 2007 [68]. The source is associated with the young supernova remnant G327.24-0.13. Using data collected in June 2007 with both the Parkes radio telescope and the Australia Telescope Compact Array, the source was unambiguously classified as a transient magnetar by measuring P ∼ 2.069 s and P˙ ∼ 2.3 × 10−11 s/s [69]. During January 22, 2009, the source entered in a rather strong state of burst activity (first detected by Swift BAT), accompanied by a strong enhancement of the continuum X−ray flux, which culminated when more than 200 bursts (some of which were classified as IFs) were recorded by the INT EGRAL SPI instrument in a few hours [106]. Moreover, the distance to 1E 1547.0-5408 was independently found to be in the 4−5 kpc range on the basis of the possible association with the supernova remnant G327.24−0.13 [68], and, more convincingly, from the analysis of multiple expanding rings around the source (due to scattering by different layers of interstellar dust of a bright burst emitted by the source on January 22, 2010; [71]). Several tens of bursts were also detected by Swift BAT for several weeks since the outburst onset, ensuring a reliable dataset to carry out time-resolved spectroscopy of the brightest events and to prove (or disprove) the findings inferred for SGR 1900+14. About 1300 spectra were analysed, similarly to the case of SGR 1900+14, in an automatic and systematic fashion (see [65] for the details). The radius and luminosity values were corrected for the distance of the source (we assumed 4.5 kpc) and were compared with those of SGR 1900+14 already presented in Figure 3 (rescaled to 15 kpc with respect to Figure 3). Figure 6 summarizes the comparison between the two sources. A number of properties can be immediately noticed: i) the datapoint distributions for the two sources in the kT versus R2BB plane are very similar, ii) the two distributions have a significant relative shift both

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in kT and R2BB, which could partially be caused by the different distances of the two sources iii) the “saturation” effect (the sharp edge in the distribution of datapoints described by the R2 = kT −3 relation) and the cut-off at around (10-15) keV is present in both sources, iv) the “saturation” is also clearly present in the Lhard versus Lsoft plane, where the Lsoft inferred for 1E 1547.0-5408 saturates at a flux of about 2 × 1040erg/s, a factor of 10 smaller then that of SGR 1900+14 [65]. While the greatest part of the above listed properties are not that unexpected, it is worth commenting on the overall shift of the Lsoft distributions. In fact, according to Eq. 6 the saturation occurs when the magnetic field ability to confine the fireball is itself saturated. It is therefore strictly dependent on the value of the magnetic field at the given radius. If this hypothesis is correct, then it would be possible to infer a number of properties comparing the distributions and checking that the so obtained results quantities (such as B or d) are in agreement with the same quantities obtained with different approaches (e.g. from timing analysis or other techniques). In particular, Eq. 6 can be rewritten in the following form ! !−1/2 !5/4 " # B sur f 1/4 RNS 5/8 d F max kT ≃ 0.4 × kpc keV 10km 1014G 10−5 erg/cm2 /s

(7)

where the flux and the distance have been explicitly reported (decoupling them from L and R). The importance of this relationship is that, if the magnetic field strength has been inferred by means of different techniques (timing analysis as an example) it is then possible to derive an approximate value for the distance by using the saturation flux value recorded for the sources. Viceversa, if the distance is known from other considerations (the presence of a supernova remnant as an example, or a dust-scattering X-ray rings) it is then possible to infer the magnetic field strength. In fact, due to the different power-law indices of the BB luminosity (kT −4 ) and of the saturation (kT −3 ) in the left panel of Figure 6, the cut-off value (around 1015 keV) of the the BBhard component represents the highest luminosity value observed from the given source. By inserting the (unabsorbed) bolometric fluxes (3 and 6 times 10−5 ergs cm−2 s−1 for SGR 1900+14 and 1E 1547.0-5408, respectively) and the kT values corresponding to the cut-off regions (∼13 keV and ∼11 keV for SGR 1900+14 and 1E 1547.0-5408, respectively) in relation (7) above, the following distance estimates are obtained: dS GR1900 ∼ 8.5 kpc and d1E1547 ∼ 4.0 kpc. Note that bona fide values of the magnetic field strength of ∼ 5 ×1014 G and ∼ 2.2 ×1014 G were assumed for SGR 1900+14 and 1E 1547.0-5408, respectively [72, 63]2 . It is worth noticing that the distance to SGR 1900+14 is highly uncertain, with only a lower limit of 5 kpc and a maximum possible distance in the 12-15 kpc range [57, 58]. On the other hand, 1E 1547.0-5408 has a reliable distance measurement obtained in two independent ways, SNR-association and dust (expanding) rings, both pointing to a distance in the 4-5 kpc range. These numbers corroborate the idea of using the saturation observed in magnetars as a powerful and alternative Note that both sources have displayed, during years, a relatively large range of P˙ values corresponding to an similarly large range of B values. This is particularly true for SGR 1900+14 for which values in between 2 and 8 times 1014 G were inferred for the magnetic field [72]. 2


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way of assessing either the distance or the magnetic field strength if one of the two quantities is already inferred independently. Since the distance is in many cases the quantity inferred with the largest uncertainty, the above relation is likely more suited for inferring the distance once B is known from the timing analysis, especially when the weak dependence of d on B in eq. 7 is considered. Acknowledgements This research is based on observations with the NASA/UK/ASI Swift mission. Authors acknowledge the support from ASI (ASI/INAF contracts AAE DA-044, DA-006 and DA-017 ). GLI thanks Dr. H. Kumar for providing Figure 5 with high resolution.

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Activated Magnetospheres of Magnetars Andrei M. Beloborodov

Abstract Like the solar corona, the external magnetic field of magnetars is twisted by surface motions of the star. The twist energy is dissipated over time. We discuss the theory of this activity and its observational status. (1) Theory predicts that the magnetosphere tends to untwist in a peculiar way: a bundle of electric currents (the “j-bundle”) is formed with a sharp boundary, which shrinks toward the magnetic dipole axis. Recent observations of shrinking hot spots on magnetars are consistent with this behavior. (2) Continual discharge fills the j-bundle with e± plasma, maintaining a nonthermal corona around the neutron star. The corona outside a few stellar radii strongly interacts with the stellar radiation and forms a “radiatively locked” outflow with a high e± multiplicity. The locked plasma annihilates near the apexes of the closed magnetic field lines. (3) New radiative-transfer simulations suggest a simple mechanism that shapes the observed X-ray spectrum from 0.1 keV to 1 MeV: part of the thermal X-rays emitted by the neutron star are reflected from the outer corona and then upscattered by the inner relativistic outflow in the j-bundle, producing a beam of hard X-rays.

1 Introduction Term “magnetars” was coined for neutron stars with ultrastrong magnetic fields B ∼ 1014 −1015 G (Duncan & Thompson 1992; Paczyński 1992). There is substantial evidence for ultrastrong fields in soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs) (see e.g. reviews by Woods & Thompson 2006; Mereghetti 2008). Alternative models for SGRs and AXPs are not discussed here. The current magnetar catalogue contains 18 objects (13 confirmed and 5 candidates).1 Host supernova remnants were identified for some of them, confirming their young ages t ∼ 103 − 105 yr. The young age, combined with the currently observed number of objects, implies that > ∼ 20% of all neutron stars are born as magnetars. Andrei M. Beloborodov Physics Department and Columbia Astrophysics Laboratory, Columbia University, 538 West 120th Street New York, NY 10027, e-mail: [email protected] 1

http://www.physics.mcgill.ca/ pulsar/magnetar/main.html

N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_24, © Springer-Verlag Berlin Heidelberg 2011

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The rotation rates of all observed magnetars are moderate by neutron-star standards. Their spin periods P are in a rather narrow range from 2 to 12 s. On the other hand, their spindown rates P˙ show large temporal variations, usually related to the X-ray outbursts. This activity contrasts with the traditional view of neutron stars as passive stellar remnants. Unlike ordinary pulsars, whose activity is associated with the open field lines that extend to the light cylinder, the magnetar activity must be generated in the closed magnetosphere. Its energy output greatly exceeds the rotational energy of the star and must be fed by magnetic energy. A distinct feature of these objects is their huge nonthermal luminosity, exceeding the spindown power by 1-3 orders of magnitude. Between the outbursts, magnetars display persistent or slowly decaying X-ray emission with luminosities L ∼ 1034 − 1035 erg s−1 . Two peaks are observed in the X-ray spectrum: one near keV and the other above 100 keV (see e.g. Kuiper et al. 2008). The energy fluxes in the two peaks are comparable. The keV peak is dominated by emission from the hot surface of the neutron star. The 100-keV component is clearly nonthermal and demonstrates the existence of a hot corona around magnetars, which provides a large fraction of the total observed luminosity. For comparison, the corona of the sun radiates only ∼ 10−6 of the solar luminosity. The observed magnetospheric activity must be generated by motions of the star surface. The crust of a magnetar is stressed by the ultrastrong magnetic field and can yield to the stresses through episodic starquakes or a slow plastic flow (Thompson & Duncan 1996). The magnetosphere is anchored in the crust and inevitably twisted by the crustal motions, resembling the behavior of the solar corona. It becomes non-potential, ∇ × B , 0, and threaded by electric currents (Thompson et al. 2002, hereafter TLK02; Beloborodov & Thompson 2007, hereafter BT07). The currents can flow only along B, and the twisted magnetosphere remains nearly force-free, j × B = 0. No quantitative theory has been developed for the crust motion in magnetars. The theory does not predict the geometry of the magnetosphere and its deformations, however, it is possible to predict what happens after a twist has been implanted. Part of the magnetosphere becomes filled with plasma and gradually dissipates the magnetic energy, creating a long-lived luminous corona. The theory of this activity can be tested with observations of the post-burst behavior of magnetars. Besides the nonthermal emission, bright hot spots are observed on magnetars after their bursting activity. The spots slowly shrink, on a timescale of months to years. Understanding this behavior may help reconstruct the geometry of the implanted twists and perhaps the crust motion that created them. The theory is developed in two steps. First, an electrodynamic model is formulated to describe the deformed magnetosphere and its evolution (§ 2). Second, basic properties of plasma filling the magnetosphere are evaluated (§§ 4 and 5). Observational tests of the theory are discussed in §§ 3 and 6. In this contribution, we focus on the X-ray emission mechanism in magnetars. The related topics of their spindown behavior and optical/IR/radio emission are discussed elsewhere in this volume.

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2 Electrodynamics of untwisting Twisted force-free magnetospheres were extensively studied in the context of the solar corona. In axial symmetry, they are described by the Grad-Shafranov equation, and various force-free equilibria can be constructed numerically by solving this equation. A simple example is a self-similarly twisted dipole (Wolfson 1995). Pavan et al. (2009) studied multipolar self-similar solutions. Realistic non-self-similar equilibria do not admit a simple description and are less explored, except for the case of weak twists (Wolfson & Low 1992; Beloborodov 2009, hereafter B09). The twisted magnetosphere stores additional energy – the magnetic energy of the electric currents maintaining ∇ × B. The magnetosphere tends to dissipate the stored energy and untwists with time. Apart from the rare flares, the evolution proceeds slowly through a sequence of force-free equilibria. A key agent in this evolution is the moderate electric field Ek parallel to B. It has three important functions (BT07): (1) maintains the current flow, (2) regulates the dissipation rate E k j and the observed luminosity, and (3) determines the evolution of B in the untwisting magnetosphere. This section describes the untwisting theory for axisymmetric magnetospheres. A simple electrodynamic equation governs the evolution of B.

2.1 Evolution equation for axisymmetric twist Any axisymmetric magnetic field B may be expressed in the following form, B=

∇ f × eφ + Bφ eφ . 2πr sin θ

(1)

Here r, θ, φ are spherical coordinates, φ is the angle of rotation about the axis of symmetry, and eφ is the unit vector in the φ direction. For example, a dipole magnetosphere with dipole moment µ has f (r, θ) = 2πµ sin2 θ/r and Bφ = 0. Function f (r, θ) has the meaning of the magnetic flux through the circle 0 < φ < 2π of constant r and θ. Note that f is constant along any field line ( B · ∇ f = 0) and by symmetry f is also constant on any 2D “flux surface” formed by rotating a field line about the symmetry axis. Any axisymmetric magnetosphere can be thought of as a set of nested flux surfaces labeled by f . Note that f = 0 on the axis. If Bφ = 0 then the axisymmetric magnetosphere is potential, ∇× B = 0, and carries no electric currents. Any axisymmetric starquake is, in essence, a latitude-dependent rotation of the crust. It inevitably imparts a twist into the magnetosphere. Its amplitude is measured by the azimuthal extension of field lines outside the star, ψ( f ) = φ Q − φP =

Z

Q P

Bφ dl , B r sin θ

(2)

where the intergal is taken along the field line between its footprints P and Q on the star surface. The appearance of Bφ , 0 implies a non-zero circulation of B along cir-

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z P1 P2 Fig. 1 Field line C1 with footprints P1 , Q1 on a flux surface f1 and its neighbor field line C2 with footprints P2 , Q2 on a flux surface f2 . Closed contour C is formed by connecting P1 with P2 and Q1 with Q2 along the star surface.

Q2 Q1

C2

C1

cles of constant r, θ. The circulation must be sustained by an electric current through the circle, according to Stokes’ theorem. Current can flow only along B and must be maintained by a longitudinal voltage, Φe =

Z

Q P

E k dl,

(3)

where Ek is the electric field component parallel to B. Note that both footprints P, Q of the field line are “grounded” in a good conductor — the neutron star — and the electrostatic voltage between P and Q is negligible. Voltage Φe is inductive, not Relectrostatic. RIt is directly related to the rate of untwisting of the magnetic field, E k dl = c−1 (∂Ak /∂t) dl where A is the magnetic vector potential (BT07). The gradual dissipation of the magnetospheric twist is, in essence, Ohmic dissipation in the electric circuit. The dissipation rate is proportional to Φe . How does the twist ψ( f ) evolve as a result of Ohmic dissipation? The electrodynamic equation ∂ B/∂t = −c∇ × E states that electric field determines the evolution of magnetic field. Its integral version (Faraday’s law) can be used to derive the evolution equation for ψ. Consider two infinitesimally close field lines C1 and C2 on different flux surfaces f1 and f2 = f1 + δ f . A closed contour C can be formed by connecting the footprints along the stellar surface: P1 with P2 and Q1 with Q2 (Fig. 1). Let δΦ be the magnetic flux through contour C. The Faraday’s law states I Z Z 1 dδΦ =− E · dl, = Ek dl − E k dl, (4) c dt C C2 C1 where we neglected the infinitesimal contribution from curves P1 P2 and Q1 Q2 to the H line integral C . Only Bφ contributes to flux δΦ. This can be seen if we continuously deform C1 and C2 so that their points slide at constant r, θ in the φ-direction until both C1 and C2 end up in one meridional plane φ = 0. In this deformation, C1 and C2 slide along their flux surfaces f1 and f2 , and hence δΦ remains unchanged by the deformation (magnetic flux through any part of a flux surface is zero). Only Bφ


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contributes to the magnetic flux through the deformed contour in the meriodinal plane. One can show that δΦ is related to the twist angle ψ( f ) by δΦ =

ψ( f ) δ f . 2π

(5)

This geometrical identity gives a quick way to derive the evolution equation for ψ( f , t). Combining equations (3), (4), and (5) we immediately obtain2 ∂ψ ∂Φ = 2πc e . (6) ∂t f ∂f

Here we used d/dt = (∂/∂t) f taking into account that contour C remains on the same flux surfaces f , f + δ f as the magnetosphere untwists (the flux surfaces can change their shapes in the evolving magnetosphere). Equation (6) describes the twist evolution assuming that the footprints of field lines are frozen in the static crust of the star. The untwisting of field lines is due to their “slipping” in the magnetosphere, which changes the connectivity between the footprints so that ψ is reduced. It is straightforward to generalize the evolution equation for magnetospheres with moving footprints, ∂ψ ∂Φe = 2πc + ω( f, t), ∂t ∂f

(7)

where ω = dφ Q/dt − dφ P/dt is the differential angular velocity of the moving crust.

2.2 j-bundle Equation (6) has an interesting feature: the evolution of ψ on a given flux surface f is governed by the transverse gradient of the voltage ∂Φe /∂ f rather than its value Φe ( f ). This leads to a paradoxical result: if Φe ( f ) = const i.e. the voltage is the same for all field lines, then the twist must “freeze” — the magnetic configuration does not change with time. How can this be reconciled with the continuing Ohmic dissipation in the electric circuit Φe j , 0? The circuit is ought to dissipate the magnetic (twist) energy, and the unchanged B appears to violate energy conservation. The paradox is resolved if one notices that Φe cannot be the same for all field lines. In particular, field lines f > fR are confined inside the star where Ek ≈ 0. To fix ideas, suppose the star is a perfect conductor, which implies Φe ( f ) = 0 for f > fR . Only field lines extending beyond the stellar surface, i.e. forming the magnetosphere, have Φe , 0, which implies a gradient ∂Φe /∂ f , 0 near the flux surface f = fR . Then the twist evolution equation (6) implies that ∂ψ/∂t < 0 is maintained 2

This evolution equation was derived in B09 for weak twists ψ ≪ 1. As the derivation here shows, the same equation is also valid for strong twists. Equation (17) in B09 is not accurate for strong twists, it neglects the motion of flux surfaces in the process of untwisting.

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near f = fR . Effectively, the magnetospheric electric currents are “sucked” into the star through the flux surface fR . This behavior is demonstrated by the explicit solutions to the evolution equation (6) in B09. There is another nontrivial feature of the untwisting process. Under normal conditions, plasma density in the closed magnetosphere3 is not sufficient to conduct interesting electric currents. Plasma in the twisted magnetosphere is supplied by a continual discharge, which has a threshold voltage Φe = V( f ) ∼ 109 V (BT07). The voltage is well described by a step function (see § 3 for details),   V j>0    0 j=0 Φe =  (8)    −V j < 0

The threshold nature of the discharge has a rather peculiar implication. Two distinct regions immediately form in an untwisting magnetosphere: “cavity” near the flux surface fR and “j-bundle” where j , 0 (see B09 and Fig. 2). The two regions are separated by a sharp boundary along a flux surface f⋆ . The untwisting process is the slow motion of the boundary f⋆ that gradually erases the remaining electric currents. The erased magnetospheric currents end up closed below the stellar surface. If the discharge voltage V( f ) = const, the twist freezes in the j-bundle f < f⋆ and passively waits for the front f⋆ to come. Realistically, V( f ) , const and dV/d f > 0 is possible. Then equation (6) gives ∂ψ/∂t > 0, i.e. the twist grows inside the jbundle while waiting for the front to come. In all cases, the magnetic energy of the shrinking j-bundle decreases with rate equal to the rate of Ohmic dissipation. The behavior of untwisting magnetospheres is illustrated in B09 by solving the electrodynamic equation (6) for a concrete configuration: a centered dipole with a weak twist ψ < 1. The “cavity + j-bundle” structure forms immediately, and then the cavity gradually expands, while the twist angle ψ inside the j-bundle grows linearly with time. This growth leads to ψ > 1 where the model breaks. General considerations (e.g. Uzdensky 2002) show that the magnetosphere with ψ > ψcr = O(1) must lose equilibrium and restructure itself. Two possible types of restructuring are known: (1) Partial opening of field lines, which can lead to a configuration with lower energy (Wolfson & Low 1992). In an axisymmetric magnetosphere, this change may occur without breaking the symmetry. (2) Kink instability, which breaks the axial symmetry. Then an asymmetric plasmoid must be ejected by the magnetosphere and the twist amplitude must be reduced. The exact threshold for the kink, the energy of the ejected plasmoid, and the new equilibrium configuration following the kink are unknown. One can expect that the amplitude of the growing twist is regulated by the instability so that it remains close to the critical value ψ ∼ 1. The j-bundle and its footprints can be a bright source of radiation, with luminosity equal to the rate of Ohmic dissipation in the bundle. If the footprint of the j-bundle experiences heating by the bombarding magnetospheric particles (BT07) then f⋆ defines the boundary of a hot spot on the star θ < θ⋆ . The area of this spot is given 3

The usual estimate for plasma density is ρGJ /e where ρGJ = −Ω · B/2πc is the charge density induced by rotation of the star with an angular velocity Ω (Goldreich & Julian 1969).


305

Fig. 2 Snapshot of the magnetospheric evolution. A global twist with a moderate ψ = 0.2 was implanted into the magnetosphere at t = 0, and the snapshot shows the magnetosphere at t ∼ 1 yr. Details of the calculations are described in B09. The plane of the figure is the poloidal cross section of the magnetosphere. The black curves are the poloidal magnetic field lines; they are symmetric about the vertical axis and the equatorial plane. Left panel: current density. The cavity is shown in white ( j = 0); its boundary f⋆ is marked by the magenta curve. The cavity expands with time, and the j-bundle shrinks toward the vertical axis. Right panel: twist amplitude ψ at the same time. The neutron star is shown by the black circle.

by

A ≈ π(R sin θ⋆ )2 = πR2 u⋆ .

(9)

Here we used the dimensionless variable u = f / fR and approximated the poloidal structure of the magnetosphere by the dipole field.4 As the cavity expands in an untwisting magnetosphere (Fig. 2), the spot θ < θ⋆ shrinks. The simplest model with V(u) = const gives the following estimate for the jbundle luminosity (B09), L = VI⋆ ≈

u 2 cµ ⋆ 2 34 ψ V u ≈ 1.3 × 10 V B R ψ erg s−1 , 9 14 6 ⋆ 0.1 4R2

(10)

where V9 ≡ V/109 V and B14 = Bpole /1014 G. The evolution timescale of the luminosity is given by u L µu⋆ ⋆ tev = − ≈ ≈ 1.5 V9−1 B14 R26 ψ yr. (11) dL/dt cRV 0.1 Similar calculations have been done for the more detailed model where voltage V is different on different field lines (B09). The theoretical expectations are compared with observations in the next section. Dipole field has f /2π = µ sin2 θ/r = µ/Rmax , where µ is the magnetic dipole moment. Then u = R/Rmax = sin2 θ1 where θ1 is the polar angle of the field-line footprint on the stellar surface. 4

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3 Transient magnetars Recent observations revealed that many magnetars spend a significant fraction of time in a quiescent state with a low luminosity L ∼ 1033 − 1034 erg s−1 and remain unknown until they produce an X-ray outburst. The post-outburst decay of the luminosity back to the quiescent level is monitored in these “transient magnetars.” The data can be compared with the theoretical model of untwisting magnetosphere.

3.1 Magnetospheric activity or deep crustal heating? The mechanism of the magnetar bursts (e.g. Thompson & Duncan 1995; Woods & Thompson 2006) is not settled yet. It may be associated with starquakes. It may also be associated with sudden reconnection events in the magnetosphere that is slowly deformed by the plastic crustal flow (Lyutikov 2003). In either case, a strong and brief magnetospheric dissipation is invoked to explain the burst emission. Following the burst, a bright afterglow is observed, which continues to decay for months to years. The blackbody area of this emission is much smaller than the surface area of the neutron star, and it can be associated with the hot footprint of the j-bundle in the untwisting magnetosphere. This model relies on the external heating of the stellar surface by the energetic particles accelerated in the j-bundle. An alternative to external heating was considered by Lyubarsky et al. (2002). Their model assumed that during the burst a significant heat is deposited inside a deep region of the stellar crust. The subsequent passive cooling of this region due to heat diffusion through the crust can produce a bright thermal afterglow. Its expected spectrum is quasi-blackbody. Observations of several transient magnetars in the past few years give enough information to judge which of the two heating mechanisms — external or internal — is responsible for the long-lived afterglow. Two features point to external heating. • Nonthermal X-ray spectrum. The X-ray emission shows significant deviations from blackbody (BB) and is usually fitted by BB + power-law model. A highenergy X-ray component was discovered in the transient magnetar 1E 1547.05408 (Enoto et al. 2010a). Its luminosity is comparable to the luminosity of the blackbody component, and the overall spectrum of 1E 1547.0-5408 was similar to the spectra of magnetars with persistent coronal activity. The energy dependence of pulse profiles resembled that of persistent emission in 4U 0142+61 and 1RXS J170849-400910 (den Hartog et al. 2008a,b), suggesting a similar magnetospheric emission mechanism. In another transient magnetar SGR 0501+4516, bright 100-keV emission was reported at t = 4 d after the outburst (Enoto et al. 2010b), with a similar spectrum. • Shrinking area of the hot spot. The emission area of the blackbody component A decreases following the outburst together with its luminosity L. The transient blackbody emission evolves along tracks in the A-L plane as seen in Figure 3.


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Fig. 3 Area A and luminosity L of the hot spots observed on five transient magnetars at different times following their outbursts; see text for references and discussion of the individual objects. One can see from the figure that the spot area decreases together with its luminosity. The j-bundle model is shown by the strip between the two lines. It predicts the relation L = 1.3 × 1033 B14 R−3 V9 ψ A211 erg s−1 . 6 B14 R−3 V ψ = 1 on the lower 9 6 line and 20 on the upper line.

The tracks are inconsistent with the model of impulsively heated deep crust, as cooling due to heat diffusion would give a hot spot that tends to spread with time, not shrink. The shrinking spot is consistent with the untwisting magnetosphere model (§ 2.2). The theoretical relation between A and L (obtained from eqs. 9 and 10, see caption to Fig. 3) appears to agree with the data. Caution should be taken though when interpreting the details in Figure 3, as there may be significant systematic errors in observed A — it depends on the details of spectral fits. Besides, the distance d is poorly known for many magnetars. Note, however, that the shape of the observed track in the A-L plane does not depend on d, because both A and L scale as d2 . These observations do not rule out deep crustal heating during the burst. The internal heating may dominate the thermal afterglow during first few days following the burst. After a few days, the observed light curve significantly flattens (Woods & Thompson 2006), suggesting a possible transition from internal to external heating.

3.2 Individual objects XTE J1810-197 is a canonical transient magnetar. It has spin period P = 5.54 s and magnetic dipole moment µ ≈ 1.5 × 1032 G cm3 , which corresponds to the surface field B ≈ 3 × 1014 G. An X-ray outburst was detected from this object in January 2004 (Ibrahim et al. 2004) and then its luminosity approximately followed an ex-

308

Andrei M. Beloborodov Fig. 4 Comparison of the model with the observed evolution of the area A and luminosity L of the hot spot after the outburst in XTE J1810-197. The data (open squares) are from Gotthelf & Halpern (2007). Dashed line shows the object luminosity in quiescence. Solid curves show the proposed theoretical model. The starquake occurred in the region u < u0 = 0.15 with amplitude ψ0 = 0.5. The discharge voltage is assumed to drop linearly from 5.5 GeV at u = 0.15 to 1 GeV at u = 0. (From B09.)

ponential decay on a timescale of 233 days for 3 years (Gotthelf & Halpern 2007). All data points for this object in Figure 3 were taken during the afterglow of this outburst. Remarkably, the source switched on as a bright radio pulsar (Camilo et al. 2007). The radio observations provided an estimate for the distance d = 3.3 kpc (which is used in Fig. 3) and accurate measurements of the spindown rate. In a few years, the object returned to its quiescent (pre-outburst) state: the radio pulsations and the spindown enhancement gradually disappeared, and the X-ray luminosity decreased to its quiescent level. These observations show that the magnetosphere of XTE J1810-197 changed in the outburst. Its footpoints must have moved, imparting a twist in the magnetosphere. The data give significant hints about the twist geometry and evolution: (1) The change in spindown rate suggests that the open field-line bundle was strongly affected, and hence the twist reached large amplitudes ψ > ∼ 1 near the magnetic dipole axis. Recall also that ψ is limited to ψcr = O(1) by the MHD instability. (2) The luminosity was observed to decrease from ∼ 1035 erg/s to ∼ 1033 erg/s. The theoretically expected luminosity from a global twist with ψ ∼ 1 would be much higher: L ∼ 1037 V9 erg/s (eq. 10). We conclude that the twisted region was small: the current-carrying field lines formed a narrow bundle emerging from a small spot on the star surface.


309

(3) The spot was discovered: a hot blackbody component with a small emission area was found in the X-ray spectrum following the outburst (Gotthelf & Halpern 2007; Perna & Gotthelf 2008; Bernardini et al. 2009). Its emission area shrank with time until the spot became undetectable (Fig. 4). (4) The X-ray and radio pulse profiles had almost simultaneous peaks, consistent with the X-ray emitting spot being on the magnetic dipole axis (Camilo et al. 2007). This behavior is consistent with the untwisting magnetosphere model described in § 2. The theoretical estimates for A, L, and tev (eqs. 9, 10, 11) are in remarkable agreement with the data. Figure 4 compares the detailed model with observations of XTE J1810-197. The data constrain the magnetospheric voltage V to be between 1 and 6 GeV, which is close to its expected theoretical value (§ 4). 1E 1547.0-5408 is known as the magnetar with the shortest spin period P = 2 s. Its estimated magnetic field is B ∼ 2 × 1014 G. The object shares many features of XTE J1810-197. A similar dynamic hot spot was detected (Halpern et al. 2008). The data points for 1E 1547.0-5408 in Figure 3 assume d = 4 kpc following Tiengo et al. (2010). One data point shows a pre-outburst state and two points show the decay after the outburst in 2007. The spot size was decreasing, however later the luminosity and the spot grew again. In October 2008 new burst activity was detected, the emission area quickly increased to A ≈ 1012 cm2 and remained approximately constant for 20 days (Israel et al. 2010). A similar luminosity and area were observed after the outburst in January 2009 (Enoto et al. 2010a); this gave another data point in Figure 3. The activity level of 1E 1547.0-5408 is clearly higher than that of XTE J1810-197. Apparently, many deformation events occurred in its magnetosphere in the past few years, and it may be hard to see the long-timescale untwisting behavior because it is interrupted by new bursting activity. CXOU J164710.2-455216 is a transient magnetar with spin period P = 10.6 s and magnetic field B ∼ 9 × 1013 G. Its outburst in September 2006 was accompanied by the increase of persistent luminosity from ∼ 1033 erg s−1 to ∼ 1035 erg s−1 (Muno et al. 2007). The subsequent slow decay of emission was observed for about 150 days (Woods et al. 2010). All eight data points for this object in Figure 3 are based on these observations; distance d = 5 kpc was assumed following Muno et al. (2007). The decay timescale is comparable to that in XTE J1810-197. SGR 0501+4516 was discovered due to its bursting activity in August 2008 and then its post-burst behavior was observed (Rea et al. 2009). The results of these observations are shown by the five data points in Figure 3, assuming d = 5 kpc. The object has spin period P = 5.7 s and magnetic field B ∼ 2 × 1014 G. Its postoutburst track in Figure 3 is consistent with a shrinking hot spot on the star. The track is close to that of XTE J1810-197. The luminosity decayed on a timescale of ∼ 24 days, about 10 times faster than in XTE J1810-197. This behavior is consistent with the j-bundle model if the voltage V in SGR 0501+4516 is ∼ 3 times higher and the twist amplitude ψ is ∼ 3 times smaller than the corresponding parameters in XTE J1810-197. This difference in parameters may not affect much the track in the

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A-L plane since L ∝ ψ V (eq. 10). At the same time, it explains the short evolution timescale since tev ∝ ψ−1 V (eq. 11).

SGR 0418+5729 was discovered due to its outburst in 2009 and its post-outburst behavior was followed for 160 days (Esposito et al. 2010). Its track in the A-L plane is shown in Figure 3 assuming a distance d = 5 kpc. The object has spin period 13 P = 9.1 s and magnetic field B < ∼ 3 × 10 G. The low magnetic field (by magnetar standards) makes this object special, which could explain the offset of its track from the tracks of other transient magnetars. Note also that the track location would be different for different d. A large distance d ∼ 15 kpc would imply ∼ 10 times larger L and A, and would place the track of SGR 0418+5729 into the strip between the two lines in Figure 3. The timescale of the post-burst decay is a few months (the luminosity decreased by a factor of 6 in four months). SGR 1627-41 is another transient magnetar whose spin period and magnetic field are close to those of 1E 1547.0-5408. The object displayed bursting activity in 1998 and then its luminosity gradually decayed toward the quiescent state with no new bursts detected until 2008 (Kouveliotou et al. 2003; Mereghetti et al. 2006; Esposito et al. 2008). The luminosity decayed in ∼ 3−5-years, with a light curve similar to the post-outburst behavior of XTE J1810-197. The published spectral analysis provides almost no information on the blackbody emission area in this object except for one XMM observation when the source luminosity was only 4 × 1033 erg −1 (Mereghetti et al. 2006). A large fraction of observed magnetars are persistent bright sources with luminosities L ∼ 1035 erg s−1 . The 100-keV emission component was observed in several of these “persistent magnetars,” indicating quasi-steady magnetospheric activity 12 2 (Kuiper et al. 2008). Their blackbody components have emission areas A > ∼ 10 cm (e.g. Perna et al. 2001), significantly larger than in transient magnetars with similar luminosities L ∼ 1035 erg−1. The reason for this difference is presently unclear. Quasi-steady magnetospheric emission is expected if the twist decay timescale tev is longer than the timescale of the crust motion imparting the twist. Note that tev may be long if the voltage along the twisted field lines is somewhat below 109 V and/or the magnetic flux in the j-bundle is large (i.e. u⋆ is large, cf. eq. 11). Moreover, it is possible that the j-bundle is persistently deformed by the plastic flow of the crust, and a quasi-steady twist is maintained near the threshold of MHD stability, ψ ∼ 1. The luminosity of persistent magnetars L ∼ 1035 erg s (e.g. Durant & van Kerkwijk 2006) is consistent with a twist created by rotation of a small cap on the star, 12 with area A < ∼ 10 cm (see eq. 10 and B09). Apparently, the footprints of the jbundle in persistent magnetars are not strongly heated, as no hot spots with small A were detected in these objects. Persistent magnetars also display sudden increases and gradual decays of luminosity. For example, the outburst of SGR 1900+14 in 1998 led to a rise in its persistent luminosity, and in a few months it decayed back to the pre-outburst level (Woods et al. 2001). Similar behavior was observed in AXPs, for instance in 1E 2259+586 (Woods et al. 2004) and 4U 0142+61 (Gavriil et al. 2009; Gonzalez et al. 2010). The rise in luminosity and its subsequent decay was reported for 1E 1048.15937 (Dib et


311

al. 2009). The transient behavior in these objects is not necessarily associated with the same j-bundle that creates their persistent activity. The additional energy may be released on different field lines and after their untwisting the object returns to the pre-outburst persistent state. The timescale for this additional activity depends on the voltage, twist amplitude, and magnetic flux of the transiently deformed field lines. The variations in tev may be similar to those in transient magnetars – at least a factor of 10. Observations of PSR J1846-0258 suggest that the transient activity of the closed magnetosphere may also occur in rotation-powered pulsars (Gavriil et al. 2008).

4 Pair creation Magnetospheric activity manifests itself through relativistic particles that can bombard the stellar surface and also generate nonthermal emission. We now discuss the origin of these particles, their energies, number, and circulation in the magnetosphere. Particles are accelerated along the magnetic field lines by the longitudinal voltage R Φe = Ek dl. The particles can resonantly scatter the stellar photons of energy h¯ ω once they reach the Lorentz factor 3

γ ≈ 10 B15

h¯ ω 10 keV

!−1

,

(12)

which requires Φe ∼ 109 B15 (¯hω/10 keV)−1 V. The scattered photons are boosted in energy by the factor of ∼ γ2 . These high-energy photons convert to e± pairs off the magnetic field, creating more particles. A similar process of e± creation operates in the polar-cap discharge of ordinary pulsars, but in a different mode. In ordinary pulsars, the high-energy photons convert to e± with a delay. The scattered photon initially moves nearly parallel to B and converts to e± only when it propagates a sufficient distance where its angle θγ with respect to B increases so that the threshold condition for conversion is satisfied. This delay leads to the large unscreened voltage in the polar-cap models for pulsars. In contrast, the magnetic field of magnetars is so strong that pair creation can occur immediately following resonant scattering (BT07). The energy of the scattered photon is related to its angle θγ by   1/2  m2e c4 2   E B   2 E(θγ ) = 1 − cos θγ + 2 sin θγ   , EB sin2 θγ

(13)

where E B = (2B/B Q + 1)1/2 me c2 is the energy of the first Landau level and BQ = m2e c3 /¯he ≈ 4.4 × 1013 G. The scattered photon may immediately be above the threshold for conversion, E > Ethr = 2me c2 / sin θγ , if B > 4BQ. This suggests that e± discharge in magnetars screens E k more efficiently and buffers the voltage growth.

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Pair creation on field lines with apexes Rmax < ∼ 2R

The discharge on closed field lines can be explored using a direct numerical experiment where plasma is represented by a large number of individual particles. The existing numerical simulations (BT07) describe the discharge on field lines that extend to a moderate radius Rmax < ∼ 2R, where R is the radius of the neutron star. The magnetic field is ultrastrong everywhere along such field lines, B ≫ B Q, and resonant scattering events may be effectively treated as events of pair creation – a significant fraction of scattered photons immediately convert to e± . The simulations demonstrate that voltage and pair creation self-organize so that a particle scatters on average ∼ 1 photon as it travels through the electric circuit, maintaining the near-critical multiplicity of pair creation M ∼ 1. This criticality condition requires voltage V ∼ 109 V, which accelerates e± particles to Lorentz factors γ ∼ 103 . The electric circuit operates as a global discharge, in the sense that the accelerating voltage is distributed along the entire field line between its footprints on the star. It is quite different from the localized “gap” that is often pictured above polar caps in pulsars. The discharge fluctuates on the light-crossing timescale ∼ R/c and persists in the state of self-organized criticality. The behavior of the circuit resembles a continually repeating lightning: voltage between the footprints of the field line quasiperiodically builds up and discharges through enhanced production of charges. The average plasma density in the circuit n is close to the minimum density nmin = j/ec, as required by the criticality condition M = n/nmin ∼ 1. As discussed in § 2.2, the currents tend to be quickly erased on field lines with small Rmax . It may be that this part of the magnetospheres of observed magnetars is potential, ∇ × B = 0, with no discharge. Then the observed activity is associated with currents on field lines with large Rmax , i.e. extending far from the star. Pair creation on field lines with apexes Rmax ≫ R

The discharge on extended field lines is likely to have a similar threshold voltage V ∼ 109 V, because the conversion of upscattered photons to e± is efficient near the footprints where B ≫ B Q. In this zone, particles are able to resonantly scatter soft X-rays once they are accelerated to γ ∼ 103 (cf. eq. 12), which requires voltage ∼ 109 V. Further growth of voltage should be stopped as it would cause the excessive creation of e± moving in both directions, toward and away from the star, leading to efficient screening of E k . The discharge is expected to occur near the star, and some of the created particles outflow to r ≫ R along the extended field lines. The rate of resonant scattering by a relativistic particle increases as it moves from B ≫ BQ to B < ∼ B Q. The particle scatters many more photons, because the resonance condition shifts toward photons of lower energy h¯ ωres ∝ B whose number density is larger. Note also that the effective cross section for resonant scattering, σres = 2π2 re c/ωres increases as B−1 . Photons 12 ± scattered in the region B > ∼ 10 G convert to e , which scatter more photons. In essense, the particles outflowing from the discharge zone lose energy to scattering as they enter weaker fields, and this energy is transformed to new generations


313

of e± . A similar cascade above polar caps of pulsars was studied recently by Medin & Lai (2010). As a result, the e± multiplicity of the outflow increases from M ∼ 1 to M ≫ 1.5 It means no charge starvation in the outer corona — there are plenty of charges to conduct the current demanded by the twisted magnetic field.

5 Plasma circulation in the magnetosphere Dynamics of the e± flow in the outer corona (r ≫ R) is strongly influenced by resonant scattering, which exerts a strong force F on the particles along the magnetic field lines. F vanishes only if the particle has the “saturation momentum” p⋆ such that the radiation flux measured in the rest frame of the particle is perpendicular to B. In a weakly twisted magnetosphere with approximately dipole magnetic field exposed to central radiation p⋆ is given by6 p⋆ (r, θ) =

2 cos θ sin θ

(14)

(momentum in units of me c). The radiative force always pushes the particle toward p = p⋆ . This effect may be measured by the dimensionless “drag coefficient,” D≡

rF . p me c2

(15)

Momentum p⋆ is a strong attractor in the sense that deviations p − p⋆ generate D ≫ 1 in the outer corona. Consider a steady e± outflow in the outer region where no new pairs are produced. The outflow satisfies two conditions: (a) it is nearly neutral, n+ ≈ n− , and (b) it carries the electric current j demanded by ∇× B. Electric field E k immediately reacts to violations of these conditions and enforces them. From (a) and (b) one can derive the relation between the velocities β± of e± (details are given in Beloborodov 2010), 1−

β− 2 = . β+ M + 1

(16)

Here “+” corresponds to positrons, which carry current j+ > 0 and “−” corresponds to electrons, which carry j− < 0; we assume a positive net current j = j+ + j− for definiteness. The multiplicity is defined by M = ( j+ + | j− |)/ j. An electric field Ek must be generated in the outflow to sustain the condition (16) against the radiative drag that tends to equalize β− and β+ at β⋆ . This electric field is generated by a small deviation from neutrality, δn = n+ − n− ≪ n+ . 5

A steady relativistic outflow without pair creation would have M = const along the field lines. This follows from conservation of magnetic flux, charge, and particle number, which give n/B = const, j/B = const, and n/ j = const along a field line. 6 This expression is valid in the region where 1 − B /B > (R/r)2 . In this region, stellar radiation r may be approximated as a central flow of photons, neglecting the angular size of the star ∼ R/r.

314


Fig. 5 Lorentz factors γ+ (left panel) and γ− (right panel) in the two-fluid model of outer corona. In this example, the electric current is carried by the e± outflow of a fixed multiplicity M = 50. The plasma is injected at radius r = 2R and outflows along the magnetic field lines (white curves). The flow is illuminated by the star with temperature kT = 0.5 keV (magenta circle at the origin), which exerts radiative forces F (γ± ) on the e± plasma. The Lorentz factors γ+ and γ− change as the flow enters the drag-dominated region |D| ≫ 1. The region |D| > 3 is shown by the thick black curve and shadowed in black. D < 0 for positrons (γ+ > γ⋆ ) and D > 0 for electrons (γ− < γ⋆ ). The radiative drag stops the plasma in the equatorial plane outside ∼ 8R. A nearly dipole magnetic field (weakly twisted) with Bpole = 1015 G is assumed in this example. R is the neutron-star radius.

The two-fluid dynamics of the outflow is governed by equations, me c2

dγ+ = F (γ+ ) + eE k, dl

me c 2

dγ− = F (γ− ) − eEk , dl

(17)

where l is the length measured along the magnetic field line. Since γ− and γ+ are not independent — they are related by condition (16) — it is sufficient to solve one dynamic equation, e.g. for γ+ (and use the dynamic equation for γ− to exclude E k ). Straightforward algebra gives, me c 2

dγ+ F (γ+ ) + F (γ− ) = , dl 1 + dγ− /dγ+

dγ− M−1 = dγ+ M+1

!2

γ− γ+

!3

.

(18)

In the region of strong drag, |D| ≫ 1, one finds F (γ+ ) ≈ −F (γ− ) ≈ −eE k . Here both e+ and e− components of the outflow have velocities that are “locked” by the balance of two strong forces — radiative and electric. To illustrate the drag effect on the e± flow around magnetars, consider the following simplified model. Suppose that the e± plasma is injected near the star with


315

a given multiplicity, e.g. M = 50, and a given high Lorentz factor, e.g. γ+ = 100. The corresponding γ− is determined by equation (16). Suppose that the plasma is illuminated by the blackbody radiation of the star of temperature kT = 0.5 keV and neglect the radiation from the magnetosphere itself (see below). The steady-state solution for γ± established in the outer corona is shown in Figure 5. The solution is not sensitive to the precise radius of e± injection as long as it is small enough, before the plasma enters the drag-dominated region. The most significant electric field develops in the region where |D| ≫ 1. It is given by eEk ≈ −F (γ+ ), and the corresponding longitudinal voltage establishedR in the outer corona is found by integrating F (γ+ ) along the field line, eΦe ≈ − F (γ+ ) dl. Its typical value for the model in Figure 5 is ∼ 107 V. Flows with lower M develop stronger electric fields, however in all cases of interest (M ≫ 1) the drag-induced voltage is below 109 V. The calculations shown in Figure 5 assume that the plasma is optically thin to resonant scattering. This is not so for real magnetars. TLK02 showed that the optical depth of a strongly twisted magnetosphere is comparable to unity. When the large pair multiplicity M is taken into account, the estimate for the optical depth becomes τ∼

Mψ ≫ 1. β±

(19)

The large optical depth has two implications. First, there is a lot of scattered radiation in the magnetosphere, which is quasi-isotropic. This increases the drag and reduces p⋆ . Second, there is a self-shielding effect: the drag force F experienced by an electron (or positron) is reduced by the factor of τ−1 . These two effects will change γ± (r, θ) shown in Figure 5. However, the main feature will persist: the outflow remains to be drag-dominated in the equatorial region at r ∼ (10 − 20)R. The initial momentum of the e± flow ejected from the discharge zone to the outer corona is taken away by the radiative drag and the e± pairs accumulate near the apexes of the closed magnetic field lines. The pairs annihilate there. The annihilation rate is given by N˙ ann ≈ 2M(I/e). Here I is the electric current through the annihilation region, I ∼ (ψcµ/4R21 ), ψ is the twist amplitude, R1 is the inner boundary of the annihilation region, and µ is the magnetic moment of the star. The corresponding annihilation luminosity is given by Lann = 2me c2 M

R −2 I 1 ∼ 4 × 1031M ψ µ32 erg s−1 . e 8R

(20)

The proposed picture of the magnetar corona is schematically shown in Figure 6. The exact position R1 of the boundary between the two regions in Figure 6 has not been calculated and may be inside 8R. Consider, for instance, the plasma flow along the field lines with Rmax = 5R. It experiences scattering with rate that is high enough to generate a large e± multiplicity, however, not enough to bring the plasma to a stop at the equatorial plane. The opposite flows in the northern and southern hemispheres meet in the equatorial plane and try to penetrate each other. The two-stream instability then develops and a strong Langmuir turbulence is generated, which will inhibit the penetration. Effectively, the opposite flows collide in the equatorial plane and

316


+

−

+−

+

−

− Fig. 6 Schematic picture of plasma circulation in the magnetosphere with surface B ∼ 1015 G. Two regions are indicated. (1) “Inner corona.” Here e± have a moderate multiplicity M ∼ 1. The particles do not stop in the equatorial plane. The electric field Ek ensures that electrons and positrons circulate in the opposite directions along the magnetic field lines, maintaining the electric current demanded by ∇ × B. The particles are lost as they reach the footprints of the field line and continually replenished by pair creation. (2) “Outer corona” — extended field lines with Rmax ≫ R. Electrons and positrons are created by the discharge near the star and some of them flow outward to the region of weaker B. Here resonant scattering enhances the pair multiplicity, M ≫ 1, and decelerates the outflow. The e± particles stop at the apexes of magnetic field lines (blue region in the equatorial plane), accumulate, and annihilate there. The number fluxes of electrons and positrons toward the annihilation region differ by a small fraction ∼ M−1 , so that the outflow carries the required electric current j = (c/4π)∇ × B.

should stop there. This behavior contrasts with the inner corona where the counterstreaming e− and e+ never stop; their circulation is maintained by the induced electric field. The outer corona is different because of its high pair multiplicity M; then the electric current is organized while both e− and e+ outflow from the star. The above analysis assumed a steady e± outflow. Then the current is organized by locking the electrons and positrons at two different velocities β− and β+ . In reality, the two-fluid flow is prone to two-stream instability that generates strong Langmuir waves and broadens the momentum distribution of e± . The robust generation of plasma waves gives a mechanism for low-frequency emission from magnetars (different from drag-induced waves in normal pulsars, cf. Lyubarsky & Petrova 2000). The instability has been simulated numerically, and the results are described in detail elsewhere (Beloborodov 2010). The fluctuating electric field E k is so strong that it could stop a particle with Lorentz factor γ+ on a short scale, much shorter than the free path to resonant scattering. A strong anomalous resistivity could be expected in this situation. Surprisingly, the simulations indicate that the effective resistivity (and the corresponding voltage) remain low. A complicated time-dependent pattern is organized in the phase-space, which allows the charges to find small-resistance paths through the waves of Ek and conduct the current at a low net voltage and a low dissipation rate.


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6 Magnetospheric emission Various ideas have been proposed for the mechanism of hard X-ray emission from magnetars (Thompson & Beloborodov 2005; Heyl & Hernquist 2005; BT07; Baring & Harding 2007; Lyubarsky & Eichler 2008). One possible source is the transition layer between the corona and the star. The layer can reach temperatures kT > ∼ 100 keV and produce bremsstrahlung emission. The other possible source is the extended corona itself. It generates nonthermal X-rays via resonant scattering of the thermal X-rays emitted by the neutron star. A simplest model assumes that the high-energy spectrum forms via single scattering by an optically thin flow that interacts with the stellar radiation. This model was developed for ordinary pulsars (e.g. Kardashev, Mitrofanov, & Novikov 1984; Daugherty & Harding 1989; Sturner 1995; Lyubarsky & Petrova 2000) and also applied to magnetars (Baring & Harding 2007). It does not, however, explain the magnetar spectrum. Several works emphasized that radiative transfer with multiple resonant scattering in the closed magnetosphere has a strong impact on the observed X-ray spectrum (TLK02; Lyutikov & Gavriil 2006; Fernandez & Thompson 2007; Nobili, Turolla & Zane 2008; Rea et al. 2008; Pavan et al. 2009; Zane et al. 2009). The key unsettled problem is what parameters of the scattering plasma should be assumed in the transfer calculations. Resonant scattering depends on the Lorentz factors of the coronal particles and the direction of their motion. One popular assumption is that the corona is filled with counter-streaming positive and negative charges with mildly relativistic velocities. The scattering in this picture can reproduce the 1-10 keV part of the magnetar spectrum (e.g. Rea et al. 2008). However its theoretical basis is problematic. The keV photons are resonantly scattered at radii r ∼ 10R where B ∼ 1011 − 1012 G. The plasma strongly interacts with the stellar radiation in this region, and the counter-streaming model needs Ek to push charges of one sign toward the star against the radiative drag. This electric field accelerates the charges of the opposite sign away from the star. In the presence of e± plasma (which is inevitable), no self-consistent solution exists for the mildly relativistic counter-streaming model. A different picture of plasma circulation is shown in Figure 6. We argued that in the outer corona both + and − charges must outflow from the star and annihilate in the equatorial plane of the magnetic dipole. A moderate electric field Ek is generated to maintain a small difference ∆β/β ∼ M−1 ≪ 1 between the average velocities of the positive and negative charges, so that the outflow carries the required electric current. This picture offers a self-consistent solution for the drag-dominated electric circuit, which needs to be tested against observations. The theoretical X-ray spectrum can be found by solving for the transfer of the stellar radiation through the e± outflow. Then one can compare the theoretical prediction with the data. The technical difficulty is that the outflow dynamics is coupled to the radiation field, and hence the radiative transfer must be solved together with the plasma motion. This nonlinear problem is well defined and can be solved exactly (numerically), however this is a rather formidable task. As a first step, let us consider a simplified model which provides the Lorentz factor γ(r, θ) of the scattering medium, motivated

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Andrei M. Beloborodov Fig. 7 Magnetar spectrum formed by resonant scattering in the e± outflow. Solid histograms show models A and B (see text). The line of sight is chosen at angle θ = 60o with respect to the magnetic axis. The star is assumed to emit the blackbody radiation with temperature kT = 0.5 keV. The result of single (first) scattering in Model B is shown by the dotted histogram.

by the results of § 5. Given γ(r, θ) it is straightforward to calculate the transfer of the stellar radiation through the corona. The result will not depend on the optical depth τ as long as τ ≫ 1 (this is a special feature of resonant scattering). We use the MonteCarlo method for the transfer calculations; it is described elsewhere (Beloborodov 2010). First, consider the outflow model in Figure 5 and suppose γ(r, θ) = γ+ (r, θ) (model A). The emerging spectrum after multiple scattering in this outflow is shown in Figure 7 for an inclination angle θ = π/3. The model is inconsistent, as Figure 5 assumed that the drag force F is created by the central thermal radiation field, neglecting the scattered radiation, which would be appropriate only if τ ≪ 1. The central radiative drag leads to the artificially high γ+ near the axis where the central radiation is beamed along the outflow direction. In reality, τ ≫ 1 (even for moderate twists, see eq. 19), the scattered radiation fills the magnetosphere and contributes to the drag force, decelerating the outflow near the axis. This will lead to small γ(r, θ) at all θ in the outer corona and change the scattered radiation spectrum. To see the trend of this change, let us modify the drag force F in Figure 5. Let α be the angle between the photons and the outflow velocity. In the region where cos α > 0.5 for all photons emitted by the star, let us set cos α = 0.5 when calculating F . This intrusion makes the radiation field less anisotropic so that it is never strongly beamed along the outflow. Re-calculating γ± (r, θ), we find that they are reduced compared with those in Figure 5. Now consider the scattering medium with the new Lorentz factor γ = γ+ and calculate the radiative transfer through this medium (model B). The result is shown in Figure 7. Toy models A and B allow one to make some preliminary conclusions. In both models, the spectrum has two distinct peaks, at a few keV and near 1 MeV, and a


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minimum near 10 keV. This shape appears to be a robust result of radiative transfer through the e± outflow. The result is consistent with the observed spectra of magnetars (e.g. Kuiper et al. 2008). The photon index Γ above 10 keV is close to the typical observed Γ ∼ 1. Multiple scattering is essential for the formation of the high-energy peak. For illustration, the dotted histogram in Figure 7 shows the spectrum obtained in model B after single scattering; its high-energy component is weak. The first scattering of the thermal keV photons occurs mainly at radii r ∼ 10R where the outflow is slow. It generates quasi-isotropic radiation with a spectrum that is slightly modified from blackbody. A fraction of the scattered photons propagate back to the star and approach head-on the relativistic outflow in the inner region. The second scattering for such photons dramatically boosts their energy, contributing to the high-energy component in the observed spectrum. This mechanism will also operate in the exact model where the accurate distribution of the Lorentz factor in the outflow is found consistently with the radiative transfer. In this model, the high-energy luminosity will be explicitly fed by the initial power of the outflow injected near the star (which is determined by the electric current and the discharge voltage). The radiative drag transforms this power to radiation. Similar spectra are generated when the outflow is confined to the j-bundle of moderate magnetic flux u⋆ > ∼ 0.1. The spectrum evolves as the j-bundle shrinks to u⋆ ≪ 0.1. Note also that the high-energy component is anisotropic — it is preferentially beamed along the magnetic dipole axis. This may help explain the energy dependence of the pulse profiles in observed magnetars (den Hartog et al. 2008a,b). The pulse profiles of magnetars are expected to change as the magnetosphere untwists and the j-bundle shrinks. Previous discussion of pulse profiles assumed that the entire magnetosphere is twisted in a self-similar way and has a moderate optical depth τ proportional to the amplitude of the global twist ψ (e.g. Fernández & Thompson 2007). The calculations presented here suggest a different picture. The twists of magnetars quickly evolve to narrow j-bundles (and twists may always be confined to a small part of the magnetosphere). The plasma in the j-bundle is opaque to resonant scattering even for weak twists ψ ∼ 0.1. The result of radiative transfer (and the corresponding pulse profile) does not directly depend on τ as long as τ ≫ 1. It may depend on τ indirectly, because the deceleration of the e± outflow depends on its optical depth. Further analysis is needed to explore the implications for the pulse profile and to test the model against observations. A robust result of the radiative transfer (especially in the more reasonable model B) is the sharp break in the spectrum at Ebr ≈ 2me c2 ≈ 1 MeV. It is caused by photon absorption in the strong magnetic field. The emission of multi-MeV photons occurs in the region where B ∼ 1013 G, and they see a large optical depth to absorption. Absorption is reduced for photons emitted along the magnetic axis, and the emerging high-energy spectrum depends on the line of sight. Note that somewhat smaller Ebr ∼ 0.5 MeV could be possible for the emission produced by the transition layer between the corona and star (Thompson & Beloborodov 2005; BT07). In that model, Ebr may be controlled by the temperature of

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the layer rather than absorption in the magnetosphere. Observations of Ebr may help distinguish between the two mechanisms of high-energy emission.

7 Conclusions Nonthermal X-ray emission and shrinking hot spots on magnetars are associated with magnetospheric activity — the release of the energy stored in the twisted closed magnetosphere. The rate of energy release is proportional to the voltage established along the magnetic field lines, which is regulated by the continual discharge to Φe ∼ 109 V. This voltage has a pure inductive origin, directly related to the rate of untwisting of the magnetic field. For axisymmetric configurations, the untwisting evolution is described by the electrodynamic equation (7). The untwisting theory predicts the formation of shrinking hot spots on “transient magnetars” whose magnetospheres are temporarily activated and gradually relax back to the quiescent state. Shrinking hot spots were indeed reported in these objects (Fig. 5), and their evolution appears to agree with the theoretical expectations. Self-similar twists (Wolfson 1995; TLK02) do not form in magnetars, because the electric currents tend to be quickly removed from field lines with moderate apex radius Rmax . Currents have longest lifetime on field lines with Rmax ≫ R, forming the extended j-bundle. An e± outflow of a high multiplicity streams in the j-bundle and creates the outer corona around the neutron star. The outflow stops at the apexes of the closed magnetic field lines and the e± pairs annihilate there. The e± outflow is opaque to resonant scattering and impacts the observed X-ray spectrum. The simulations of radiative transfer through the outflow suggest a natural explanation for the hard X-ray component in magnetar spectra. The strong radiative drag and the imposed electric current lock the j-bundle plasma in a peculiar two-fluid state. The two-stream instability is then inevitable; it creates strong Langmuir oscillations, which can convert to escaping low-frequency radiation. This mechanism is discussed in more detail elsewhere (Beloborodov 2010). Acknowledgements This work was supported by NASA grant NNX-10-AI72G.

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Suzaku Detection of Hard X-ray Emission in SGR 0501+4516 Short Burst Spectrum Yujin E. Nakagawa, Teruaki Enoto, Kazuo Makishima, Atsumasa Yoshida, Kazutaka Yamaoka, Takanori Sakamoto, Nanda Rea, Kevin Hurley, Suzaku SGR 0501+4516 Team and HETE-2 Team

Abstract Spectral studies of bursts from SGR 0501+4516 are presented using Suzaku data. We discovered hard X-ray emission in a summed spectrum of short bursts with low fluences, which has been found only in quiescent emission spectra so far. This result supports our idea that there are common emission mechanisms between the quiescent emission and the bursts of soft gamma repeaters and anomalous X-ray pulsars. The quiescent emission could consist of numerous micro-bursts. If this is the case, total released energy of small fluence (< 10−8 erg cm−2 , 2-100 keV) bursts of a cumulative number-intensity distribution can be comparable to the energy released in the quiescent emission. We found that the total released energy can easily maintain the quiescent emission energy.

Yujin E. Nakagawa, Kazuo Makishima Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan, e-mail: [email protected],[email protected], Teruaki Enoto University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan, e-mail: enoto@juno. phys.s.u-tokyo.ac.jp, Atsumasa Yoshida, Kazutaka Yamaoka Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan, e-mail: [email protected],[email protected], Takanori Sakamoto NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA, e-mail: takanori@milkyway. gsfc.nasa.gov, Nanda Rea Institut de Ciencies de l’Espai (ICE-CSIC, IEEC), Torre C5-parell, 2a planta, 08193, Bellaterra (Barcelona), Spain, e-mail: [email protected], Kevin Hurley Space Sciences Laboratory, 7 Gauss Way, University of California, Berkeley, CA 94720-7450, USA, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_25, © Springer-Verlag Berlin Heidelberg 2011

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Yujin E. Nakagawa, Teruaki Enoto and Kazuo Makishima et al.

1 Introduction Astrophysical interest in magnetars, strongly magnetized neutron stars with surface fields up to ∼ 1015 G [1], has been growing for the last decade. They emit X-, and gamma-ray photons through magnetic field dissipation. The magnetars are unique objects to study interactions between magnetic fields and photons. Soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are phenomenologically defined to be magnetars. They exhibit X-, and gamma-ray quiescent emission (∼ 10−11 erg cm−2 s−1 , 2-10 keV) and super-Eddington burst activity (∼ 10−6 erg cm−2 s−1 , 2-100 keV). Since there are several common characteristics between the SGRs and the AXPs such as rotation periods of 2-12 s, they are thought to be same class of objects. However the emission mechanisms of the quiescent and burst phases remain unknown. The X-ray quiescent emission spectra below 10 keV are well modeled by a photoelectrically absorbed two blackbody function (2BB) or blackbody plus a power law (BB+PL). Hard X-ray emission above 10 keV discovered by INTEGRAL (e.g., [5]) is well described by a power law (PL) with very hard indices of ∼ −1. The most acceptable spectral model of SGR short bursts detected by the High Energy Transient Explorer 2 (HETE-2) is 2BB [6]. Given that the quiescent emission and the bursts are both energized by the magnetic fields which is thought to be a promising energy source, there could be very similar physical processes between them. Consequently, their spectra could emerge alike. Interestingly, the spectra of both the bursts and the quiescent emission show a strong linear correlation between the lower and higher temperatures of the 2BB spectrum [7]. This correlation suggests common radiation mechanisms between the bursts and the quiescent emission [7]. If this is the case, the burst spectra may also display hard X-ray emission which has only been found in the quiescent emission spectra so far. In this paper, we present spectral studies of bursts from SGR 0501+4516 detected by Suzaku. All quoted errors are 90% confidence levels.

2 Hard X-ray Emission in Burst Spectra SGR 0501+4516 was discovered by Swift on 22 August 2008. Since it was undergoing intense burst activity, a Suzaku ToO observation was performed on 26 August 2008 with the Suzaku narrow field instruments; the X-ray imaging spectrometer (0.2-12 keV) [4], and the hard X-ray detector (10-700 keV) [9]. Suzaku detected the X-, and gamma-ray quiescent emission, and 32 bursts during a ∼20 ks observation [2] (Paper I). Analyses of a strong burst were reported in Paper I. Then we analyzed 31 short bursts with low fluences which were not affected by pile-up. Since there was not enough statistics in each short burst, we summed their light curves and spectra. The summed light curve is shown in figure 2. In spectral analyses, the photoelectric absorption was fixed to 8.9 × 1021 cm−2 (Paper I).

Suzaku Detection of Hard X-ray Emission in SGR 0501+4516 Short Burst Spectrum 10

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Fig. 2 Panel (a): a summed spectrum of 31 short bursts fitted with 2BB+PL. Panel (b) and (c): residuals using 2BB and 2BB+PL.

The summed spectrum of the 31 short bursts cannot be reproduced by 2BB, despite the fact that this model is known as the most acceptable model for the SGR short bursts [6]. As shown in figure 2 (b), there is an excess above ∼20 keV. The which is comparable to excess is well reproduced by a PL with an index of −1.0+0.4 −0.3 the indices of the hard X-ray emission in the quiescent emission spectra. Therefore we have discovered hard X-ray emission in a burst spectrum which was found only in the quiescent emission spectra so far.

3 Discussion From what has been shown in section 2, we suggest that the quiescent emission and the bursts are similar, comprising not only a soft X-ray 2BB spectrum, but also a hard X-ray PL spectrum. If there are common emission mechanisms between the quiescent emission and the bursts, the quiescent emission could be formed as a result of numerous micro-bursts. The hard X-ray emission was not reported for bright short bursts (∼10−6 erg cm−2s−1, 2-100 keV) from SGR 1806−20 and SGR 1900+14 detected by HETE-2. To estimate contributions of the hard X-ray emission to short burst spectra, we analyzed 50 and 5 short bursts from SGR 1806−20 and SGR 1900+14 respectively using 2BB+PL. All short bursts were not affected by pile-up. The indices were fixed to −1.3 for SGR 1806−20 derived from Suzaku data and −3.1 for SGR 1900+14 [3]. Hard X-ray emission fluxes for 8 short bursts from SGR 1806−20 were constrained. Figure 4 presents a relation between bolometric luminosities of 2BB and 2-100 keV luminosities of PL which were derived from the Suzaku and HETE-2 data. There seems to be a correlation over a few orders of magnitude.

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Yujin E. Nakagawa, Teruaki Enoto and Kazuo Makishima et al. 5

SGR 0501+4516

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We also estimated a contribution of the hard X-ray emission for the strong burst. Since the strong burst was subject to pile-up, we used a pile-up corrected spectrum examined by Paper I. The spectrum was fitted by 2BB+PL with a fixed photon index of −1 which was estimated from the summed spectrum of the 31 short bursts. The photoelectric absorption was fixed to 8.9 × 1021 cm−2 (Paper I). The 2-100 keV flux of hard X-ray emission was < 2 × 10−8 erg cm−2 s−1 . The energy released in low fluence ( 106 me c2 (see below), the electron Lorentz factor, which is ∼ 1 at the star surface, monotonically increases up to a value which is much higher than Fig. 1 Geometry of the curvature emission. See text for details.

The magnetar emission in the IR band: the role of magnetospheric currents

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γres,max ∼ 500(1 keV/ǫ)(B p/B Q) ≈ 5000. This ensures that the resonant condition (γres = γ) is met after the electron travelled a typical distance λacc,res = γ|dx/d(γβ)| ≈ γres L/(eΦ0 /me c2 ) ≪ L. On the other hand, this is not a sufficient condition for RCS to occur: even if they can be accelerated up to γres , electrons are able to scatter only if λ < λacc,res , where λ ∼ (ǫ/me c2 )/(n phσe f f ) ≈ 10−3 (T/1 keV)−2 (R/R NS )2 cm is the particle mean free path for resonant scattering (here n ph is the density of thermal photons and σe f f = 3πσT /4αF ; e.g. Dermer 1990). This translates into: eΦ0 B < 5 × 1011 BQ me c 2

!

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We approximate the left hand quantity with the potential drop which produces the conduction current in a 1D, relativistic double layer (where j ∝ Φ20 ; Carlqvist 1982): eΦ0 ≈ 2 × 109 me c 2

r

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where m+ is the mass of the positive charge. If the magnetosphere is populated by e− /e+ pairs then m+ = me , and for a polar magnetic field ∼ 10B Q the inequality given by Eq. (1) is satisfied up to B/BQ > 0.05, or R/R NS < 6. The upscattered photon produced in the region B/B Q > 0.05 has an energy 2 ǫ ′ ∼ γres ǫ/(1 + γres ǫ/me c2 ) and may convert into a e± pair in the strong magnetic field provided that the threshold condition ǫ ′ > 2me c2 / sin θ′ is met, where θ′ is the angle of the scattered photon with the magnetic field. For ǫ ∼ 1 keV, pair creation requires γres > 30 (i.e. B > 0.05BQ). Since electrons are relativistic, the scattered photon initially moves parallel to B and a pair can be produced only after a large enough pitch angle has built up. Moreover, pair production is efficient only if its characteristic length-scale is less than the dimension of the circuit, i.e. α± > 1/RNS where α± is the absorption coefficient for ordinary and extraordinary photons (see Baring 2007). Accordingly, the limiting value of magnetic field above which the process is effective decreases with increasing photon energy, and it is B ∼ 0.05B Q for pairs created near threshold. In summary, in the region B > 0.05BQ a quasi-equilibrium configuration is reached with a pair multiplicity ∼ L/λacc,res of a few. Screening of the electric field limits the potential drop to eΦ0 /me c2 ≈ γres ∼ 500(B/BQ) and the maximum e± Lorentz factor is γres . Charges undergo only few scatterings with thermal photons, but they loose most of their kinetic energy in each collision. A steady situation is maintained against such Compton losses because e− /e+ are re-accelerated by the electric field before they can scatter again. RCS may occur also at larger radii provided that the charges Lorentz factor is limited to ∼ γres , which decreases as B ∼ 1/R3 . The pairs energy depends on the electrostatic potential (in turn fixed by conduction current), and also on the efficiency of the radiative (Compton) drag. If pairs with γ ∼ γres are injected in the external region (B/BQ < 0.05), the circuit is likely to behave much differently from a double layer, allowing the current to be conducted with only a small potential drop (see also Beloborodov, this volume).

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Silvia Zane, Luciano Nobili and Roberto Turolla

Fig. 2 Model spectra for different values of θobs and B p = 4.3 × 1014 G. The XMM-Newton X-ray spectrum of 1RXS J1708−4009 is from Rea et al. (2008; red solid line). The AXPs IR/optical data are from Duncan & van Kerkwijk 2005 (4U 0142+614 and 1E 1048.1−5937) and Mignani et al. 2007 (XTE J1810−197 and 1E 2259+586). The adopted distances for de-reddening are 5 kpc (4U 0142+614, 1RXS J1708−4009), 3 kpc (1E 1048.1−5937, 1E 2259+586), 4 kpc (XTE J1810−197 ), 8.5 kpc (1E 1841−045). Left: Spectra computed for incoherent curvature emission. Right: Same as in the left panel, but accounting for particle bunching.

3 IR/Optical emission In order to estimate the amount of curvature emission from the inner magnetosphere, as seen by a distant observer, we use a simple geometrical model. We approximate the twisted field with a dipole, B = B p(R/RNS )−3 (cos θ, sin θ/2, 0), while the current is still taken to be j = (c/4π)|∇ × B|twist ≈ B(R/RNS )−1 . The particle density is then n± = B(R, θ) (R/RNS )−1 / (4πe), for a pair velocity ≃ c. With reference to a generic flux tube labelled by θ0 (0 ≤ θ0 ≤ π/2), curvature photons will reach the observer if they are emitted in the volume ∆V = XRc sin θobs | dZ/dθ0 | ∆θ0 /γ2 , around the point P of cartesian co-ordinates (X, Z) where B is parallel to the LOS (Fig.1). Here θobs is the viewing angle,i.e. the angle between the line-of-sight (LOS) and the magnetic axis. In general there are two emitting regions along each flux tube one above the other below the magnetic equator, because of electrons and positrons, and for any θ0 there are two azimuthally symmetric flux tubes. The(polarization CR ispectral hR ∞ power i can be expressed as h R ∞ per particle Raveraged) ∞ ′ ′ ˙ p(ǫ) = E/ǫc (ǫ/ǫc ) ǫ/ǫ K5/3 (x)dx / 0 xdx x K5/3 (x )dx , where K5/3 (x) is the c modified Bessel function, ǫc = (3/2)¯hcγ3 /Rc , E˙ = (2/3)e2cγ4 /R2c , and Rc is the curvature radius of the field line. The monochromatic luminosity emitted by the volume ∆V is ∆L = p(ǫ)n± ∆V, and, since radiation is collimated in the solid angle ∆Ω = π/γ2 , the observer at infinity measures a luminosity 4π∆L/∆Ω. The total received power is then obtained summing the individual contributions over all the flux tubes, assuming the pair Lorentz factor is locked at γres . Fig. 2 (left panel) shows the computed CR spectrum for B p = 4.3 × 1014 and different viewing angles θobs , together with the optical/IR luminosities observed for a sample of AXPs. It should be noted that all these sources typically show variability in all energy bands. The data shown in Fig. 2 were not selected according to any


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particular criterion and are just meant to be representative of the IR emission of magnetar candidates. As it appears from Fig. 2, model spectra severely underpredicts optical/IR data. Basically, this is due to the fact that the particle density is too low for incoherent CR emission to produce the required power. The point has been already noted, on the basis of a qualitative analysis, by BT07 who concluded that particle bunching would be likely present, providing the required amplification of CR emission. Many models have been suggested to explain the origin of the interactions which push particles together and can lead to the formation of bunches of charged particles localized in phase-space, but the most promising explanation seems to be connected with plasma instabilities, like the two-stream (electron-positron/electron-ion) instability. If N particles are contained in a bunch of spatial scale lB , they radiate like a single particle of charge Q = Ne. This collective emission produces an amplification of the radiated power by a factor N with respect to the standard, non-coherent emissivity by N individual charges. The details of the emission depend on the shape of the bunch. In the simplest, one-dimensional case the power per unit frequency emitted by a bunch is pB (ν) ∼ N 2 p(ν) sin2 (πν/νl )/(πν/νl )2 = N 2 P(ν) (Saggion 1975). The main source of uncertainties lies in the size of the bunch, and here we assume that lB is associated to the local plasma frequency, lB ∼ c/ν pe = πme c2 /(γe2 ne ) (e.g. Lesch 1998). Since a single bunch emits a spectral power (ne l3B )2 P(ν) and there are NB ∼ ∆V/l3B bunches in each emitting volume, the total spectral power radiated within ∆V is ∆LB = NB (ne l3B )2 P(ν) = (ne l3B )∆L. We stress that it has to be N = ne l3B > 1 for the process to be effective, meaning that only emission at frequencies ν < νl < νco = n1/3 e c is efficiently amplified. Where N < 1 emission is from individual particles. Finally, because of the strong absorption below the plasma frequency, a low-energy cut-off is present around ν pe . We have recalculated the emergent spectrum including particle bunching (Fig. 2, right panel), finding that coherent curvature radiation can indeed produce sufficient IR/optical emission to account for the observed one. Given the limitations of our model, we are not in a position to attempt any fit of the data. What we aim to, instead, is verifying that magnetospheric CR emission is able of reproduce the gross characteristics of the observed low-energy emission, its energetics in particular. The predicted spectrum vary with the viewing angle, and the luminosity is higher when the star is viewed nearly pole-on. The curvature spectrum is far below the observed one in the soft X-rays, indicating that a different mechanism is necessary to account for the X-ray emission below ∼ 10 keV. In the twisted magnetosphere scenario this is RCS onto mildly relativistic pairs populating the external magnetosphere.

4 Discussion and Conclusion Despite the magnetar scenario is now regarded as the most likely interpretation for the observed properties of SGRs and AXPs, and the many investigations aimed at

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producing detailed models for the spectral and timing properties of magnetars, a number of key issues are still unresolved. In particular, the origin of the low-energy emission (in the IR/optical band) of a magnetar is still under debate. In this paper we gave a quantitative estimate of the IR/optical emission, under the assumption that it arises from curvature radiation from pairs in the inner magnetosphere. A comparison with observations of AXPs shows that the predictions of the model are in general agreement with observations, provided that curvature radiation is not coherent and a bunching mechanism is at work at long wavelengths. Our model is based on a number of simplifying assumptions. For instance, the computation is based on a globally twisted dipolar magnetosphere while in some magnetars, the transient AXPs in particular, the twist might affect only a limited bundle of field lines close to a magnetic pole (Beloborodov 2009) . If the inner part of the magnetosphere is (or becomes) untwisted, no currents are present that can produce the IR/optical curvature radiation. Also, we used a simple double layer model (eq. 1) for the linear accelerator, which may not be valid in presence of intense pair creation (BT07). Furthermore, and more important, the details of the charges motion in the external region of a twisted magnetosphere, which are essential ingredients in providing a model for the high energy emission in the soft and hard X-ray band (∼ 0.5–200 keV), are still unclear. In order to reach firmer conclusions about the entire multi-wavelength spectrum a more detailed study of the magnetosphere is required, and will be matter of future work (see also Beloborodov, this volume). Acknowledgements LN and RT are partially supported by the INAF/ASI grant AAE-I/088/06/0. The authors thank the organizers of the Sant Cugat forum for the hospitality and support.

References 1. Baring, M.G.. In: Astrophysics of Compact Objects, AIP Conference Proceedings, 968, 93 (2008) 2. Beloborodov, A.M., & Thompson, C.: ApJ, 657, 967 (2007) 3. Beloborodov, A.M.: ApJ, 703, 1044 (2009) 4. Carlqvist, P.: Ap&SS, 87, 21 (1982) 5. Dermer, C.D.: ApJ, 360, 197 (1990) 6. Dhillon, V.S., et al.: MNRAS, 394, L112 (2009) 7. Duncan, R.C., & Thompson, C.: ApJ, 392, L9 (1992) 8. Durant, M., & van Kerkwijk, M.H.: ApJ, 627, 376 (2005) 9. Eichler, D., Gedalin, M., & Lyubarsky, Yu.: ApJ, 578, L121 (2002) 10. Kern, B., & Martin, C.: Nature, 417, 527 (2002) 11. Lesch, H., Jessner, A., Kramer, M., & Kunzl, T.: A&A, 332, L21 (1998) 12. Mereghetti, S.: A&A Review, 15, 225 (2008) 13. Mignani, R., et al.: A&A, 471, 265 (2007) 14. Perna, R., Hernquist, H., & Narayan, R.: ApJ, 541, 344 (2000) 15. Rea, N., Zane, S., Turolla, R., et al.: ApJ, 686, 1245 (2008) 16. Saggion, A.: A&A, 44, 285 (1975) 17. Zane, S., Rea, N., Turolla, R., & Nobili, L.: MNRAS, 398, 1403 (2009)


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18. Woods P. M., Thompson C.. In: Lewin W.H.G., van der Klis M. (eds.) Compact Stellar X-ray Sources, p. 547 Cambridge University Press (2006)

Double features in mean pulsar profiles and the nature of their radio emission George I. Melikidze and Janusz Gil

Abstract In the talk presented at this Workshop by J.Dyks, the author claimed that the long-sought Rosetta Stone needed to decipher the nature of pulsar radio emission has been finally identified as the double features in averaged pulsar profiles. The author argued that highly symmetric bifurcated features are produced by a split-fan beams of extraordinary-mode curvature radiation emitted by thin microscopic streams of magnetospheric plasma conducted by a very narrow bundle of magnetic field lines. We examined arguments leading to these intriguing conclusions and found a number of flaws. At least one of them is fatal, namely there is not enough available energy within such thin microscopic plasma streams.

1 Frequency dependence of the bifurcation angle Generally, the pulsar radio emission can be generated by means of either a maser– like or the coherent curvature mechanism. Without any doubt this radiation is emitted in a strongly magnetized electron–positron plasma well inside the light cylinder. Once the waves are generated in the emission region, in the propagation region they naturally split into the ordinary and extraordinary waves corresponding to the normal modes of this plasma. The ordinary waves interact strongly with plasma particles (causing charge-separation along field lines), and thus encounter difficulty in escaping from the magnetosphere. On the other hand, the extraordinary waves can propagate freely through the plasma and escape to the interstellar medium. G. Melikidze J.Kepler Institute of Astronomy, University of Zielona Gora, Lubuska 2, Zielona Gora, Poland Abastumani Astrophysical Observatory,Ilia State University, 2a Kazbegi ave, Tbilisi 0160, Georgia e-mail: [email protected] J.Gil J.Kepler Institute of Astronomy, University of Zielona Gora, Lubuska 2, 65-265, Zielona Gora, Poland e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_27, © Springer-Verlag Berlin Heidelberg 2011

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0,6

log( /

cr

)

0,4

0,2

0,0

-0,2

-0,1

0,0

0,1

log( /

cr

0,2

0,3

)

Fig. 1 Frequency dependence of the opening angle of the extraordinary mode of coherent curvature radiation in the pulsar magnetospheric plasma (thick line). The formal power-low fit is represented by the dashed line and the 95% upper and lower limits are represented by short dashed lines.

Therefore, from a theoretical point of view the bulk of the observed pulsar radiation originates when the extraordinary waves escape from the magnetosphere. There exists also strong observational indication that the extraordinary mode is dominant in pulsar radiation [1], as the radiation observed at a given longitude is polarized perpendicularly to the plane of dipolar magnetic field lines, along which the sources are moving [2]. The analysis of highly polarized (nearly 100%) single pulses in a number of strong pulsars show that they can be produced only by the extraordinary mode excited in the plasma by means of the curvature radiation [3]. Recently, the double symmetrical features (called the bifurcated components; BFC hereafter) observed in mean profiles of some pulsars were used to decipher the nature of the observed radio emission [4, DRD hereafter]. The idea was to fit these features with the elementary emission pattern of selected radiation mechanisms: the parallel acceleration beam and the curvature radiation beam. Although we do not believe that the actual pulsar radiation mechanism can be identified from the analysis of the properties of average waveforms alone, we do not intent to argue with the approach itself. Rather, we intend to verify the arguments and claims of DRD using different and independent methods. The most important feature considered by DRD is a bifurcated component (BFC) in the mean profile of PSR J1012+5307. This feature has a high degree of a mirror symmetry and as DRD argues it reflects a pure morphology of an extraordinary mode of curvature radiation. Indeed, waves polarized perpendicularly to the plane of the charge motion are not emitted along the instant velocity vector (see lower panel of Figure 3 in [2]). DRD argued that the important property of BFC supporting the model of curvature radiation is the frequency dependence of the bifurcation angle (angular separation between component peaks) ∆bfc ∝ ν−0.35 . Interestingly, the value obs of this exponent is close to 1/3 = 0.33, which indeed follows from the properties of

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the particle curvature radiation in vacuum (provided that ∆bfc = 1/γ and νobs ∝ γ3 ). However, in the realistic theory, i.e. in the strongly magnetized electron-positron plasma, this exponent can differ from 1/3 and/or 0.35. As an example we explored the formalism developed in [2], which corresponds to the general case of curvature radiation emitted by the point–like (smaller than the emitted wave–length) charged bunch/soliton moving relativistically along curved magnetic field lines. The results are presented in Fig.1, where on the horizontal axis is the normalized observational frequency ν/νcr (where νcr = 7.2 × 109γ3 /ρ [Hz], and γ is the Lorentz factor of the charge moving along the trajectory with the radius of curvature ρ), while on the vertical axis is the normalized angle ϕ/ϕcr between the direction of maximum power emission and the local magnetic field vector (where ϕcr = 1/γ). Unlike the vacuum case, the bifurcation frequency dependence is not exactly a power–law like for the curvature radiation in a plasma (thick solid line in Fig. 1). However, when the formal power–law fit was applied we obtained ϕ/ϕcr ∝ (ν/νcr )−a , where a = 0.45 ± 0.01. This value of bifurcation exponent is far from 1/3 that can be derived for the vacuum case. Moreover, it does not depend on the actual bunching mechanism (e.g. soliton model), just any point–like emitter of curvature radiation will give the BFC exponent equal to 0.45 in the pulsar plasma [2].

2 Energy considerations We can make simple estimates of the upper limits of a possible emission power, and compare them to the observed radio luminosities. The mean flux density from PSR J1012+5307 at 1.4 GHz is about 3 mJy (ATNF database), which for the distance d = 0.52 kpc translates into the radio luminosity Lr ∼ 6 × 1027 erg s−1 . Judging from the mean profiles shown in Fig. 2 of DRD it is reasonable to assume that the BFC feature contains not less than about 10% of the total energy associated with the whole pulse profile. The same must hold for the emitted power, so we can assume that LBFC ∼ 0.1Lr = 6 × 1026 erg s−1 . The highest available energy source is determined by the spin down power LSD ∼ 4.7×1033 erg s−1 . We can now calculate the socalled pulsar kinematic luminosity Lkin , which is the power carried by charged particles accelerated within the pulsar inner gap [2]. This luminosity can be expressed as Lkin = γpr me c3 nGJ S PC erg s−1 , where γpr < 5 × 106 is the “primary” Lorentz factor of electrons (or positrons) leaving the acceleration region (“polar gap”), nGJ is the Goldreich-Julian number density and S PC is the canonical polar cap surface area. For the parameters of this pulsar nGJ = 8 × 109 cm−3 and S PC = 1.3 × 1011 cm2 and thus Lkin < 1032 erg s−1 , which is few percent of L SD (as should be expected in general). The radiation efficiency η of the observed radio emission referred to the kinematic pulsar luminosity is η = Lr /Lkin = 6 × 10−5 , which is quite typical for radio pulsars. Below we argue that such low efficiency should also be expected in conversion of the particle’s kinematic luminosity into the power of coherent curvature radiation. Indeed, the charge density inside the coherently emitting bunches moving with the Lorentz factor γ cannot exceed the Goldreich-Julian value, and

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thus we can estimate the kinetic energy flux of the bunches as L˜ kin = γme c3 nGJ S . If we assume that the entire L˜ kin is converted into the radio emission (i.e. Lr = L˜ kin ), the efficiency would be ηCR = L˜ kin /Lkin = γ/γpr . For the typical values of γ = 400 and γ pr = 106 (see [2] for details), we get ηCR = 4 × 10−4 as a maximum possible efficiency estimate. According to DRD the BFC feature is emitted via curvature radiation of sources flowing within a very narrow flux tube of magnetic field lines, although its actual cross–section is not specified. On one hand, this flux tube should be broad enough to carry much more than LBFC = 6 × 1026 erg/s in the particle flux. On the other hand, to reveal signatures of elementary emitters it should be narrow enough so that its divergence ∆χ = ε/γ is much smaller than the opening angle of curvature radiation 1/γ. Thus, the auxiliary dimensionless parameter ε 1014 G [15], the measurement of the field strength through observations of the cyclotron resonance scattering feature (CRSF) in the X-ray spectrum of this source gives B0 ≃ 4 × 1012 G [12]. Furthermore, the spin-down time of a neutron star in the spin-powered pulsar and propeller stages is under the conditions of interest comparable to or even longer than the typical time of the magnetic field decay of magnetars [3], [9]. Therefore, LPXPs could be considered as magnetar descendants rather than magnetars [14]. These inconsistencies raise a question about the correctness of the magnetar hypothesis on LPXPs. If the surface field of the neutron star is indeed close to B0 derived from observations of CRSF, then the spin-down torque applied to the star is significantly larger (s) than Ksd,0 . The magnetospheric radius of the neutron star in this case turns out to be significantly smaller than its corotation radius. This makes ineffective the models of spin evolution based on the assumption Rm ∼ Rcor (see, e.g., [10], [18]). Furthermore, the month-long rapid spin-up events observed in this source can be explained in terms of the transient disk formation scenario with the surface field being consistent with B0 measured through observations of CRSF [11]. This indicates that the accretion flow during the spin-down trends has quasi-spherical rather than disk geometry. The maximum possible value of the spin-down torque applied to a neutron star ˙ from a non-rotating hot spherical envelope surroundaccreting material at a rate M (sph) ˙ s R2m , where αdis is the efficiency paraming its magnetosphere is Ksd = αdis Mω (sph)

eter. One finds this value from the equation Ksd = αdis (1/ωs )(dEkin,φ /dt), where ˙ s Rm )2 is the rate of transformation of the rotational energy of the dEkin,φ /dt = M(ω star to the kinetic energy of material penetrating into the magnetopause. Solving the (sph) inequality Ksd ≥ 2πI ν˙ sd for the parameters of GX 301–2 (see, e.g., [6]) yields, ˙ −1/2 ν˙ 1/2 Rm ≥ 1.5 × 109 α−1/2 I 1/2 M 17 −13 0.5 45

Ps 680 s

1/2

cm.

(1)

Here α0.5 = αdis /0.5 and ν˙ −13 = ν˙ /10−13 Hz s−1 . This indicates that the required rate of the spin-down can be achieved if the magnetospheric radius of the star is a factor of 3 larger than the canonical Alfvén radius. As shown in [5], such a situation can be realized if the magnetosphere of the neutron star is surrounded by a turbulencedominated hot envelope. The upper limit to the Alfvén radius of the star in this

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−4/9 ˙ −2/9 case is RA,max ≃ 2 × 109 µ4/9 m2/9 V7.6 M17 cm. Hence, the observed spin-down 30.3 may reflect that the neutron star is accreting material from a turbulence-dominated accretion flow or a hot envelope surrounding its magnetosphere. The rate of energy transfer into the envelope material required for keeping it hot and turbulent significantly exceeds the rotational energy loss rate by the neutron star. It, however, constitutes only about 0.1% of the energy release rate at the stellar surface. Therefore, a reconstruction of the accretion process from the turbulence-dominated medium requires a feedback from the neutron star on the accretion flow to be taken into account. An evaluation of the efficiency of the feedback needs further investigations of the dissipative processes in the magnetosphere of an accreting neutron star (e.g., anomalous dissipation of electric currents in the magnetopause, emission of MHD-waves, and non-thermal processes of energy release).

Acknowledgements N.R.I acknowledges support from NASA Postdoctoral Program at NASA Marshall Space Flight Center, administered by Oak Ridge Associated Universities through a contract with NASA. The research has been partly supported by the program of Prezidium of RAS “Origin and Evolution of Stars and Galaxies”, the program of the Department of Physical Sciences of RAS “Extended Objects in the Universe”, and the Grant from President of the Russian Federation ”The Basic Scientific Schools” NSh-3645.2010.2.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.

Anzer, U., Börner, G. 1995, A&A, 299, 62 Bisnovatyi-Kogan, G.S. 1991, A&A, 245, 528 Colpi, M., Geppert, U., Page, D. 2000, ApJ, 529, L29 Davidson, K., Ostriker, J.P. 1973, ApJ, 179, 585 Davies, R.E., Pringle, J.E. 1981, MNRAS, 196, 209 Doroshenko, V., et al. 2010, A&A, in press (arXiv 0907.3844) Finger, M.H., et al. 2010, ApJ, 709, 1249 Ghosh, P., Lamb, F.K. 1978, ApJ, 223, L83 Ikhsanov, N.R. 2007, MNRAS, 375, 698 Kli´zniak, W., Rappaport, S. 2007, ApJ, 671, 1990 Koh, D.T., et al. 1997, ApJ, 479, 933 La Barbera, A., et al. 2005, A&A, 438, 617 La Palombara, N., Mereghetti, S. 2007, A&A, 474, 137 Li, X.-D., van den Heuvel, E.P.J. 1999, ApJ, 513, L45 Lipunov, V.M. 1982, Soviet Astronomy, 26, 537 Lipunov, V.M. 1992, Astrophysics of neutron stars, Springer-Verlag, Heidelberg Lynden-Bell, D., Pringle, J.E. 1974, MNRAS, 168, 603 Perna, R., Bozzo, E., Stella, L. 2006, ApJ, 639, 363 Pringle, J.E., Rees, M.J. 1972, A&A, 21, 1 Ruffert, M. 1999, A&A, 346, 861 Shakura, N.I. 1975, Sov. Astron. Letters, 1, 223

X-ray emission from isolated neutron stars Sandro Mereghetti

Abstract X-ray emission is a common feature of all varieties of isolated neutron stars (INS) and, thanks to the advent of sensitive instruments with good spectroscopic, timing, and imaging capabilities, X-ray observations have become an essential tool in the study of these objects. Non-thermal X-rays from young, energetic radio pulsars have been detected since the beginning of X-ray astronomy, and the long-sought thermal emission from cooling neutron star’s surfaces can now be studied in detail in many pulsars spanning different ages, magnetic fields, and, possibly, surface compositions. In addition, other different manifestations of INS have been discovered with X-ray observations. These new classes of high-energy sources, comprising the nearby X-ray Dim Isolated Neutron Stars, the Central Compact Objects in supernova remnants, the Anomalous X-ray Pulsars, and the Soft Gamma-ray Repeaters, now add up to several tens of confirmed members, plus many candidates, and allow us to study a variety of phenomena unobservable in ”standard” radio pulsars.

1 Introduction With more than 1800 detections, rotation powered pulsars (RPP) constitute by far the largest class of isolated neutron stars (INS), despite only one out of ∼10 radio pulsars is visible because of beaming. Accounting for the selection effects of radio observations, a total population of ∼ 106 RPP is estimated for the whole Galaxy [40]. Observations at gamma-ray energy, where pulsar beaming angles are larger, are now contributing to increase the number of known RPP [1]. About one hundred RPP have been detected also at X-ray energies [7]: they include the youngest and more energetic pulsars (like the Crab), a few older neutron stars at small distances Sandro Mereghetti INAF, IASF-Milano, v. E.Bassini 15, I-20133 Milano, Italy e-mail: sandro@iasf-milano. inaf.it N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_29, © Springer-Verlag Berlin Heidelberg 2011

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(e.g. Vela and Geminga) and several tens of recycled millisecond pulsars (most of which are found in globular clusters [56]). All kinds of INS, not only the RPP, are X-ray emitters. X-ray observations have been crucial to discover other manifestations of INS, that for various reasons were missed in the standard searches for radio pulsars. The nearby X-ray Dim Isolated Neutron Stars (XDINS), the Central Compact Objects (CCOs) in supernova remnants, the Anomalous X-ray Pulsars (AXPs), and the Soft Gamma-ray Repeaters (SGRs) are examples of these new classes, which, despite totalling only a few tens of sources, are particularly interesting because they offer a different view on a variety of phenomena unobservable in ”standard” radio pulsars. This review is focussed on the main properties of the X-ray emission from these new classes of INS. For an excellent review of the X-ray emission from RPP see [7]. The location on a P–P˙ plot diagram of some of the objects discussed here is shown in Fig. 1. The figure also gives lines of constant magnetic field (computed ˙ 1/2 G), characteristic age (τc = 1 P/P), ˙ assuming dipole braking, B = 3.2 1019 (P P) 2 46 3 −1 ˙ ˙ and spin-down luminosity (LS D = I ΩΩ = 4 10 P / P erg s ).

Fig. 1 P–P˙ diagram for different classes of INS: XDINS (×), CCO (⋄), AXP (squares), SGR (△), RRAT (+). The vertical bars indicate the range of P˙ variations observed in SGR and AXP. Lines of constant magnetic field (dashed), characteristic age (dotted), and spin-down luminosity (dashdotted) are also indicated.

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2 Origin of the X-ray emission in isolated neutron stars The X-ray emission observed from INS can be powered by internal heat, rotational energy, accretion, and magnetic field decay. The relative importance of these energy sources, that can also operate at the same time, depends on the age and physical properties of the neutron star. Neutron stars have internal temperatures of ∼ 1011 K at birth, that rapidly drop to ∼ 109 K. For the following ∼ 105 − 106 years the dominant cooling mechanism is neutrino emission from the star’s isothermal core. This leads to surface temperatures of several 105 to 106 K, with thermal emission peaking in the soft X-ray band. Temperature gradients on the star’s surface generally produce observable modulations at the rotation period. Thermal X-ray emission can be observed in INS with ages of ∼ 104 − 106 years, provided they are sufficiently close and not too absorbed by the interstellar medium. Older neutron stars are too cool to significantly emit X-rays, while in the youngest pulsars the thermal radiation is difficult to detect because it is outshined by the brighter non-thermal emission. A recent review on the thermal emission from neutron star is given by [171]. Non-thermal emission, that extends over a broad energy range, originates from charged particles accelerated in the NS magnetospheres at the expense of rotational energy (see, e.g., [17]). Non-thermal X-rays are characterized by power-law spectra and strongly anisotropic emission patterns, giving rise to large pulsed fractions. The pulse profiles often show narrow (double) peaks, but in many cases nearly sinusoidal profiles are observed. The most luminous RPP are the Crab and two young pulsars in the Large Magellanic Cloud (the only three pulsars with LS D > 1038 erg s−1 ). The efficiency with which the rotational energy is converted to non-thermal luminosity is about 10−3 [8, 90], but there is a large dispersion around the average value [130], as expected because of different viewing orientations and, possibly, also other effects. Studies of the LX –LS D relation with a large sample are complicated by the fact that a significant fraction of the rotational energy loss powers pulsar wind nebulae, which are difficult to disentangle in the more distant and/or fainter objects without adequate spatial resolution. Accretion is a well established process in X-ray binaries (e.g., [43]). In the lack of a companion star, accreting matter could originate directly from the interstellar medium. However, the relatively large space velocity of neutron stars, and the low density of the interstellar medium, make this process unable to provide sufficiently high luminosities. Alternatively, the matter could be supplied by a debris disk formed by fall-back in the supernova explosion that produced the neutron star. Although this possibility seems more promising, no unambiguous evidence for an INS powered by accretion has been found yet. The relevance of magnetic energy in powering the emission from neutron stars has been recognized only recently, with the observation of SGRs and AXPs (see [166, 101] for reviews). High magnetic fields (B∼1014 –1015 G) were first invoked to explain the SGRs and, in particular, the unique properties of the exceptional event of March 5, 1979 from SGR 0526−66 [119, 29]. Objects in which magnetic field decay is the dominant energy source have been named Magnetars. They are particularly

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interesting because they offer the unique possibility to study physical processes in magnetic fields of unequalled strength.

3 The X-ray Dim Isolated Neutron Stars A handful of X-ray sources with large X-ray-to-optical flux ratios, F x /Fopt ∼104 – 105 , typical of INS, were discovered in the ROSAT satellite All Sky Survey. Their INS nature was confirmed by the measurement of a large proper motion in the brightest source, RX J1856.5−3754 [161], and by the discovery of pulsations at few seconds in other sources [58, 65]. The original members of this class1 and two new candidates are listed in Table 1. Recent reviews on the XDINS are given in [57, 154]. XDINS have very soft thermal spectra (blackbody temperatures TBB ∼40–110 eV), X–ray luminosities L X ∼ 1030 − 1032 erg s−1 , spin periods in the 3–12 s range, faint optical counterparts (V>25), and no radio emission. Period derivatives of the order of 10−14 –10−13 s s−1 have been measured for several XDINS through phase connected timing, but in some cases these values are still poorly constrained (see Table 1). The temperatures of XDINS are consistent with neutron stars cooling curves if they have ages of 105 –106 years and the effect of their strong magnetic field is taken into account [2]. It is thus generally believed that the XDINS are powered by residual thermal energy. X-ray sources with such soft spectra can only observed if the interstellar absorption is small: all the M7 are closer than ∼0.5 kpc and have NH 2.5mG) if interpreted as the result of synchrotron break. This has resulted in a number of different interpretations, including the suggestion that the pulsar in 3C 58 underwent a rapid decline in its output at some early epoch [21], the possibility that the low-frequency break is inherent in the injection spectrum from the pulsar, and the suggestion that 3C 58 is not actually associated with SN 1181, but is an older nebula [11, 5]. The X-ray emission from 3C 58 (Figure 4) is dominated by a power law component, typical of synchrotron emission. However, a faint thermal component is clearly detected in the outer regions of the PWN, and also contributes to the interior regions [17, 97, 22]. The temperature is ∼ 0.25 keV, and enhanced abundances of Ne and Mg are observed, indicative of ∼ 0.5M⊙ of ejecta that has been swept up by the PWN. This is much larger than the expected mass if the PWN is associated with SN 1181, and suggests a larger age for the system [11]. To investigate the evolution of 3C 58, we have carried out Spitzer observations using IRAC [38]. These observations reveal the PWN in both the 3.6 and 4.5 µm

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Fig. 4 Top: Chandra image of 3C 58. The pulsar is at the center, and is surrounded by a elongated compact nebula with a curved jet extending to the west. A softening of the spectrum with radius is observed – an effect resulting from both synchrotron aging of the electrons and the presence of a soft thermal shell. Bottom: Chandra image of the pulsar in 3C58, and its associated torus and jet (left) and the IRAC 8 µm image of the same region. The elliptical region indicates the torus, and has the same center and size in each image.

bands, representing the first detection of synchrotron emission from this important young PWN anywhere in the five decades of frequency separating the radio and X-ray bands. The morphology of the IR emission from 3C 58 is strikingly similar to that seen in the radio and X-ray bands. The emission extends all the way to the radio boundaries, indicating that no synchrotron loss breaks occur below the band, and some regions of enhanced or diminished emission match well with those seen in the other bands (notably the large cavity on the eastern side), suggesting that we are observing primarily synchrotron radiation. Optical filaments in 3C 58 [97, 33], which presumably originate from supernova ejecta overtaken by the expansion of the PWN, do not show a good spatial correspondence with the radio or IR structures, suggesting that the IR emission is not dominated by dust contributions. This is similar to results from Spitzer observations of the Crab Nebula [42], where emission in the IRAC band is also identified primarily with synchrotron radiation. The IRAC data also reveal emission from the torus surrounding the pulsar in 3C 58 [36] in all four bands (Figure 4).2 Optical emission from the torus is detected 2

We also show preliminary results from MIPS observations at 24 µm where we also detect the torus.

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Fig. 5 The flux of all of 3C 58 (upper) and its torus (lower), plotted from the radio to the X-ray band. While the torus is not detected in the radio band, the IR data require a flattening of the Xray spectrum when extrapolated back to the longer wavelength band. (From [38]. Reproduced by permission of the AAS.)

as well [35]. These observations provide new constraints on the evolution of the particles as they flow from the termination shock in 3C 58. There is little question that this emission is synchrotron in nature; there is insufficient dust in the environment of the pulsar termination shock to provide a shocked dust component to the emission. The spectrum (Figure 5) requires a break of some sort between the IR and X-ray bands, suggesting that the synchrotron loss break appears just above the IR band. Most importantly, these results indicate that the spectrum of particles injected into the PWN through the termination shock does not follow an unbroken power law. As a result, structure in the PWN spectrum is, at least in part, the imprint of structure from the injection region. From Figure 5, it is clear that additional observations of 3C 58, and particularly its torus, at longer wavelengths will be crucially important to understand the nature of the injected particles and the subsequent long-term evolution of the PWN. Deep observations of the central regions of other PWNe are clearly of importance as well.

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Fig. 6 ROSAT PSPC image of Vela SNR. The single contour represents the outer boundary of the radio nebula Vela X. The point source at the northern extreme of Vela X is the Vela pulsar and the box inside the PWN indicates the XMM MOS region of the cocoon shown in the inset.

4.2 Vela X Located at a distance of only 280 pc, the Vela SNR houses a young pulsar that powers the extended nebula Vela X. This nebula lies within a limb-brightened shell of thermal X-rays. The outer shell is cool, and the exceptionally low foreground absorption (NH ∼ 1 − 5 × 1020 cm−2 ) allows us to see strong emission lines from O, Ne, and Mg. In X-rays, the overall brightness asymmetry of Vela is evident (Figure 6). The SNR is much brighter in the northeastern hemisphere, toward the Galactic plane. This is apparently the result of large-scale inhomogeneities in the ISM, with n0 ≈ 0.06 cm−3 in the south [7], and n0 ≈ 1 cm−3 on the north side of the SNR [13]. Radio observations of the PWN [28] reveal a morphology concentrated to the south of the pulsar itself, suggesting that the nebula has been disrupted by the impact of the reverse shock which propagated more rapidly from the northeast due to the higher ambient density in this direction. Higher resolution radio images show a network of filamentary structure in the PWN [15], possibly formed by R-T instabilities in this interaction with the reverse shock. ROSAT observations of the Vela X region [27] reveal a large emission structure – the so-called “cocoon” – extending to the south of the pulsar. The region is characterized by a hard spectrum and ap-


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Fig. 7 XMM-Newton spectrum from the “cocoon” region in Vela X. The best-fit model, shown in black, is composed of two components – a thermal plasma with enhanced, ejecta-like abundances (light dashed curve) and a power law (dark dashed curve). (From [23]. Reproduced by permission of the AAS.)

pears to lie along a bright elongated radio structure. ASCA observations established a two-component X-ray spectrum with the hard component adequately described by either a power law or a hot thermal plasma [29]. The PWN is observed at energies up to ∼ 200 keV with BeppoSAX [26], and observations with H.E.S.S. [2] reveal extended VHE γ-ray emission with the brightest emission concentrated directly along the cocoon. Our initial studies of a small region along the cocoon [23] reveal a bright X-ray structure shown as an inset to Figure 6. The emission is concentrated into several distinct regions, at least some of which appear to be filamentary structures. The integrated emission from these regions is characterized by two distinct components – a power law with a spectral index of ∼ 2.2 and a thermal plasma with enhanced abundances of O, Ne, and Mg, presumably associated with ejecta that has been mixed into the PWN upon its interaction with the reverse shock (Figure 7). It is of particular interest that our broadband modeling of the nonthermal emission from this central region of Vela X indicates a disconnect between the radioemitting particles and those that produce the X-ray and TeV γ-ray emission [23]. A model with a single spectral break between the bands either underpredicts the radio flux or produces an incorrect radio spectral index (Figure 8), while a model with two breaks can satisfy the data. Treating the poorly-characterized low-energy electron component as a separate population of particles, de Jager, Slane, & LaMassa

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Fig. 8 Broadband spectral model consisting of synchrotron emission in the radio and X-ray bands accompanied by IC emission in the VHE γ-ray band. The upper panel shows a model with two spectral breaks in the electron spectrum. Models with a single break (lower panel) either underpredict the radio emission, or produce a radio flux whose spectral index does not agree with observations. (From [23]. Reproduced by permission of the AAS.)

[12] showed that enhanced IC emission from this component could be expected in the GeV band. This has now been confirmed with observations by AGILE [31] and Fermi [1]. Interestingly, a similar excess is observed in Fermi observations of HESS J1640−465 [39], another evolved PWN that appears to have undergone a RS interaction (see Section 4.4). The nature of the low-energy particle spectrum in Vela X is poorly understood, but the Fermi studies in particular suggest a difference in the cocoon emission from that of its surroundings; the LAT emission appears to be concentrated distinctly to the west of the TeV emission. Whether or not this emission component is somehow associated with the reverse shock interaction is not clear. An XMM-Newton Large Project to map a significant portion of Vela X is underway to investigate the distribution of nonthermal particles and thermal ejecta in the nebula.

4.3 G327.1−1.1 G327.1−1.1 is a composite SNR with a bright central PWN whose structure is complex in both the radio and X-ray bands. As shown in Figure 9, the SNR is character-


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Fig. 9 Composite radio (red and orange) and X-ray (blue) image of G327.1−1.1. The outer radio shell defines the SNR boundary, while the bright central nebula is the PWN. The compact source to the northwest of the nebula is the neutron star. It is embedded in a cometary-shaped structure accompanied by a tail of X-ray emission extending into the radio nebula, as well as prong-like structures (seen in inset) that appear to inflate a faint bubble in the northwest.

ized by a faint radio shell accompanied by a bright radio PWN. The PWN is offset from the SNR center, and a finger-like structure extends toward the west/northwest. The morphology is suggestive of a PWN that has been disrupted by an asymmetric reverse shock interaction that has arrived preferentially from the northwestern direction. Detailed Chandra observations [43] appear to confirm this scenario in detail.3 A compact X-ray source resides at the tip of the radio finger, and a trail of nonthermal X-ray emission extends from the source back into the radio nebula. The compact X-ray source itself is resolved, with possible evidence of a jet or torus structure, and the source is embedded in a cometary nebula whose structure is suggestive of a bow shock. A pair of prong-like structures originate from the vicinity of the compact core 3

See also the contribution by T. Temim in these Proceedings.

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and extend out to the west/northwest. Their axes are not aligned with the compact core, and they do not appear to be jets from the pulsar. The most unusual feature in G327.1-1.1 is a large bubble-like structure that extends out from the prongs. The bubble is very faint, but it is apparent in images taken with both Chandra and XMMNewton. The spectral index in the tail of X-ray emission that extends into the brighter radio PWN appears to vary from ∼ 1.8 to ∼ 2.1, although significantly better statistics are needed to map this fully. Faint loop-like structures, possibly associated with Rayleigh-Taylor filaments or magnetic loops, are evident in the southern part of the tail and they appear to extend from radio structures inside the relic PWN. Deeper X-ray observations are required to better characterize these and, more importantly, to study the detailed properties of the complex structures seen in the immediate vicinity of the pulsar, and to investigate the apparent upstream diffusion of particles that form the bubble-like structure. The overall X-ray morphology of the PWN in G327.1-1.1 presents several challenges. It appears clear from the displacement of the radio nebula that the PWN has undergone an interaction with the SNR reverse shock, and that this shock arrived earlier from the northwest, possibly as a result of pulsar motion in this direction. In such a scenario, we expect the ongoing pulsar wind production to begin forming a new PWN around the pulsar, shaped by the surrounding pressure conditions. Radio emission from the displaced relic nebula will persist, but the compression from the reverse shock will temporarily increase the magnetic field in the nebula, causing rapid synchrotron losses for the more energetic particles. The X-ray emission is thus expected to be concentrated closer to the pulsar, as observed. Spectral steeping of the X-ray spectrum in the direction of the relic nebula is expected if the synchrotron loss timescale is shorter than the particle flow timescale; mapping this spectral evolution along the extended X-ray tail thus constrains the conditions in the relic nebula. In the direction from which the reverse shock propagated, the structure of the medium is complicated. The density in the immediate post-shock region is enhanced, but declines downstream due to adiabatic expansion of the SNR. At least qualitatively, this could provide the environment in which freshly-injected wind from the pulsar inflates the observed bubble. The cometary feature surrounding the putative pulsar complicates the above picture. The morphology is suggestive of a bow shock that forms when the pulsar motion exceeds the sound speed in the the ambient medium, yielding a structure quite different from that of a static PWN. The wind termination shock in such systems is compressed in the direction of motion, and extended in the backward direction. X-ray emission is then observed between the termination shock and the contact discontinuity, and forms three distinct structures: the “head” that surrounds the pulsar; an enhanced region behind the pulsar, associated with the termination shock; and an elongated tail where the swept-back wind is concentrated [17, 9]. For G327.11.1, such a geometry would require a significant pulsar velocity component perpendicular to the plane of the sky, but the overall velocity that would be required (770 km s−1 ) is not unreasonable.


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Given the similarity between G327.1−1.1 and Vela, in the context of both being systems in which an interaction between the PWN and the SNR reverse shock has occurred, it is of considerable interest to determine whether or not G327.1−1.1, like Vela X, produces γ-rays. Preliminary investigation of Fermi-LAT data indicates faint emission that is positionally coincident with G327.1−1.1, but further analysis is required to assess this in detail.

4.4 HESS J1640−465 HESS J1640−465 (see Figure 10) is an extended source of very-high-energy γ-ray emission discovered with the High Energy Stereoscopic System (H.E.S.S.) during a survey of the Galactic plane [3]. Centered within the radio SNR G338.3−0.0 [34], the deconvolved TeV image of the source has an RMS width of 2.7 ± 0.5 arcmin [16]. HI measurements show absorption against G338.3−0.0 out to velocities corresponding to the tangent point, indicating a distance of at least 8 kpc [24], and thus implying a rather large size for the PWN (RPWN > 6.4d10 pc, where d10 is the distance in units of 10 kpc). X-ray observations with XMM-Newton [16] and Chandra [24] establish the presence of an accompanying X-ray nebula and an X-ray point source that appears to be the associated neutron star. The point source is offset from the center of the PWN, and both are offset from the center of the SNR, suggesting that an asymmetric interaction with the SNR reverse shock has occurred. We have investigated Fermi-LAT data acquired from the region surrounding HESS J1640−465 and detect the source with high significance [39]. The spectrum is well-described by a power law with Γ = 2.30 ± 0.09 and a F(> 100 MeV) = 2.8 × 10−7 photons cm−2 s−1 . We have modeled the emission assuming a 1-zone model in which particles are injected into the nebula with a simple power law distribution. We use a radius of RS NR ∼ 11.6d10 pc for G338.3−0.0, based on radio observations. The observed extent of HESS J1640−465 constrains the radius of the PWN to RPWN > 6.4d10 pc. As indicated in Figure 2, where a horizontal line indicates the radius of G338.3−0.0, reasonable values for the SNR and PWN parameters indicate that the SNR reverse shock has almost certainly begun to impact the PWN. The broadband emission model results are shown in Figure 11 where we plot the Fermi and H.E.S.S spectra along with the radio upper limit from GMRT observations [20] and spectral confidence bands derived from Chandra [24]. The black curves represent the model prediction for the synchrotron (left) and IC (right) emission that best describes the X-ray and TeV γ-ray spectra, similar to results from [24]; the parameters for the model are summarized in the caption. As seen in Figure 11, this model significantly underpredicts the observed Fermi-LAT emission. Our spectral fits can formally accommodate up to about ∼ 20% of the observed flux in a pulsar-like component characterized by a power law with an exponential cutoff energy between 1 and 8 GeV, and there are several known radio pulsars located within the error circle of HESS J1640−465 that could potentially produce observable γ-ray

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Right Ascension (J2000) Fig. 10 Fermi-LAT image of HESS J1640−465. The solid (cyan) circle indicates the uncertainty in the centroid of the Fermi-LAT source, the magenta dashed circle indicates the 95% encircled flux distribution of the H.E.S.S. image, and the white dashed circle indicates that for 3EG J1639−4702. The white contours outline radio emission from G338.3−0.0 while the black contours at the center outline extended X-ray emission observed with XMM-Newton. A compact X-ray source detected with Chandra resides within the X-ray contours. (From [39]. Reproduced by permission of the AAS.)

emission. Even in this case, however, the Fermi-LAT emission still greatly exceeds the predicted flux from HESS J1640−465. As described in Section 4.2, simple power-law models for the particles in Vela X, another evolved PWN, fail to reproduce the observed broadband spectrum. The presence of an excess population of low-energy electrons is inferred, and models for the IC scattering of photons from this population predict an excess of γ-rays in the GeV range. Motivated by these results from Vela X, we modified the evolved power law spectrum from our model for HESS J1640−465 by truncating the lower end of the power law and adding a distinct low-energy component. Based on results from simulations of shock acceleration [40], we chose a Maxwellian distribution for this population. Our resulting (ad hoc) particle spectrum is shown in the upper panel in Figure 11, and the resulting broadband emission is shown in the lighter (magenta) curves in the lower panel. Here we have adjusted the normalization of the Maxwellian to reproduce the emission in the Fermi-LAT band, which is produced primarily by upscattered infrared (IR) photons from local dust. We find a mean value of γ ≈ 2 × 105 for the electrons in the Maxwellian component, and roughly


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Fig. 11 Electron spectrum (upper) and broadband emission model (lower) for HESS J1640−465 assuming the evolutionary history described in the text. The black curves represent a PWN with an age T = 10 kyr, and B(T ) = 5µG, assuming E˙0 = 4 × 1036 erg s−1 and an injection spectrum with σ = 10−3 , γ = 2.5, and Emin = 115 GeV. The light curves represent the scenario with a lowenergy Maxwellian electron component replacing the low-energy portion of the electron powerlaw spectrum. The mean temperature for the IR and optical photon fields are 15 K and 5000 K, respectively, and the energy densities relative to the CMB are 4 and 1.15. The dashed curve in the upper panel represents the truncated portion of the power law that was replaced by a Maxwellian. The dashed curve in the lower panel represents a model for which all of the γ-ray emission results from pion decay. (From [39]. Reproduced by permission of the AAS.)

5% of the total electron energy in the power law tail, consistent with results from particle-in-cell simulations. Recent work by Fang & Zhang (2010) [14] uses a similar input distribution to successfully model the emission for several PWNe including HESS J1640−465. However, their results for HESS J1640−465 underpredict the observed GeV emission from this source, apparently due to use of a slightly lower bulk Lorentz factor and a larger fraction of the total energy in the power law tail than we have used in this analysis. An alternative scenario for the γ-ray emission is that it arises from the SNR itself, and not the PWN. The dashed blue curve in Figure 11 represents a model

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for the emission from the collision of protons accelerated in the SNR with ambient material, leading to γ-rays from the production and subsequent decay of neutral pions. Assuming a shock compression ratio of 4 and that 25% of the total supernova energy appears in the form of relativistic protons, an ambient density n0 ≈ 100 cm−3 is required to produce the model shown in the Figure. This is much higher than can be accommodated for the observed size of the SNR and the lack of observed thermal X-ray emission from the SNR. Such high densities are found in dense molecular clouds, suggesting that the γ-rays could be produced by particles that stream away to interact with high-density material outside the SNR. However, only the most energetic particles can escape the acceleration region, which is in conflict with the proton spectrum we require to match the data. Moreover, the observed TeV emission appears to originate from within the SNR boundaries, making such an escapingparticle scenario appear problematic. Based on this, along with the lack of a spectral cutoff that might suggest emission from a central pulsar, we conclude that the GeV γ-ray emission most likely arises from the PWN.

5 Summary The broadband spectra of PWNe provide information about both the structure and evolution of these objects. New multiwavelength observations have begun to probe PWNe from the sites of particle injection to the ejecta-laden outer boundaries, providing crucial input for modeling these systems. Observations in the γ-ray band have uncovered previously unknown systems in the late phase of evolution, while X-ray observations continue to provide detailed information about the geometry and the composition of the pulsar winds. These observations continue to inform theoretical models of relativistic shocks which, in turn, have broad importance across the realm of high-energy astrophysics. At the same time, these recent results have pointed the way to new and deeper observations of PWNe across the electromagnetic spectrum. Acknowledgements I would like to acknowledge the considerable contributions of many colleagues to the work described here, including Bryan Gaensler, David Helfand, Stephen Reynolds, Okkie de Jager, and Stefan Funk. In particular, I would like to thank Yosi Gelfand, Tea Temim, Daniel Castro, Stephanie LaMassa, and Anne Lemiere who, as students as postdocs, led much of the work described here. This work was supported in part by NASA contract NAS8-03060, NASA grants NNX09AT68G, and NNX09AP99G, and Spitzer RSA 1375009.

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Multi-wavelength Observations of Composite Supernova Remnants Tea Temim

Abstract Multi-wavelength studies of composite supernova remnants (SNRs) lead to a better understanding of their evolutionary development, the interaction of supernovae (SNe) and pulsar wind nebulae (PWNe) with their surroundings, particle injection and loss processes, nucleosynthesis, and the production and processing of dust grains in SNe. This paper summarizes the basic evolutionary development of composite SNRs and describes two unique systems in different stages of evolution; G54.1+0.3, a PWN in the early stage of evolution that is expanding into inner SN ejecta, and G327.1-1.1, a composite SNR in the late stage of evolution whose PWN has interacted with the SNR reverse shock. Both systems exhibit unique properties that have not been observed previously.

1 Introduction Composite supernova remnants (SNRs) are those for which we see distinct evidence of both a pulsar wind nebula (PWN) and an SNR shell [5]. While the basic theoretical framework for their origin and evolution has been developed [1, 12, 4], the details are still not well-understood. We still lack a detailed understanding of the phases of evolution in which the PWN interacts with the SNR reverse shock and what structures form during these interactions. Detailed knowledge about the evolution of composite SNRs is also crucial for the understanding of the injected particle spectrum in PWNe and the eventual escape of these particles into the Galaxy. Initially, the young PWN expands supersonically inside the remnant and drives a shock into the freely-expanding inner SN ejecta. At this stage, we expect to observe synchrotron emission from the expanding PWN, surrounded by a skin of shocked SN ejecta [97, 4]. The reverse shock eventually crushes the PWN and causes it to Tea Temim Smithsonian Astrophysical Observatory, 60 Garden Street, MS 21, Cambridge, MA 02138, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_33, © Springer-Verlag Berlin Heidelberg 2011

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reverberate. The interaction can result in complex filamentary structures and mixing of the PWN material with ejecta gas [1]. After the interaction with the reverse shock, the PWN continues to expand subsonically into the reheated SN ejecta. The evolution becomes more complicated if the pulsar has a high space velocity and displaces the PWN off-center from the SNR shell. In that case, the reverse shock interacts with the PWN asymmetrically, sweeping it off to one side and producing a relic PWN. A new PWN continues to form around the pulsar, and as the pulsar’s motion eventually becomes supersonic, this newly forming PWN deforms into a bow shock nebula and takes on a cometary morphology [1, 12]. Here, we summarize observational studies of two systems that exhibit the properties described above.

2 G54.1+0.3: Expansion into SN Ejecta G54.1+0.3 is a young PWN closely resembling the Crab for which no thermal emission has been detected in X-rays. The SNR blast wave is presumed to be undetectable because it is expanding into a low density cavity and has not interacted with enough ISM material [6]. The Spitzer 24 µm image of G54.1+0.3 shows that the PWN is surrounded by an IR shell that contains a dozen point sources arranged in a ring-like structure, and a bright extended region of emission that appears to be aligned with the pulsar’s jet [7, 11]. These features are shown in Figure 1. Spitzer IR spectroscopy of the shell provided the first evidence for SN ejecta in G54.1+0.3 [11]. A number of emission lines are present in the IR spectrum, including [ArII], [NeII], [ClII], [SIII], [FeII], and [SiII]. Several are broadened to velocities of ∼ 1000 km s−1, suggesting that the IR shell is composed of rapidly expanding SN ejecta. The pulsar’s jet appears to be driving a ∼ 25 km s−1 shock into the shell material and compressing it to produce a region of higher density. The spectra also

Fig. 1 Three-color image of G54.1+0.3. Chandra X-ray emission is shown in blue, Spitzer 8 µm emission in green, and Spitzer 24 µm emission in red and yellow. The PWN is surrounding by an IR shell, 2.4 arcminutes in diameter (4.3 pc a distance of 6.2 kpc), containing a dozen point sources and a bright extended region of a higher density that is aligned with the pulsar’s jet. X-ray: NASA/CXC/SAO/T.Temim et al.; IR: NASA/JPLCaltech/T.Temim et al.

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reveal an unidentified dust feature at 21 µm that is likely produced by the same dust species as the freshly formed dust in Cas A [11]. The Chandra X-ray and Spitzer IR observations of G54.1+0.3 are best described by a scenario in which the shell emission arises entirely from SN ejecta and freshly formed dust. The dust is likely being illuminated by the members of a young stellar cluster in which the SN exploded. The point sources in the IR shell are attributed to radiatively heated dust that is blowing past these stars (see Figure 1). A simple Dust model shows that such a scenario can reproduce the observed IR emission from the shell and the embedded point sources, and that approximately 0.1 M⊙ of dust would be required [11]. If this scenario is correct, we are actually observing unshocked SN dust, before it has been processed by the reverse shock.

3 G327.1-1.1: Interaction with the Reverse Shock G327.1-1.1 is a composite supernova remnant that has an unusual morphology consisting of a symmetric radio shell and an off-center non-thermal component, seen in Figure 2. A narrow ridge of emission extends from the PWN structure toward the northwest. Chandra X-ray images reveal a compact source at the tip of the ridge, embedded in a cometary structure that resembles a bow-shock nebula. Two pronglike structures originate near the compact core and extend into a large bubble (Figure 2). There is a trail of X-ray emission whose spectrum steepens with increasing distance from the pulsar and loop-like structures that coincide with structures inside the radio PWN (Figure 2). An XMM-Newton detection of a 0.3 keV X-ray thermal component that spatially coincides with the radio shell leads to an age estimate of ∼ 18000 yr, for an assumed distance of 9 kpc [10].

Fig. 2 Left: MOST 843 MHz radio image of G327.1-1.1 with the PWN radio contours overlaid. Right: Chandra ACIS image of G327.1-1.1 is shown in blue, and the ATCA 13 cm radio image of the inner PWN region in red.

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G327.1-1.1 is one of the best examples of a composite SNR whose PWN has been asymmetrically disrupted by the SNR reverse shock. This shock likely arrived earlier from the northwest, possibly as a result of a combination of the pulsar’s motion in this direction and a density gradient in the ISM. It swept the PWN to the side, producing a relic nebula seen in the radio. Filamentary radio and X-ray structures, seen in Figure 2, are likely a result of this violent interaction. The pulsar is presumably forming a new PWN, represented by the compact core and the cometary structure that appears to be a bow shock. The presence of prong and bubble structures complicate the bow shock scenario, since such structures are not expected to form beyond the confines of the shock. Deeper imaging is required to explain the nature of the observed structures and determine if the PWN in G327.1-1.1 has deformed into a bow shock.

4 Conclusions Multi-wavelength observations of composite SNRs offer a wealth of information about their properties and evolution. The study of the interactions between the PWN and the evolving SNR can provide important information about the SNR properties that may otherwise be unobservable. G54.1+0.3 is a system in early stage of evolution, comprised of a PWN expanding into the inner SN ejecta. The unique environment of G54.1+0.3 allowed us to detect and characterize the SN ejecta and freshly formed dust that has not yet been processed by the SNR reverse shock. The study implies that IR searches for SN ejecta and dust around PWNe in stellar clusters may be an effective way of studying SNR properties. G327.1-1.1 is an ideal object for the study of several aspects of the late stages of PWN evolution. Its unusual morphology may be giving us a unique view into the transitional phase of evolution in which the PWN deforms into a bow shock nebula, following an asymmetric reverse shock interaction.

References 1. Blondin, J. M., Chevalier, R. A., & Frierson, D. M. 2001, ApJ, 563, 806 2. Bucciantini, N. 2002, A&A, 387, 1066 3. Gaensler, B. M., van der Swaluw, E., Camilo, F., Kaspi, V. M., Baganoff, F. K., Yusef-Zadeh, F., & Manchester, R. N. 2004, ApJ, 616, 383 4. Gaensler, B. M., & Slane, P. O. 2006, ARA&A, 44, 17 5. Helfand, D. J., & Becker, R. H. 1987, ApJ, 314, 203 6. Hester, J. J. 2008, ARA&A, 46, 127 7. Koo, B.-C., et al. 2008, ApJL, 673, L147 8. Rho, J., et al. 2008, ApJ, 673, 271 9. Slane, P., Helfand, D. J., van der Swaluw, E., & Murray, S. S. 2004, ApJ, 616, 403 10. Temim, T., Slane, P., Gaensler, B., Hughes, J., & Van Der Swaluw, E. 2009, ApJ, 691, 895 11. Temim, T., Slane, P., Reynolds, S., Raymond, J., & Borkowski, K. 2010, ApJ, 710, 309

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Fermi-LAT Results on Pulsar Wind Nebulae after 1.5 year of Observations M.-H. Grondin & M. Lemoine-Goumard for the Fermi-LAT Collaboration and the Pulsar Timing Consortium

Abstract Prior to the Fermi Gamma-ray Space Telescope, only six pulsars and one associated pulsar wind nebula, the Crab Nebula, had been detected in γ-rays by EGRET. Since then, the Large Area Telescope (LAT) aboard Fermi has significantly increased the number of detected pulsars in the 100 MeV to 30 GeV energy range. The new pulsar population established by early LAT observations show that we are detecting many nearby young pulsars in addition to the population of millisecond ˙ from ∼ 3 × 1033 pulsars. All Fermi-LAT pulsars have high energy loss rate (E), −1 38 −1 erg s to 5 × 10 erg s . A large fraction of these pulsars are associated to pulsar wind nebulae candidates observed in the TeV energy range by Cherenkov telescopes. These pulsars are thus likely to power a PWN detectable by Fermi, as it has already been done for the Crab. Here, we will review the results obtained so far by Fermi-LAT after 1.5 year of observations.

1 Introduction The catalog of pulsars detected using only 6 months of Fermi-LAT observations included 46 sources [1] and this number is still increasing [35], [4]. Yet most of the pulsar spin-down luminosity is not observed as pulsed photon emission and is carried away as a magnetized particle wind. Indeed, the deceleration of the pulsardriven wind as it sweeps up ejecta from the supernova explosion generates a termination shock at which the particles are pitch-angle scattered and further accelerated to ultra-relativistic energies. The pulsar wind nebula (PWN) emission, including synchrotron and inverse Compton components, extends across the electromagnetic spectrum from radio to TeV energies [21]. In the TeV range, PWNe are the major M.-H. Grondin & M. Lemoine-Goumard Centres d’Etudes Nucléaires de Bordeaux Gradignan, CNRS-IN2P3, Université Bordeaux I, Chemin du Solarium, BP120, 33175 GRADIGNAN Cedex, FRANCE e-mail: [email protected]; e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_34, © Springer-Verlag Berlin Heidelberg 2011

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class of Galactic sources. However, the study of PWNe is complex. First, at high energies (HE; 100 MeV - 100 GeV), the pulsed emission highly dominates the signal from the associated PWN. Second, these sources are often faint in the Fermi-LAT energy range. Third, PWNe can be extended with respect to the LAT point-spreadfunction [16]; their study thus requires an adapted analysis method. Several years after EGRET, the Large Area Telescope (LAT), aboard Fermi, offers the opportunity to study faint and extended gamma-ray sources. The LAT is an electron-positron pair conversion telescope, sensitive to γ-rays with energies between 30 MeV and 300 GeV, with improved performance (a large effective area, a broad field of view, and a very good angular resolution) [16] compared to its predecessor. Only gamma-rays in the Diffuse class events were selected to perform the analyses presented in the following (with the tightest background rejection), and from this sample, we excluded those coming from a zenith angle larger than 105◦ to the detector axis because of the possible contamination from Earth albedo photons. The spectral analysis of the gamma-ray emission was performed using a maximumlikelihood method [30] implemented in the Fermi SSC science tools as the “gtlike” code.

2 The Crab Nebula The Crab Nebula is powered by the Crab Pulsar, one of the most energetic pulsars known (E˙ = 4.6 × 1038 erg s−1 ). It is the remnant of the 1054 A.D. supernova explosion, located at a distance of 2 kpc. The γ-ray detection of the Crab Pulsar and Nebula was reported by the EGRET collaboration in 1993 but their spectral parameters derived after several years of observations had large uncertainties [27]. The improved sensitivity and unprecedented statistics obtained using 8 months of Fermi-LAT data enable precise measurement of the Crab Nebula spectrum as can be observed in Figure 1. This spectrum was obtained using only the off-pulse window to avoid any contamination from pulsed photons of the Crab Pulsar. It is well described by the sum of two power-law spectra between 100 MeV and 100 GeV: dN = Nsync (EGeV )−Γsync + NIC (EGeV )−ΓIC dE

cm−2 s−1 MeV−1

where Nsync =(9.1±2.1±0.7)×10−13cm−2 s−1 MeV−1,and NIC =(6.4±0.7±0.1)×10−12 cm−2 s−1 MeV−1 are the prefactors determined on 35% of the total phase, and Γ sync = (3.99 ± 0.12 ± 0.08) and Γ IC = (1.64 ± 0.05 ± 0.07) are the spectral indices of the synchrotron and inverse Compton (IC) components respectively. The corresponding flux above 100 MeV is (9.8 ± 0.7 ± 1.0) × 10−7 cm−2 s−1 , renormalized to the total phase. The first error is statistical, whereas the second is due to systematic effects from the uncertainty of the LAT effective area. The IC scattering of relativistic electrons on the synchrotron, far infrared, cosmic microwave background radiation fields is considered to be the most probable mech-

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anism for production of γ-rays above 1 GeV. However, using a sophisticated approach done in the framework of the MHD flow of [26], Atoyan and Aharonian (1996) have commented on the apparent deficit of GeV photons in their calculations and proposed that the high γ-ray flux observed by EGRET would be due to the enhancement of the bremsstrahlung emission of electrons captured in dense filaments. Figure 1 presents the broad band energy spectrum of the Crab Nebula together with the predictions from [15] for three different values of the mean magnetic field for the nebula. As can be observed, the Fermi-LAT data are in good agreement with the γ-ray flux predicted via simple IC scattering in a magnetic field strength between 100 µG and 200 µG, below the canonical equipartition field of the Crab Nebula of 300 µG, and do not require any additional component. Concerning the synchrotron part of the nebular spectrum, the LAT spectral points, combined with COMPTEL’s (taking into account statistical errors only for the latter), can be fit with a power-law with an exponential cut-off, as done in [25]. The cut-off energy is estimated at Ec,sync = (97 ± 12) MeV. The increase of this energy compared to [25] is due to the higher flux obtained with Fermi than by EGRET for the synchrotron component. The fit is represented with a blue dashed curve in Figure 1. More details can be found in [2].

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3 The Vela-X PWN The Vela pulsar (PSR B0833−45) at a distance of 290 pc is one of the closest pulsars to Earth. Emerging towards the south from the Vela pulsar is Vela-X, a nebular structure visible in radio, X-rays and in very high energy (VHE; E > 100 GeV) γ-rays with a complex morphology. The bright X-ray and VHE γ-ray structure usually referred to as the “cocoon”, has an extension of ∼ 0.5◦ × 1.5◦, whereas the radio emission (“halo”) presents a larger extension of 2◦ × 3◦ . The γ-ray emission detected by the LAT lies within this latter area south of the Vela pulsar. The γ-ray emission is significantly spatially extended with a best-fit radius of 0.88◦ ± 0.12◦ for an assumed radially symmetric uniform disk. We have also examined the correspondence of the gamma-ray emission with different source morphologies by using gtlike with assumed multi-frequency templates. The Test Statistic (TS) provided by gtlike is defined as twice the difference between the log-likelihood L1 obtained by fitting a source model plus the background model to the data, and the log-likelihood L0 obtained by fitting the background model only, i.e TS = 2(L1 - L0 ). Fitting a disk to the data improves the TS by 40.4 in comparison to the point-source hypothesis. Replacing the disk with spatial template provided by the H.E.S.S. observations (smoothed according to the LAT PSF) decreases the TS with respect to the disk hypothesis (∆TS = −31.3), implying that the LAT emission does not correspond well to the TeV flux. In contrast, using the radio contours as spatial template improves the value of the Test Statistic, but only by ∆TS = +11.7. Thus while the best match is with the radio morphology, as expected from the double electron population scenario [20], we cannot (at high significance) rule out a simple disk morphology. Assuming a uniform disk morphology, the 200 MeV to 20 GeV LAT spectrum of this source is well described by a power-law with a spectral index of 2.41 ± 0.09 ± 0.15 and integral flux above 100 MeV of (4.73 ± 0.63 ± 1.32) × 10−7 cm−2 s−1 . Different scenarios have been proposed to interpret the multi-wavelength observations of Vela-X. Horns et al. (2006) proposed a hadronic model wherein the gammaray emission is the result of the decay of neutral pions produced in proton-proton collisions in the cocoon. However, this model requires a particle density larger than 0.6 cm−3 , which seems disfavored by the recent best fit estimate of thermal particle density of ∼ 0.1 cm−3 using XMM observations [28]. LaMassa et al. (2008) proposed a leptonic model with radio and X-ray emissions resulting from synchrotron radiation and gamma-ray emission arising from IC scattering. In this model, the authors need a 3-component broken power-law to describe the electron population and adequately fit the data [28]. A model with a single break can also reproduce the multi-wavelength data if a separate electron population produces the radio emission [20]. In this case, the morphology of the gamma-ray emission observed by Fermi should be similar to that in the radio since they are produced by the same electron population. As can be observed in Figure 2, the detailed multi-wavelength spectral analysis favors a scenario with two distinct electron populations. Our new LAT detection and improved low energy measurements allow us to test the plausible injection spectrum for the Vela-X PWN. The cocoon emission evidently represents significantly cooled electrons, dominated by relatively recent injection of high en-


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ergy electrons from the pulsar and its termination shock. The halo component, on the other hand, represents old electrons – these are easily produced over the lifetime of the pulsar for any initial spin period ≤ 60 ms. More details can be found in [5].

Fig. 2 Spectral energy distribution of the regions within Vela-X. Upper panel: Emission from the low energy electron population (halo). WMAP, Fermi γ-ray points and the ROSAT upper limit are for the large radio-bright portion of Vela-X. The Compton components from scattering on the CMB (magenta long dashed line), dust emission (magenta dashed line) and starlight (magenta dotted line) are shown. Lower panel: Synchrotron and Compton emission from the high energy electron population (cocoon). X-ray (ASCA observations) and very high energy γ-ray [13] points are also from the cocoon region. Only CMB (cyan long dashed line) and dust (cyan dashed line) scattered flux is shown as the starlight is Klein-Nishina suppressed.

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4 The PWN in MSH 15−52 The composite supernova remnant (SNR) MSH 15−52 [aka G320.4−1.2; [17]] is usually associated to the radio pulsar PSR B1509−58. Einstein X-ray observations of MSH 15−52 revealed an elongated non-thermal source centered on the pulsar [36], later confirmed by ROSAT and interpreted as a pulsar wind nebula powered by PSR B1509−58 [39]. This PWN, composed of a torus and bipolar jets, is especially bright in X-rays [38, 46, 19, 41], and at very high energies [34, 14, 31]. Using 1 year of survey data with the Fermi-Large Area Telescope (LAT), we detected an extended γ-ray emission above 1 GeV spatially coincident with the PWN in the composite supernova remnant SNR G320.4−1.2. The nebular spectrum in the 1 – 100 GeV energy range is well described by a power-law with a spectral index of (1.57 ± 0.17 ± 0.13) and a flux above 1 GeV of (2.91 ± 0.79 ± 1.35) ×10−9 cm−2 s−1 . The LAT spectrum connects nicely with Cherenkov observations and brings new elements to the discussion on the emission models responsible for the high to very high emission from this source (Figure 3). The multi-wavelength spectrum can be explained by synchrotron and IC processes, assuming a broken power-law spectrum for the electrons. We confirm that the γ-ray emission from the PWN is dominated by the IC scattering off the IR photons from interstellar dust grains with a density of 1.4 eV cm−3 , which is the nominal value of the GALPROP ISRF [32]. The contribution of optical photon field is negligible because of the Klein-Nishina effect. The spectral break, constrained by multi-wavelength observations, is likely due to an intrinsic break of electrons injected from the pulsar wind. About 4 % of the pulsar’s loss of rotational energy would be required to power the γ-rays detected by the LAT, well in the range observed for other pulsar wind nebulae. We also consider a π0 decay model, assuming a proton spectrum described by a power-law with a cut-off to fit the data points, though there are few theoretical indications supporting an injection of such hard protons. We obtain an index of protons of 1.9 with a cut-off energy of of 60 TeV, which yields the accumulated energy of protons above 1 GeV of 1.2 × 1051(1.0 cm3 )/n ergs, where n is a number density of target nuclei. This scenario is highly disfavoured from the energetics: even with a very high density of ∼ 10 cm−3 as mentioned by [18] for the northwest limb of MSH 15−52, the energy required would significantly exceed the total energy that the pulsar can supply to its nebula (Etot = 7.5 × 1049 ergs). More details can be found in [6].

5 PSR J1907+0602 and its TeV PWN The TeV source MGRO J1908+06 was discovered by the Milagro Collaboration at a median energy of 20 TeV [8] with a flux ∼80% of the Crab at these energies. It was subsequently detected in the 300 GeV–20 TeV range by the H.E.S.S. [9] and VERITAS [40] experiments. The Fermi discovery of the radio-quiet pulsar PSR J1907+0602 [7] within the extent of the TeV source suggests that HESS


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J1908+063 is the PWN powered by PSR J1907+0602. The detection of very faint (flux density of ∼ 3.4µJy) radio pulsations with the Arecibo telescope at 1.5 GHz having a dispersion measure DM = 82.1 ± 1.1 cm−3 pc was also recently reported [3]. This indicates a distance of 3.2 ± 0.6 kpc. Given the nominal PWN spectrum, we constrain the overall flux to be ≤ 25% of that of the pulsar. If only the H.E.S.S. band is considered, and assuming the DM distance, the TeV lumi˙ However, since the TeV emission is generally thought to nosity LPWN = 5–8%E. come from a relic population of electrons the luminosity is likely a function of the spin-down history of the pulsar rather than the current spin-down luminosity. These numbers support the association of the TeV source with the pulsar. Using FermiLAT data from 2008 August 4 through 2009 September 18, we searched for the γray emission of the extended source HESS J1908+063. We measured upper limits on the gamma-ray flux in the energy range 0.1-25 GeV using the off-pulse emission of the pulsar PSR J1907+0602 [3]. The upper limits thus derived strongly suggest that the spectrum of HESS J1908+063 has a low-energy turnover between 20 GeV and 300 GeV as can be seen in Figure 4.

6 The PWN HESS J1640-465 HESS J1640-465 is an extended source of VHE gamma-ray emission discovered during a survey of the Galactic Plane [12]. Centered within the radio SNR G338.3-

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0.0, the deconvolved TeV image has an RMS width of 2.7 ±0.5 arcmin [20]. HI measurements show absorption against SNR G338.3-0.0 out to velocities corresponding to the tangent point, indicating a distance of at least 8 kpc [29]. X-ray observations with XMM [20] and Chandra [29] establish the presence of an accompanying X-ray nebula and an X-ray point source that appears to be the associate neutron star. The source is detected at high confidence using Fermi-LAT data from 2008 August 4 through 2009 November 13. [31]. The centroid of the LAT emission is located at 16h 40m 46s , −46◦ 30′ 44′′ , in good agreement with the position of HESS J1640-465, and the brightness distribution is consistent with an unresolved source. The LAT spectrum in the 200 MeV – 50 GeV energy range is well described by a power-law with Γ = 2.30 ± 0.09 and an integral flux of F(> 100MeV) = (2.8 ± 0.4) cm−2 s−1 . A lower limit of 40 GeV for any exponential cut-off energy in the spectrum can be estimated which implies that the bulk of the emission does not arise directly from an unseen pulsar in HESS J1640-465. Addition of a second power-law, with an exponential cut-off can accomodate ∼ 20% of the observed flux in the second power-law for cut-off energies between 1 and 8 GeV (as observed on average for Fermi-LAT pulsars). Pulsations from the putative pulsar has not been detected at ˙ x obtained any wavelength. However, we can use the empirical relationship for E/L 36 −1 ˙ by [33] which yields E = 4 × 10 erg s . Broad-band modeling of the PWN implies an approximate age of 10 kyr and a low magnetic field of ∼ 4µG. However, the Fermi flux significantly exceeds the one predicted by a one-zone model, as can be seen in Figure 5. Slane et al (2010) suggested that this emission could be a signature


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of a distinct population of low-energy electrons similar to that inferred from studies of the Crab Nebula and Vela-X. An alternative scenario for the γ-ray emission is that it arises from the SNR itself, and not from the PWN. The dashed blue curve in Figure 5 represents a model for the emission from the collision of protons accelerated in the SNR with ambient material, leading to γ-rays from the production and subsequent decay of neutral pions. Assuming a shock compression ratio of 4 and that 25% of the total supernova energy appears in the form of relativistic protons, an ambient density n0 ≈ 100 cm−3 is required to produce the model shown in Figure 5. This is much higher than can be accommodated for the observed size of the SNR and the lack of observed thermal X-ray emission from the SNR. Based on this, along with the lack of a spectral cutoff that might suggest emission from a central pulsar, we conclude that the GeV γ-ray emission most likely arises from the PWN HESS J1640-465. More details can be found in [31].

7 A plausible pulsar wind nebula candidate powered by PSR J1023-5746 In 2007, H.E.S.S. reported the detection of VHE gamma-rays from an extended source, HESS J1023-575, in the direction of the young stellar cluster Westerlund 2 [10]. Four scenarios trying to explain the TeV emission were suggested: colliding stellar winds in the WR 20a binary system (although this scenario can hardly reproduce a source extension of 0.18◦), collective effects of stellar winds in the Westerlund 2 cluster (although the cluster appears too narrow to account for the VHE gamma-ray emission), diffusive shock acceleration in the wind-blown bubble itself and supersonic winds breaking out in the interstellar medium. Recently, Fermi-LAT detected the very young and energetic pulsar J1023-5746, coincident with the TeV source HESS J1023-575 [35]. In addition, J1023-5746 shows a significant signal in its off-pulse window, with an emission above 10 GeV significant at more than 3σ level. To provide a better information on the off-pulse spectrum and avoid relying on a given spectral shape, we derived the spectral points by dividing the 100 MeV – 200 GeV range into 7 logarithmically-spaced energy bins and performing a maximum likelihood spectral analysis in each interval assuming a point source at the position of the pulsar. The result, renormalized to the total phase interval, is presented in Figure 6 with red stars. The signal is mainly significant above 10 GeV and is consistent with the H.E.S.S. spectral points. The connection between the GeV flux as observed by Fermi and the TeV flux as seen by H.E.S.S. supports a common origin of the gamma-ray emission. The estimated luminosity above 380 GeV (for an assumed distance of 8 kpc) is 1.5 × 1035 erg s−1 , which is less than 1.5% of the pulsar rotational energy. The extension of the H.E.S.S. source, the detection of this very young pulsar with significant signal in its off-pulse and the energetics point towards a pulsar wind nebula origin. The

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Fig. 5 Electron spectrum (upper) and broadband emission model (lower) for PWN assuming the evolutionary history described in [31]. The black curves represent a PWN with an age T = 10 kyr, and B(T ) = 5µG, assuming E˙0 = 4 × 1036 erg s−1 and an injection spectrum with σ = 10−3 , γ = 2.5, and Emin = 115 GeV. The magnetic field evolution is characterized by α = 0.65. The magenta curves represent the scenario with a low-energy Maxwellian electron component replacing the low-energy portion of the electron power-law spectrum. The mean temperature for the IR and optical photon fields are 15 K and 5000 K, respectively, and the energy densities relative to the CMB are 4 and 1.15. The dashed curve in the upper panel represents the truncated portion of the power law that was replaced by a Maxwellian. The dashed blue curve in the lower panel represents a model for which all of the γ-ray emission results from pion decay.

very large number of PWNe detected in the TeV energy range (the most numerous class of Galactic TeV sources) and the significant number of PWNe associated with Fermi-LAT pulsars make this scenario highly probable.

8 Conclusion After 1.5 year of observations, 4 pulsar wind nebulae have been detected and identified by Fermi-LAT: the Crab Nebula, Vela-X, the PWN in MSH 15-52 and HESS J1640-465. A new candidate related to the pulsar J1023-5746 is also proposed. These five sources are all powered by young (Age < 11 kyr) and very en-


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ergetic ( E˙ > 1036 erg s−1 ) pulsars. Upper limits on the flux derived in the off-pulse window of J1907+0602 can constrain the low energy spectral shape of the injected spectrum fitting the H.E.S.S. and MILAGRO TeV source. A systematic analysis is now being performed to detect these weak and steady sources using the off-pulse window of all pulsars detected by Fermi, thus providing a first population study of pulsar wind nebulae in the HE gamma-ray domain.

Acknowledgments The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat a` l’Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg

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Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre Na´ tional d’Etudes Spatiales in France.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 46. 23. 20. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 31. 38. 39.

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Pulsar Wind Nebulae: The GeV to TeV Connection O. C. de Jager

Abstract In this paper we focus on pulsar wind nebulae (PWN) which show both GeV and TeV emission. In the case of the Crab Nebula we discuss the implications of the synchrotron cutoff of the Nebula as seen by Fermi-Lat and the implications thereof for particle acceleration at the highest energies. We also show that the emission from almost all PWN as seen in the TeV domain are consistent with electrons that have mostly cooled as a result of synchrotron losses in the extended volume of the PWN, whereas flatter spectrum GeV emission is expected as a result of the relatively long cooling times for these GeV emitting electrons. Such GeV emission is also expected to show a clear scaling with the birth period of the pulsar. This predicted GeV-TeV connection is clearly seen for the PWN of PSR B1509-58. Finally, PWN with two spectral components (radio and X-ray) are also expected to show discontinuous GeV to TeV spectra as seen for Vela X and possibly also for HESS J1640-465. In the case of Vela X we also see this two-component behaviour in the spectrum and morphology of the region close to the pulsar wind termination shock.

1 Introduction Pulsar wind nebulae (PWN) or “plerions”, driven by energetic pulsars, are expected to originate from Type II supernova explosions involving massive progenitors. We may either see an associated shell in which case we refer to a composite supernova remnant, or, we may see only the pulsar with its PWN. It is however expected that the evolution of the PWN will be strongly influenced by the parent pulsar, the supernova explosion and the surrounding interstellar medium as described e.g. by [28], [8], and [32].

O. C. de Jager Unit for Space Physics, North-West University, Potchefstroom, South Africa, e-mail: okkie. [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_35, © Springer-Verlag Berlin Heidelberg 2011

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Our information about PWN have been dominated by synchrotron radio and X-ray observations (see e.g. [18] and references therein), whereas γ-ray observations of PWN have been sparse until the arrival of the so-called “third generation” Cerenkov telescopes which managed to probe the TeV gamma-ray domain of galactic and extragalactic sources. For example, the placement of the High Energy Stereoscopic System (H.E.S.S.) of Cerenkov telescopes in the Southern Hemisphere [22] with its relative wide field-of-view and high angular resolution(< 0.1 degrees) allowed a deep survey of most of the galactic plane, which revealed a number of PWN (and candidates) with properties listed by [23]. See also the review by E. de Ona Wilhelmi of TeV PWN in these proceedings. The Fermi-Lat instrument also managed to probe a few PWN in the GeV domain as reviewed by M.-H. Grondin, also in these proceedings. In this paper we will discuss the new physics we can learn from Crab Nebula observations in the sub GeV to multiple TeV domain. We will also discuss GeV to TeV observations of PWN within the context of single and two component PWN as seen from multiwavelength observations.

2 The Crab Nebula in γ-rays 2.1 The acceleration limit for electrons in the Crab Nebula de Jager et al (1996) [10] managed to measure the synchrotron cutoff of the Crab Nebula by comparing the hard CGRO COMPTEL spectrum in the 10 MeV range with the steep CGRO EGRET spectrum in the 100 MeV domain. A cutoff around 25 MeV was observed, which was shown to be consistent with the fundamental constants of nature if the acceleration timescale for leptons is equal to the gyroperiod, whereas losses is domonated by synchrotron emission. In this case the characteristic synchrotron energy is !2 ! 3 hc Emax = = 25MeV, (1) 4π r0 where r0 is the classical electron radius. For a field strength of B s = 10−4 B−4 G at the termination shock this corresponds to a maximum e+/- energy of γmax me c2 = 1.9B−1/2 −4 PeV, which is about ten times smaller than the maximum polar cap potential drop as remarked by [10]. For a nebular termination shock at a distance of R s ∼ 0.1 pc the ratio of the particle gyroradius to shock radius is R L /R s ∼ 0.2B−3/2 as inferred from the CGRO −4 EGRET observations. These particles are therefore barely contained by the shock.. Recent Fermi-Lat observations of the Crab Nebula by [3] (reproduced in Figure 2) shows a much improved spectrum, with the synchrotron cutoff followed by the steady inverse Compton nebular component which dominates above 300 MeV. The synchrotron cutoff is however higher than during the CGRO EGRET era, with the corresponding e-folding cutoff energy at E max = 97 ± 12 MeV as derived from a

Pulsar Wind Nebulae: The GeV to TeV Connection

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−9

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CANGAROO



−10

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10−12 1

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Fig. 1 The spectrum of the Crab Nebula from 1 MeV to 100 TeV showing the CGRO COMPTEL spectrum at the lowest energies followed by the CGRO EGRET and Fermi-Lat spectrum and then the ground-based gamma-ray measurements up to 100 TeV. The dashed line between 1 MeV and 300 MeV is a fit to the CGRO COMPTEL and Fermi-Lat spectra and represent the synchrotron cutoff as a result of the highest energy electrons near the pulsar wind termination shock. The three curves between ∼ 500 MeV and 100 TeV have been reproduced from [7] and correspond to field strengths of 1, 2 and 3µG (curves from top to bottom). The figure has been reproduced from [3]. Detailed references can also be found in [3].

combination of the CGRO GRO and Fermi-Lat data by [3]. 1 This is clearly seen in terms of a significantly larger Fermi-Lat flux below 300 MeV compared to the lower CGRO EGRET flux. If we take the factor four larger cutoff energy seen by Fermi-Lat as representative, it is clear that the maximum e+/- energy is now γmax me c2 = 3.8B−1/2 −4 PeV, which corresponds to a gyroradius relative to shock radius of RL /R s ∼ 0.4B−3/2 and −4 containment becomes more of an issue. Another remarkable aspect is the acceleration rate required to achieve the FermiLat synchrotron cutoff. For CGRO EGRET we already see that a rate comparable to the gyrofrequency is required to achieve the 25 MeV cutoff. The higher Fermi-LAT cutoff energy at 100 MeV would then require acceleration faster than the gyroperiod. Another way to interpret the Fermi-LAT result is to assume that escape losses rather than synchrotron losses determine the maximum electron energy. We will 1

Note however that there is a time difference of up to 17 years between the CGRO COMPTEL and Fermi-Lat observations and given that we are dealing with a tail in the acceleration spectrum, such comparisons may not be valid.

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assume that the escape time is of the order tesc ∼ R s /c and that the acceleration timescale, scales with the gyroradius as tacc =

ηR L , c

(2)

with η = 2π corresponding to the gyroperiod. 2 Setting the acceleration and loss times equal results in a maximum particle energy due to escape of γmax me c2 ∼ 9 × 1015

B−4 eV, η

(3)

and rewriting this maximum in terms of the maximum characteristic synchrotron energy, we obtain B3 E γ (max) ∼ 570 −4 MeV. (4) η2 Setting this maximum energy equal to the Fermi-Lat measured cutoff energy of 100 MeV we obtain a measurement for η under the assumed conditions: η ∼ 2.5B3/2 −4 ,

(5)

which is certainly faster than the gyroperiod limit of η = 2π. This finding is consistent with the synchrotron loss limit argument (i.e. η < 2π) and this constraint would certainly set limits on particle acceleration models. The reader is also referred to the work of [33] on MHD simulations of the Crab Nebula, which also includes synchrotron and inverse Compton calculations. The variability of the wisps near the termination shock is shown and the authors show the expected amplitudes of variability in the keV, 40 MeV, and TeV domains. The expected variability in the 40 MeV domain is the largest.

2.2 The inverse Compton spectrum of the Crab Nebula - towards the spectral tail Even before the discovery of a pulsar in the Crab Nebula it was known that a source of energetic electrons must be powering this nebula, given the small synchrotron ages relative to the historical age (AD1054) of the the Crab. The presence of the energetic electrons and soft photons prompted Gould [19] to propose a synchrotronself-Compton component in the Crab Nebula. A 1D steady MHD solution for the post shock nebular flow and radial field distribution was the calculated by [24] (KC84). The optimal magnetization parameter was found to be σ = 0.003, which implies a fixed downstream flow velocity profile and magnetic field distribution. Using this magnetic field distribution and obtaining 2

See e.g. the review on this topic given by [15] where η < 2π results in higher energy cutoffs.


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numerical representations for the synchrotron spectra at various radii, the corresponding inverse Compton (synchrotron-self-Compton) spectrum of the Crab Nebula was calculated. The predicted spectrum agreed remarkably well with the earlier observations, which indicates that the KC84 magnetic field distribution should have the correct order of magnitude [9]. At a higher level of sophistication, [7] used the same KC84 solutions to quantify the flow and magnetic field distributions, but solved the transport equation for a spectrum of particles injected at the pulsar wind termination shock, and subjected to the same MHD flow solutions in terms of propagation speed and energy losses. Their spectrum also fits the Crab Nebular spectrum remarkably well. Figure 2 shows the model inverse Compton spectra above 400 MeV corresponding to a few selected field strengths: Given the TeV data, it is clear that the equipartition field strength of ∼ 0.3 mG is too high, resulting in a too low predicted TeV flux. However, a field strength between 0.1 and 0.2 mG appears to be consistent with the Fermi-Lat (above 400 MeV) and TeV observations. Furthermore, the new Fermi-Lat spectrum is clearly better measured compared to the previous CGRO EGRET spectral data and at energies above the synchrotron cutoff (∼ 400 MeV), the Fermi-Lat spectrum also connects smoothly with the ground based TeV spectra, which extends up to ∼ 100 TeV. This clearly demonstrates that we have an overall consistency in terms of calibration between these different instruments. The last challenge for the Crab Nebula is to obtain an actual measurement of the maximum electron energy in the Crab Nebula. In the discussion of Section 2.1 we have seen that the corresponding maximum energy is in the range γmax me c2 ∼ 1.9 PeV to 3.6(2.5/η) PeV for a termination shock field strength of 0.1 mG. These maximum energies are much higher than the typical limit of ∼ 100 TeV for the detection of γ-rays by typical air Cerenkov telescopes. The next attempts to calculate the inverse Compton spectrum spectrum of the Crab Nebula should extend the calculation up to the gamma-ray cutoff near these energies, thereby forcing consistency with the CGRO COMPTEL, EGRET and Fermi-Lat spectral tails. It would then be interesting to see how severe the extreme Klein-Nishina cross section suppresses the PeV γ-ray spectrum. It would also be interesting to see what the amplitude for γ-ray variability is expected to be around 1 PeV: If the variability is only due to magnetic compressions as seen in the synchrotron band, we would not expect to see PeV variability. However, a proper numerical acceleration model at the single particle level included in these MHD simulations should show if the upper tail of the electrons is also variable as a result of MHD variations in the inner nebular region.

3 Accelerated PWN Spectra: Observations of the Cooling Effect Whereas ground based air Cerenkov telescopes revealed a large number of PWN in the galactic plane as reviewed recently by [23], the number of GeV reports are

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sparse up to now. Before we review the observed spectral properties, we first need to comment on the accelerated spectrum responsible for the observed emission. There are various acceleration models as reviewed by [25]: For example, in the pulsar case, annihilation of the ordered magnetic field in the upstream pulsar wind (or in the shock) may leave a highly turbulent, small-scale magnetic field, whose chaotic component significantly exceeds the regular field. Particle scattering off these strong inhomogeneities may then allow the first-order Fermi mechanism to operate. It is interesting that the first-order Fermi mechanism operating at an ultra-relativistic shock yields, in the case of isotropic diffusion of the accelerated particles, an energy distribution of E −2.2 as required to explain the X-ray spectrum of the Crab.

Fig. 2 The distribution of photon indices of PWN as measured by H.E.S.S. and summarized by [23]. The vertical arrow at 1.5 represents the photon index corresponding to the injected electron spectral index of ∼ 2, which would give an uncooled photon index ∼ 1.5 as observed from most pulsar wind termination shocks in the X-ray domain as discussed in the text. Cooling downstream in the wind would increase this index to ∼ 2 as shown by the middle vertical arrow. The further shift to the right (third arrow) is expected from the additional steepening of such a steepened electron spectrum (due to cooling) on the CBMR and soft galactic photon fields in the extreme Klein-Nishina limit.

This index may be universal and an electron spectral index of 2.2 at the termination shock is expected to yield a photon index of 1.6. In fact, it is well known that the uncooled X-ray photon index near the termination shock for several PWN is in the range ∼ 1.5 and cools further downstream to a value of ∼ 2 due to synchrotron cooling as shown e.g. by [30] for G21.5–0.9. The corresponding TeV photon index for G21.5–0.9 is 2.08 ± 0.22 [16]. Since this value is at the upper end of the cooled X-ray photon index, it is clear that the TeV radiation is dominated by electrons which already experienced significant synchrotron cooling in the PWN of G21.5–


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0.9. However, no GeV radiation has been reported so far for this PWN, probably due to sensitivity constraints. We also observe this effect indirectly via the distribution of TeV spectral indices of the majority of PWN as seen in Figure 2. This figure shows a histogram of the TeV photon indices as summarized by [23]. If we assume that the majority of TeV emission is dominated by inverse Compton emission from cooled electrons from the outer regions of the PWN, we would expect the distribution to peak at values > 2. This includes the effect of synchrotron cooling plus the additional spectral steepening effect due to the extreme Klein-Nishina effect as indicated in Figure 2. Why would the spectrum be dominated by the cooled electron spectrum in the outer nebula? We can understand this as a result of the decreasing flow speed towards the outer regions resulting in an increased residence time for the IC emitting electrons. Furthermore, the IC emission does not depend on variations in the field strength. The latter effect however affects the synchrotron emissivity significantly. For example, if the field strength near the termination shock is relatively strong as in the case of high σ (∼ 0.1) winds (KC84), we would expect the synchrotron emission from the total PWN to show a bright central core with the photon index dominated by the harder spectral index in the core region. We see this effect clearly in the X-ray emission of G21.5–0.9 [30] where the average photon index is 1.91 ± 0.04, whereas the spatially (radially) resolved photon index given in Figure 2 of [30] shows full cooling to a photon index ∼ 2.2 in the outer PWN region. This bias (the difference between the average photon index of 1.91 and the outer region value of 2.2) creates confusion when attempting 1D time dependent modelling: The 1D time dependent spectrum of G21.5–0.9 as modelled by [13] correctly shows the effect of full cooling, whereas the CHANDRA spectrum only shows an apparently partially cooled spectral index of 1.9, which is quite confusing.

4 A Single Spectral Component for the GeV to TeV Emission from the PWN of PSR B1509-58 Figure 4 shows the X-ray photon index vs radius as measured by [29] from XMMNEWTON data for the PWN of PSR B1509-58 in MSH15-52. We again see the cooling effect - the photon index is starting at ∼ 1.66 at a distance of ∼ 30 arcsec, increasing to > 2 at distances > 200 arcsec from the pulsar. The observed TeV photon index of ∼ 2.27 [4] is shown as a thick horisontal line. Its alignment with the upper end of the X-ray photon index vs radius graph clearly represents emission from the cooled part of the accelerated spectrum. Using simple analytic MHD principles such as Faraday’s induction law to model the radial dependence of the cooling flow as seen in synchrotron and inverse Compton from the PWN of MSH15-52 (PSR B1509-58), [29] was able to model the X-ray photon index and flux over a limited range of radii, while simultaneously predicting

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Fig. 3 Photon index as a function of radius as measured by XMM-NEWTON by [29]. The horizontal solid line represents the observed average of the TeV photon index as measured by [4], whereas the horizontal dashed indicates the corresponding Fermi-Lat index as measured by [2]. . The vertical arrow represents the amplitude of typical synchrotron cooling as reflected by the X-ray (and TeV) photon index .

the TeV flux within this range as well.3 Although the magnetization parameter σ could not be well constrained (σ > 0.005), the conversion efficiency of spindown power to electrons currently was found to be Crab-like (> 30%). For various scenarios considered the field strength was constrained to decrease from the range 10 to 35µG near the termination shock, down to the range 3 to 10µG at a distance of 7 pc from the pulsar. Below we will discussing the GeV to TeV connection for PWN and MSH15-52 in particular. The emphasis will be on the uncooled nature of the GeV emission, whereas the TeV emission appears to be cooled emission as discussed above. Recently [2] discovered unpulsed high energy emission from the direction the PWN of PSR B1509-58 with Fermi-Lat. It was shown by this Collaboration that the Fermi-Lat spectrum connects continuously with the HESS spectrum as shown Figure 6 of their paper. The corresponding photon index is ∼ 1.57 ± 0.17 ± 0.13 (errors statistical and systematic). This spectrum is significantly harder than the TeV spectrum and the photon index is consistent with the XMM-Newton photon index at the innermost region as shown in Figure 4. It is thus clear that the Fermi-Lat 3

Note that (1) The choice of the inner 300 arcsec region was to limit the analysis to recently emitted electrons, whereas the outer regions near the SNR blast wave would correspond to the full age of the SNR. (2) The PSF of H.E.S.S. is unfortunately comparable to the size of the region of the XMM-NEWTON and model analyses, so that [29] could not test the radial dependence of the observed TeV emission as well.


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emission shares the average spectral properties of the X-ray emission near the pulsar wind termination shock and that these electrons did not cool during transport to the outer nebular regions. Thus, the photon index remains hard. A detailed discussion of the radiation break energy involves a proper time dependent analysis and is beyond the scope of this paper.

5 Calorimetric GeV emission from PWN The abovementioned change from cooled electrons giving rise to TeV emission to a corresponding uncooled GeV component was anticipated by [12] for the accelerated spectral component of PWN. If GeV emitting electrons do not escape from the PWN up to the observed age, the GeV inverse Compton flux would just reflect the change in rotational kinetic energy of the pulsar, times the conversion efficiency of spindown power to electrons/positrons and the only loss process would be due to adiabatic expansion. Thus, we would expect photon indices in the 1.5 range in the Fermi-Lat range as a result of the lack of photon cooling in the GeV domain. Assuming such hard photon indices to be universal, [12] was able to predict a population of GeV PWN (such as the PWN of PSR B1509-58) to be detectable, provided that the galactic background is not too large. The conversion efficiency ǫ of spindown power into electrons, as well as the birth period P0 enters as significant parameters in this parameterization. If the current period P is comparable to the birth period period, then we have to include both to reflect the full change in the rotational kinetic energy as quantified by [12]. Note that we assumed that ǫ remains constant with time. Neglecting the effect of adiabatic losses, the predicted GeV spectrum for P ≫ P0 is then ([12]) dNγ (1 + 1.3U 25) = 4 × 10−8 I45 ǫEγ−1.5 cm−2 s−1 GeV−1 . 2 dtdEγ a10 P240 dkpc

(6)

The parameter U25 is the energy density of the galactic dust component (in units of eV/cm2) at a temperature of T ∼ 25K, which is comparable to the energy density of the CMBR in the local galactic region, but increases to ∼ 1.4 eV/cm3 at the distance of PSR B1509-58. 4 . The parameter a10 ∼ 1 depends weakly (logarithmic) on the ratio of the unknown spectral boundaries of the injected ∼ E −2 electron spectrum as a result of the assumed number index of 2. The only real free parameters is then the birth period and distance to the source. For an assumed distance of 4.2 kpc to PSR B1509-58, a reasonable birth period of 40 ms (as assumed by [12]) and the lower limit of ǫ = 0.3 as derived by [29], we arrive at a predicted integral GeV flux of F(> 1 GeV) = 4 × 10−9 cm−2 s−1 , which is remarkably close to the observed Fermi-Lat flux [2] of F(> GeV) ∼ 3 × 10−9 cm−2 s−1 . This prediction is remarkably close to the observed flux, given the signif4

See GALPROP for a mapping of the ISRF

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icant uncertainty in the birth period. In fact, this prediction indicates that the birth period of PSR B1509-58 cannot be much different from ∼ 40 ms.5

6 Discontinuous GeV and TeV Emission from Two-Component PWN 6.1 Two-Component Extended Emission from the Vela X PWN During the era of CGRO observations, de Jager et al. (1996) [11] remarked that the radio spectrum of the full 2◦ × 3◦ radio PWN of Vela X does not fit continuously with the X-ray spectrum of Vela X, so that a spectral break νb for this bright radio component is implied. We also remarked that electrons from this nebula should inverse Compton scatter photons from the CMBR, far infrared photons due to dust scattering and starlight photons. We illusrated this effect as a contour plot of the 0.1 to 1 GeV flux, with the radio cutoff frequency νb on the vertical axis and the unknown magnetic field strength (before the era of H.E.S.S., AGILE or Fermi-Lat) on the horizontal axis, as reproduced in Figure 1. de Jager, Slane & LaMassa (2008) [14] expanded on this (including X-ray and H.E.S.S. data) and predicted that the GeV and TeV spectra should also join discontinuously, thus proving the two component behaviour of Vela X also from an inverse Compton perspective, where the imaging field-of-views are large enough to include the total Vela X size. The main uncertainty was however the radio cutoff (νb ) in the mm range, since the field strength could be fixed from synchro-Compton observations. Finally, AGILE [27] and Fermi-Lat [1] discovered resolved GeV emission from Vela X. The integral flux above 100 MeV from the two instruments are compatible within statistical and systematic errors (∼ 3.5 × 10−7 cm−2 s−1 and ∼ 4.7 × 10−7 cm−2 s−1 for AGILE and Fermi-Lat respectively), although the morphologies between the two instrument are not yet convergent. From a multiwavelength study [1] found that the best fit cutoff frequency is in the νb ∼ 2 × 1011 Hz range. The field strength ranges between 4µG [1] and 5µG [14]. All three parameters (integral flux, νb and field strength are consistent with the intersection shown in Figure 1.

6.2 Radio and X-Ray Torii of Vela X near the Termination Shock: Discontinuous Spectra We obtain a better insight into the origin of the two components (radio and X-rays) if we zoom into the region close to the pulsar wind termination shock. Helfand et al. (2001) [21] discovered a double ring torus with perpendicular jet axis, which is 5

Correcting for adiabatic losses will decrease this birth period somewhat.


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Fig. 4 Contours of the expected inverse Compton flux in the 0.1 to 1 GeV range (logarithm of flux) from the Vela X radio PWN for different assumed radio cutoff frequencies and nebular magnetic field strengths. Figure reproduced from Figure 3 of [11]. The flux (above 100 MeV) at the intersection of the vertical line at ∼ 4 to 5µG and horisontal line at a cutoff frequency of ∼ 2 × 1011 Hz corresponds to the AGILE and Fermi-Lat fluxes within statistical errors.

also aligned with the spin axis and proper motion direction of the pulsar. Dodson et al. (2003) [17] made a remarkable discovery: There is no excess radio emission associated with the X-ray torus, but a radio torus was discovered, with symmetry axis (as seen from polarization vectors) aligned with the axis of the X-ray torus. The size of the radio torus is ∼ 3 times larger than the arcminute sized X-ray torus (see Figure 3). Note also that over the radio size we see no evidence of X-ray cooling, so that the smaller X-ray torus cannot be due to cooling. No satisfactory explanation has been given so far for the dissimilar X-ray and radio toroidal sizes. At larger distances (scale sizes of degrees) from the pulsar the effect of the reverse shock starts to dominate as seen from the offset morphology of the total Vela X radio PWN and the offset X-ray/TeV cocoon. Figure 6 shows the corresponding spectral behaviour for the two torii: The radio spectrum is also hard (similar to the total Vela X radio spectrum) and we see a slight difference in spectral shapes between the northern and southern parts of the radio torus. From this Figure it is clear that the spectrum of the X-ray torus also do not

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Fig. 5 2.4 GHz radio map with E-field vectors of the ∼ 12′ × 12′ region around the Vela pulsar. The northern and southern radio lobes form the radio torus. The faint double ring at the center of the radio torus indicates the orientation and size of the X-ray torus. Adapted from Figure 4 of [17]

connect smoothly with that of the radio torus, and this effect may propagate to large distances, giving rise to the observed two component spectrum of Vela X.

7 HESS J1640–465: Another Two-Component Candidate? Vela X and HESS J1640–465 shares one important feature: Both PWN appears to be older than 10 kyr. Apart from Vela X having the reverse shock induced offset morphology, [26] also discovered an offset morphology in X-rays as revealed by CHANDRA observations. Fermi-Lat recently discovered unpulsed emission from the PWN of this source, with a remarkable feature [31]: Whereas the TeV photon index is (2.42 ± 0.15), which is expected to be so steep as a result of electron cooling far away from the pulsar, the Fermi-Lat index above 0.1 GeV is also relatively steep (2.30 ± 0.09) and would also be indicative of a cooled spectrum. This represents an apparent discrepancy since the cooling time for GeV emitting electrons is typically longer than the


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Fig. 6 Energy spectrum (in νFν ) of the radio torus of the Vela pulsar split into two components: The northern lobe (closed circles) and the southern lobe (open circles). Spectral points are from [17] and [20]. The X-ray spectrum of the X-ray torus is indicated by the solid line, whereas the extrapolation to radio frequencies is indicated by a dashed line.

Fig. 7 Energy spectrum (in νFν ) of the multiwavelength spectrum of HESS J1640-465 showing the HESS, Fermi-Lat, X-ray and GMRT radio upper limit. The light gray radio/GeV component with a GeV excess was added to explain the steep Fermi-Lat spectrum. Reproduced from Figure 5 of [31].

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age of the system. We should thus have seen spectral indices in the range 1.5 to 1.6 for the GeV emission, corresponding to the uncooled index near the pulsar wind termination shock as predicted by [12] and shown in the spectral modelling by [31]. Experience from the Vela X example prompted [31] to propose a scenario similar to Vela X, where a discontinuous radio component, having the highest peak on the νF ν multiwavelength plot is also responsible for the GeV inverse Compton emission as shown in Figure 7. Without this second component we should have seen a faint but hard GeV component, which may have been undetectable. We also note that the maximum of the assumed radio spectral energy distribution for HESS J1640–465 is a factor 10 larger compared to the corresponding maximum for Vela X. The next step for verification is to employ a next generation sensitive imaging radio telescope like the South African MeerKAT forerunner for the SKA 6 to image the radio counterpart of this PWN. It would then also be interesting to see if the full SKA will be able to detect a similar radio torus (as seen from Vela X) around the pulsar counterpart of HESS J1640–465.

8 Conclusions Even though the Crab Nebula is the best studied PWN at all wavelengths, there are still several unanswered questions and challenges. We list a few: • What is the acceleration mechanism for electrons at the termination shock? From observations and the discussions in this paper we see that the acceleration timescale appears to be faster than the gyroperiod of the electron. • How does the observed wisp variability correlate with soft γ-ray observations? Long term, but frequent optical observations of wisp motions can be compared with high energy observations, where the corresponding gyroradii are comparable to the scale sizes of the wisp turbulence. • Up to the writing of this paper, no variability in the Crab Nebular emission below 300 MeV has been reported by Fermi-Lat. Will we e.g. see variabilty similar to that seen between CGRO EGRET and Fermi-Lat in future long-term Fermi-Lat data? • Will we be able in future to detect the PeV cutoff directly in the PeV γ-ray domain and is this component variable? This question actually pushes the limits of observational techniques. After combining all available PWN spectral indices as measured in the TeV domain, we see that these indices cluster around a mean value of ∼ 2.2. However, in the X-ray domain where we have better spatial resolution, we clearly see a clustering of photon indices at values ≥ 1.5, with a gradual steepening to values ∼ 2 at further distances from the pulsar as a result of synchrotron cooling (we have shown 6

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such an example for the PWN of PSR B1509-58). It is thus clear that the energy of the TeV emitting electrons in most PWN are high enough that most of these electrons also suffer from the same cooling as their X-ray counterparts, so that we see the abovementioned clustering effect. A few TeV PWN however do not show this cooling, with one clear example being Vela X [6], which has a typical flat photon spectral index of ∼ 1.5 (at energies below 13 TeV), reminiscent of spectra injected at the pulsar wind termination shock. This spectral component then propagted without any further steepening from the termination shock to the rest of the cocoon of Vela X. If we however consider electron energies well below those responsible for IC scattering in the TeV domain, the lifetimes become longer than the age of the remnant. The corresponding IC photon energies are typically in the GeV domain, as discussed by [12] and we should then see similar flat photon indices near 1.5 as seen in X-rays near PWN termination shocks. This was clearly demonstrated by TeV and Fermi-Lat observations of the PWN of PSR B1509-58: The GeV photon index is ∼ 1.6, whereas the TeV photon index is ∼ 2.3, with the spectral region in between clearly mapped out by the evolving X-ray photon index from ∼ 1.66 to ∼ 2.2 as seen by XMM-Newton. We note however that this PWN is relatively bright in TeV, so that the flat spectral GeV counterpart is clearly detected by Fermi-Lat. However, scaling the TeV emission down to the typical lower TeV flux levels as seen from the rest of the TeV PWN population, also implies correspondingly lower GeV flux levels, and given the structured galactic background, we expect that Fermi-Lat may have difficulty to detect several new PWN with similar characteristics in future. A new feature recently emerged in the GeV to TeV domain, showing that there may be a population of PWN for which we have clear evidence of two spectral components: When comparing AGILE and Fermi-Lat observations of Vela X with the higher energy H.E.S.S. observations of the same source, we clearly see this twocomponent behaviour as predicted earlier by [11] and [14]. The same behaviour may possibly also be present for HESS J1640–465. However, from the multiwavelength spectral energy distributions of both sources it is clear that the IC GeV emission already results from electrons which are also responsible for the radio spectral maxima, so that we may again be dealing with a sensitivity issue for the GeV domain if we would attempt to extend such searches to other PWN. Another interesting observation is that the two-component spectral behaviour seen from the full Vela X PWN is also clearly visible at/near the pulsar wind termination shock: (a) We observe a discontinuous radio to X-ray spectrum, and (b) these two spectral components also have different pulsar torii as their origin in the sense that the radio torus is larger than the X-ray torus. Finally, whereas ground-based TeV observations revealed a wealth of new information on PWN in the galactic plane, AGILE and Fermi-Lat will hopefully be able to contribute similarly to the GeV information in the near future.

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References 1. Abdo, A.A. et al. (Fermi-Lat Collaboration), Fermi Large Area Telescope Observations of the Vela-X Pulsar Wind Nebula, Astrophys. J. 713, 146–153 2. Abdo, A.A. et al. (Fermi-Lat Collaboration), Detection of the Energetic Pulsar PSR B1509-58 and its Pulsar Wind Nebula in MSH 15-52 Using the Fermi-Large Area Telescope, Astrophys. J. 714, 927–936 (2010) 3. Abdo, A.A. et al. (Fermi-Lat Collaboration), Fermi Large Area Telescope Observations of the Crab Pulsar And Nebula, Astrophys. J. 708, 1254–1267 (2010) 4. Aharonian,F.A. et al. (H.E.S.S. Collaboration), Discovery of extended VHE gamma-ray emission from the asymmetric pulsar wind nebula in MSH 15-52 with HESS, A&A 435, L17–L20 (2005) 5. Aharonian, F.A. (for the H.E.S.S. Collaboration), The H.E.S.S. Survey of the Inner Galaxy in Very High Energy Gamma Rays, Astrophys. J. 636, 777–797 (2006) 6. Aharonian, F.A. (for the H.E.S.S. Collaboration), First detection of a VHE gamma-ray spectral maximum from a cosmic source: HESS discovery of the Vela X nebula, A&A 448, L43– L47 (2006) 7. Atoyan, A.M., & Aharonian, F.A., On the mechanisms of gamma radiation in the Crab Nebula, Monthly Notices of the Royal Astronomical Society 278 525–541 (1996) 8. Blondin, J.M., Chevalier, R.A., Frierson, D.M., Pulsar Wind Nebulae in Evolved Supernova Remnants, Astrophys. J. 563, 806–815, (2001) 9. de Jager, O.C., Harding, A.K., The expected high-energy to ultra-high-energy gamma-ray spectrum of the Crab Nebula, Astrophys. J. 396, 161–172 (1992) 10. de Jager, O.C., Harding, A.K., Michelson, P.F., Nel, H.I., Nolan, P.L., Sreekumar, P., & Thompson, D.J., Gamma-Ray Observations of the Crab Nebula: A Study of the SynchroCompton Spectrum, Astrophys. J. 457, 253–266 (1996) 11. de Jager, O.C., Harding, A.K., Sreekumar, P., & Strickman, M., The Crab and VELA gamma ray nebulae, Astron. & Astrophys. Suppl. 120, 441–444 (1996) 12. de Jager, O.C., Estimating the Birth Period of Pulsars through GLAST LAT Observations of Their Wind Nebulae, Astrophys. J. 678, L113–L116 (2008) 13. de Jager, O.C., Ferreira, S.E.S., & Djannati-Ata¨ı, A., MHD and Radiation Modelling of G21.5–0.9, In: HIGH ENERGY GAMMA-RAY ASTRONOMY: Proceedings of the 4th International Meeting on High Energy Gamma-Ray Astronomy. AIP Conference Proceedings 1085, 199–202 (2008) 14. de Jager, O.C., Slane, P. O., & LaMassa, S., Probing the Radio to X-Ray Connection of the Vela X Pulsar Wind Nebula with Fermi LAT and H.E.S.S., Astrophys. J. 689, L125–L128. (2008) 15. de Jager, O.C., & Djannati-Ata¨ı, A., Implications of HESS Observations of Pulsar Wind Nebulae. In: Neutron Stars and Pulsars, Astrophysics and Space Science Library, Springer Berlin Heidelberg, 357, 451–479 (2009) 16. Djannati-Ata¨ı, A., de Jager, O.C., Terrier, R., et al., New Companions for the lonely Crab? VHE emission from young pulsar wind nebulae revealed by H.E.S.S., In: Proceedings of the 30th International Cosmic Ray Conference. July 3 - 11, 2007, Mrida, Yucatn, Mexico. Eds. Rogelio Caballero, Juan Carlos D’Olivo, Gustavo Medina-Tanco, Lukas Nellen, Federico A. Snchez, Jos F. Valds-Galicia. Universidad Nacional Autnoma de Mxico, Mexico City, Mexico, 2, 823–826 (2008) 17. Dodson, R., Lewis, D., McConnell, D., & Deshpande, A.A., The radio nebula surrounding the Vela pulsar, MNRAS 343, 116–124 (2003) 18. Gaensler, B.M. & Slane, P.O., The Evolution and Structure of Pulsar Wind Nebulae, Ann. Rev. of Astron. & Astrophys. 44, 17–47 (2006) 19. Gould, R.J., High-Energy Photons from the Compton-Synchrotron Process in the Crab Nebula, Physical Review Letters 15, 577–579 (1965)


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20. Hales, A.S., Casassus, S., Alvarez, H., May, J., Bronfman, L., Readhead, A.C., Pearson, T.J., Mason, B.S., & Dodson, R. Astrophys. J. 613, 977–985 (2004) 21. Helfand, D.J., Gotthelf, E.V., & Halpern, J.P., Vela Pulsar and Its Synchrotron Nebula, Astrophys. J. 556, 380–391, (2001) 22. Hinton, J. A. (H.E.S.S. Collaboration), The Status of the H.E.S.S. project, New Astron. Rev. 48, 331–337 (2004) 23. Kargaltsev, O. & Pavlov, G.: Pulsar-wind nebulae in X-rays and TeV gamma-rays. In: Proceedings of ”X-ray Astronomy 2009”, Bologna, Italy, eprint arXiv:1002.0885 to be published by AIP (2010) 24. Kennel, C.F., & Coroniti, F.V., Confinement of the Crab pulsar’s wind by its supernova remnant, Astrophys. J. 283, 694–709 (1984) 25. Kirk, J.G., Lyubarsky, Y., & Petri, J., Theory and Pulsar Winds and their Nebulae, In: Neutron Stars and Pulsars, Astrophysics and Space Science Library 357, 421, (2009) 26. Lemiere, A., Slane, P., Gaensler, B.M., Murray, S., High-resolution X-ray Observations of the Pulsar Wind Nebula Associated with the Gamma-ray Source HESS J1640-465, Astrophys. J. 706, 1269–1276 (2009). 27. Pellizzoni, A. et al. (AGILE Collaboration), Detection of Gamma-Ray Emission from the Vela Pulsar Wind Nebula with AGILE, Science 327, 663–665 (2010) 28. Reynolds, S. P., Chevalier, R. A., Evolution of pulsar-driven supernova remnants, Astrophys. J. 278, 630–648, (1984) 29. Schöck, F.M., Büsching, I., de Jager, O.C., Eger, P., & Vorster, M.J., Spatially resolved XMMNewton analysis and a model of the nonthermal emission of MSH 15-52, to appear in Astron. & Astrophys., eprint arXiv:1005.0785 30. Slane, P., Chen, Y., Shulz, N.S., Seward, F.D., Hughes, J.P., & Gaensler, B.M., Chandra observations of the Crab-like Supernova Remnant G21.5–0.9, Astrophys. J. 533, L29-L32 (2000) 31. Slane, P., Castro, D., Funk, S., Uchiyama, Y., Lemiere, A., Gelfand, J. D. Lemoine-Goumard, M., Fermi Detection of the Pulsar Wind Nebula HESS J1640-465, submitted to Astrophys. J., eprint arXiv:1004.2936, (2010) 32. van der Swaluw, E., Downes, T.P., & Keegan, R., An evolutionary model for pulsar-driven supernova remnants. A hydrodynamical model, Astron. & Astrophys. 420, 937–944 (2004) 33. Volpi, D., Del Zanna, L., Amato, E., & Bucciantini, N., Non-thermal emission from relativistic MHD simulations of pulsar wind nebulae: from synchrotron to inverse Compton, Astron. Astrophys 485, 337–349 (2008)

Extended hard X-ray emission from Vela X Fabio Mattana, Régis Terrier, Diego Götz, Gabriele Ponti, Laurent Bouchet, Maurizio Falanga, Matthieu Renaud, Stephane Schanne

Abstract Vela X powered by the Vela pulsar is the best example of an evolved pulsar wind nebula, allowing to access the particle injection history and the interaction with the supernova ejecta. We present the spectrum of Vela X in the 20–300 keV energy range as measured by IBIS/ISGRI and SPI, the main instruments onboard the INTEGRAL satellite. The apparent discrepancy between IBIS/ISGRI, SPI, and previous measurements is understood in terms of point spread function, pointing out a nebula more diffuse than previously thought. The presence of cooled electrons is also revealed by the spectral break measured including Suzaku data in the 1–10 keV range. This picture is supported by the identification of a new structure in the 20–60 keV energy band extended along the NE/SW axis and partially coincident with the cocoon, the soft X-ray filament extending towards the centre of the remnant.

1 Introduction Vela X powered by the Vela pulsar PSR B0833–45 is the most studied pulsar wind nebula (PWN) in a fairly evolved state. Located at the close distance of 290 pc [5], Vela X was discovered as a large (∼2-3◦) radio nebula embedded in the 3.5◦ radius Vela supernova remnant. In X-rays, ROSAT found a filament extending ∼45′ south/south-west from the pulsar [9]. This so-called cocoon is explained by the dynamics of the supernova remnant in the Sedov-Taylor phase (∼10 kyr since the pulsar birth). If the remnant is expanding in an inhomogeneus interstellar medium, the inward moving reverse shock reaches the PWN boundaries at different times, asymmetrically compressing the PWN and displacing the bulk of the electrons from the pulsar position [3]. This explanation has been confirmed by the H.E.S.S. detection of extended TeV emission matching the X-ray cocoon [2], with the brightness peak sigFabio Mattana AstroParticule et Cosmologie (APC: CNRS-Université Paris 7), 10 Rue Alice Domon et Léonie Duquet, F-75205 Paris Cedex 13, France, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_36, © Springer-Verlag Berlin Heidelberg 2011

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Fig. 1 IBIS/ISGRI significance map in the 20-40 keV range, Galactic coordinates. First panel: significance map

smoothed with a 3 pixel (σ∼7.5′ ) Gaussian kernel. Other panels: unsmoothed significance map. Contours: ROSAT, 0.5-2 keV (green); H.E.S.S., VHE γ-rays above 1 TeV (yellow); Spacelab 2, 2.5-12 keV (cyan).

nificantly offset from the pulsar. The multiwavelength morphology and spectrum of Vela X, complemented by the recent GeV detections by AGILE [11] and Fermi [1], suggest two populations of electrons: a younger one, responsible of the X-ray and TeV emissions, and an older one, more diffuse and peaking in radio and high energy γ-rays [4]. The angular resolution of IBIS/ISGRI on board the INTEGRAL observatory, unprecedented in the 20 keV - 1 MeV range, allows to adress the problem of the boundaries of the X-ray nebula. Here we report on the INTEGRAL identification of extended hard X-ray emission from Vela.

2 INTEGRAL identification of extended hard X-ray emission We analyzed all public IBIS/ISGRI data within 12◦ from the Vela pulsar, for a total exposure of 5.6 Ms. In the 18-40 keV mosaicked image (Fig. 2) we found a 85σ point-like source. The radius of the point spread function (PSF) ∼6′ encompasses the Vela pulsar and the structured inner nebula resolved by Chandra [6]. An hint of extended feature is also apparent in the NE/SW direction, extending ∼50′ on both sides. The NE side is larger and more significant, whereas the thinner SW side is partially coincident with the ROSAT and H.E.S.S. cocoon (Fig. 2, second and third panels, respectively). The IBIS/ISGRI feature also matches the 2.5-10 keV extended emission found by the Birmingham Spacelab 2 telescope [12] (Fig. 2, fourth panel). The individual pixels in the extended structure are at the ∼3-6σ significance level, which does not allow for a firm detection. However, such a large cluster of lowsignificance pixels is not observed in the rest of the image, and it is not reminescent of IBIS/ISGRI residual coding noise. An evidence of extended hard X-ray emission from Vela X is provided by the spectral analysis. We extracted the IBIS/ISGRI spectrum of the point-like source from mosaicked images in narrow energy bands between 20 and 200 keV (Fig.2, left panel). It can be fitted with a single power law model with photon index ΓISGRI = 1.98 ± 0.05

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PWN. Suzaku/XIS data were extracted in a circular region of 6′ radius centered on the pulsar to match the IBIS/ISGRI PSF. We modeled the pulsar contribution by fixing two black bodies and a power law, corrected by the interstellar absorption, with fixed parameters as measured by XMM-Newton [8]. Below 1 keV several narrow positive residuals are found, which most likely are due to unmodeled emission lines from the thermal supernova remnant. Right: integrated flux in the 20-40 keV band at varying extraction radii (black diamonds), along with BeppoSAX/PDS and SPI fluxes in the same band. In this case the integration radius is given by their PSF (6′ , 39′ , and 1.3◦ for IBIS/ISGRI, BeppoSAX/PDS, and SPI respectively) . The origin of the x-axis corresponds to the pulsar position. The third point of the IBIS/ISGRI integrated flux profile encloses the flux of the point-like source, that is the Vela inner compact nebula.

and flux F = (4.75 ± 0.07) × 10−11 erg cm−2 s−1 in the 20–40 keV range. We also analyzed the SPI data from the same observations, and found a power law spectrum in the 20–300 keV range with compatible photon index, ΓSPI = 2.15 ± 0.15, but higher flux, F = (9.1 ± 0.6) × 10−11 erg cm−2 s−1 in 20–40 keV, with respect to IBIS/ISGRI. A joint fit of the IBIS/ISGRI and SPI data yields a compatible photon index, but it requires a factor 1.8 to recover the higher SPI flux. Such a discrepancy can not be due to an intercalibration factor, which in the case of IBIS/ISGRI and SPI is in the 0.8-1.2 range.The photon index measured by BeppoSAX/PDS, ΓPDS = 2.01 ± 0.05, is consistent with both the INTEGRAL indices, whereas the flux lies between IBIS/ISGRI and SPI. As shown in Fig.2 (right panel, red datapoints), the IBIS/ISGRI, BeppoSAX/PDS, and SPI fluxes correlates with the respective PSF radii (6′ , 39′ , and 1.3◦ ), suggesting that each instrument samples a different size of the nebula. Due to the coded mask deconvolution of IBIS/ISGRI, the reconstructed fluxes of an extended source of 60′ radius is lower than the real one by a factor ∼50 [10]. Therefore, such a source with a 4.3 × 10−11 erg cm−2 s−1 (the difference between the SPI and ISGRI fluxes), would be lowered to 10−12 erg cm−2 s−1 , close to the sensitivity limit of IBIS/ISGRI. To support the hypotesis that an extended source is present, but diluted in the coded mask deconvolution, we refined the analysis of the ISGRI data following the prescription for extended sources. We extracted the IBIS/ISGRI flux from concentric circles centered on the pulsar with radii up to 100′ . After 15′ , this integrated flux as a function of the extraction radius (Fig 2, right panel) does not reach a plateau, as it would be expected from a point-like source, but slowly increases up to ∼60′ . Most importantly, the IBIS/ISGRI flux nicely recovers the BeppoSAX/PDS and SPI fluxes at extracting radii comparable with their PSF. This confirms that Vela X is detected in the 18-40 keV and it is extended.

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3 Combined IBIS/ISGRI and Suzaku/XIS spectral analysis The MECS and PDS on board BeppoSAX allowed to measure a spectral break with energy 12.5 ± 1.5 keV [7]. However, the different angular resolution of the two instruments required the authors to rescale the PDS flux from 39′ , its PSF, to 15′ , the maximum extraction radius of MECS. With a much smaller PSF, INTEGRAL IBIS/ISGRI can be combined with Suzaku/XIS on the same extraction radius. We analyzed public available Suzaku data. Within an extraction circle of 6′ radius from the Vela pulsar position, the derived spectrum shows a power law component with photon index 1.654 ± 0.005, and a 3-10 keV flux compatible with the MECS in the same region. To fit the IBIS/ISGRI and XIS data simultaneously, a spectral break is required at 27.4 ± 3.5, higher than the one derived by BeppoSAXon a larger regions, which could suggest an electron cooling in the propagating nebular outflow.

4 Conclusions The main concern of this contribution was to establish the diffuse hard X-ray emission from Vela X as pointed out by INTEGRAL observations. The different flux between IBIS/ISGRI, BeppoSAX/PDS, and SPI is explained by their different PSF, sampling different sizes of the PWN. The similar photon indexes found in the spectra of the three instruments suggest that the electron population radiating in hard X-rays has undergone a significant synchrotron burn-off. The detailed morphology of the hard X-ray nebula is still an open question. An indication of extended feature is present in the IBIS/ISGRI image in the 18-40 keV band. It is surprising to find that it extends mostly on the northern side, where the reverse shock scenario predicts the strongest compression. The physical implications and the details of these results will be presented in a forthcoming work.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Abdo, A. A., et al. 2010, ApJ, 713, 146 Aharonian, F., et al. 2006, A&A, 448, L43 Blondin, J. M., Chevalier, R. A., & Frierson, D. M. 2001, ApJ, 563, 806 de Jager, O. C., Slane, P. O., & LaMassa, S. 2008, ApJL, 689, L125 Dodson, R., Legge, D., Reynolds, J. E., & McCulloch, P. M. 2003, ApJ, 596, 1137 Helfand, D. J., Gotthelf, E. V., & Halpern, J. P. 2001, ApJ, 556, 380 Mangano, V., Massaro, E., Bocchino, F., Mineo, T., & Cusumano, G. 2005, A&A, 436, 917 Manzali, A., De Luca, A., & Caraveo, P. A. 2007, ApJ, 669, 570 ¨ Markwardt, C. B., & Ogelman, H. B 1995, Nature, 375, 40 Renaud, M., et al. 2006, A&A, 456, 389 Pellizzoni, A., et al. 2010, Science, 327, 663 Willmore, A. P., Eyles, C. J., Skinner, G. K., & Watt, M. P. 1992, MNRAS, 254, 139

Cherenkov Telescopes Results on Pulsar Wind Nebulae and Pulsars Emma de Oña Wilhelmi

Abstract The last few years have seen a revolution in very high γ-ray astronomy (VHE; E>100 GeV) driven largely by a new generation of Cherenkov telescopes. These new facilities, namely H.E.S.S. (High Energy Stereoscopic System), MAGIC (Major Atmospheric Gamma Imaging Cherenkov Telescope) and its upgrade MAGIC 2, VERITAS (Very Energetic Radiation Imaging Telescope Array System) and CANGAROO (Collaboration of Australia and Nippon for a Gamma Ray Observatory in the Outback) were designed to increase the flux sensitivity in the energy regime of hundreds of GeV, expanding the observed energy range from 50 to multi-TeV, and fostered as a result a period of rapid growth in our understanding of the Non-Thermal Universe. As a result of this fast development the number of pulsar wind nebulae (PWNe) detected has increased from a few in the early 90’s to more than two dozen of firm candidates nowadays. Also, the low energy threshold achieved allows to investigate the pulsed spectra of the high energy pulsars powering PWNe. A review of the most relevant VHE results concerning pulsars and their relativistic winds is discussed here in the context of Cherenkov telescopes.

1 Introduction Pulsars and their relativistic winds have been extensively observed in radio and Xray wavelength. The non-thermal synchrotron emission detected from these systems provides evidence for particle (leptons) acceleration to extremely high energies, susceptible to inverse-Compton (IC) scatter target soft photons in the surrounding medium and produce very high energy γ-ray emission (VHE; E>100 GeV). Recent observations of Galactic sources with Imaging Cherenkov Atmospheric telescopes (IACTs) have revealed PWNe as the most effective Galactic objects population in Emma de Oña Wilhelmi Max-Planck-Institut für Kernphysik, P.O. Box 103980, D 69029 Heidelberg, Germany, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_37, © Springer-Verlag Berlin Heidelberg 2011

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Fig. 1 VHE sources associated with PWNe in the Galactic Plane [58]

producing VHE γ-ray emission. As early as 2004, only the Crab PWN was detected with a steady γ-ray flux above 1 TeV of (2.1±0.1stat)×10−11 ph cm−2 s−1 [21, 61]. The development of new sensitive IACTs in the last years has raised the number of likely PWNe detected up to at least 27 sources, whereas many of the unidentified γ-ray sources are widely believed to be PWNe (or old relic PWNe). Their position in the sky are illustrated in Fig. 1 (from the TeVCat supported by [58]). These VHE PWNe are related with young and energetic pulsars which are powering a high magnetized nebula. In this scenario, particles are accelerated to VHE along their expansion into the pulsar surroundings or at the shocks produced in collisions of the winds with the surrounding medium. As a result of the interactions of relativistic leptons with the magnetic field and low energy radiation (of synchrotron origin, thermal, or microwave background), non-thermal radiation is produced from the lowest possible energies up to ∼100 TeV. On the other hand, for a few µG magnetic fields, young electrons create a small synchrotron nebula around the pulsar which should be visible in X-rays, in contrast of a often much larger TeV nebula, generated by IC processes (for a recent review see [42]). Typically only young pul33 erg s−1 ) produce prominent PWNe [46]. ˙ sars with large spin-down energy (E>10 This is illustrated in Fig. 2 where the spin-down power of radio pulsars from the ATNF catalog ([48]) is shown versus their characteristic age [34]. Pulsars powering γ-ray PWNe are marked with red bullets. The discovery of these large population of TeV PWNe has provided a large input for multi-wavelength models of particle evolution and acceleration in these objects. Theoretical MHD models (carried out by i. e. [62]) have proven that the relativistic wind of particles driven by a central pulsar blow into the ambient medium and create a termination shock that accelerates the particles to VHE in a PWN. The broadband spectrum of a PWN thus provides constrains on the integrated energy injected by the pulsar as well as on the effects of adiabatic expansion and the evolution of the

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magnetic field. The spectrum consists of two components, 1) synchrotron emission extending from the radio into the X-ray and, in some cases, the MeV band, and 2) IC emission producing GeV and TeV photons. Emission in the TeV band originates primarily from IC scattering of ambient soft photons with energetic electrons in the nebula, mainly the interstellar medium (ISM), the 2.7 K cosmic microwave background radiation (CMBR), synchrotron-self-Compton radiation and contribution of optical and far infrared photon fields. The typical energies Eγ and ǫx of the IC and synchrotron photons produced by an electron are related by Eγ ≃ 2(ǫx /0.1keV)(B/10µG)−1.

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Spin−down Power (erg s−1kpc −2)

Therefore VHE studies and comparison with the spatial and spectral structure of the X-ray emission provide essential material for modeling the synchrotron radiation in the inner part of the nebula as well as for understanding the evolution of the system. On the other hand, the comparison with TeV gamma-rays produced by the same electrons provides information about the magnetic field since the radiative energy loss of electrons is shared between synchrotron and IC channels: Lγ /Lx = ωph /ωB ≃0.1(B/10 µG)−2 . The combined observations at VHE, X-rays and radio wavelength is crucial to constrain then the evolution of the nebula magnetic field as well as the magnetic-to-kinetic energy conversion. A second goal pursued with Cherenkov telescopes has been to explore the relatively poorly known range of the electromagnetic spectrum between 10 and 100

Characteristic Age (yr)

Fig. 2 Spin-down Power versus Characteristic Age from pulsars from the ATNF database. The red bullets show the ones powering TeV PWNe [34].

438

Emma de Oña Wilhelmi Ω

Polar cap model

. B=0 Ω

rotation axis

µ

Ω

µ

γ

magnetic axis

γ

polar cap

e+

outer gap

γ

open field line

e_

γ

e_

e+ e_

γ

e_

γ

closed field lines

e+

γ

neutron star

Outer gap model outer gap

γ

γ e+

last neutron star

e−

γ

clos ed f ie

e+ e−

e−

γ e−

ld li

ne

Light cylinder

open field lines

e−

e+

0

. B= Ω

Light cylinder

Fig. 3 On the left, sketch of a pulsars magnetosphere and possible acceleration regions. On the right, illustration of the polar cap and outer gap mechanisms [52].

GeV, using very large reflectors to decrease the energy threshold to a few tens of GeV. One of the main motivations was to understand the physics phenomena in pulsars at these energies, where most of them show a sharp spectral cutoff, predicted by different theoretical models. The position of this spectral cutoff however varies depending on the emission model considered. In the polar cap model [44] electrons are accelerated above the polar cap radiating γ-rays via synchrotron-curvature radiation. Since these γ-rays are created in super-strong magnetic fields, magnetic pair production is unavoidable, and hence, only those secondary photons which survive pair creation (a few GeV for typical pulsar magnetosphere) escape to infinity as an observed pulsed emission (see Fig. 3). A natural consequence of the polar cap process is a super-exponential cutoff of the spectrum above a characteristic energy Eo . On the contrary, in the outer gap model [50, 62] γ-ray production is expected to occur near the light cylinder of the pulsar, far away from the stellar surface. In this case the cutoff is determined by photon-photon pair production, which has a weaker energy dependence compared to magnetic pair production, and therefore a higher energy cutoff may be observable. High energy (HE; 100 MeV<E100 GeV) with previous Cherenkov telescopes. Recently, the Fermi LAT collaboration has reported a large number of bright HE pulsars characterized by sharp cutoffs in the phase-average photon spectrum between 1 and 10 GeV [1]. The large sample of GeV pulsars detected and detailed modeling carried out by i. e. [51] allow to conclude that γ-ray emission from the brightest pulsars arises largely from


439

Table 1 Main characteristics of IACT Experiment

Location hei., lat., long. (m, ◦ , ◦ )

H.E.S.S.

Khomas Highland Namibia 1800 23S 15E

428

0.1

0.1

MAGIC

La Palma, Spain 2200 28N 17W

572

0.05

VERITAS

Arizona, USA 1268 31N 110W

424

CANGAROO

Woomera, Australia 160 136E 31S

172

Total Energy Mirror Threshold Area (mo ) (TeV)

Angular Energy Resolution Resolution (o )

Field of View

Sensitivity1 (c.u.)

15%

5

1

0.1

20%

3.5

1.6

0.1

0.1

15%

3.5

200 GeV) and hadron background. In the pulsar trigger the analogical photon signals are summed over a limited region around the center of the camera. In addition, pixel signals were clipped to avoid the large after-pulses of the photomultipliers. The pulsar technique was successfully tested in the first MAGIC telescope leading to the detection for the first time of the Crab pulsation above 25 GeV with an IACT.

3 Observations of pulsars with IACTs The field of γ-ray pulsars has been boosted after the launching of the new satellite Fermi-LAT, which started operating in August 2008. Previously only six pulsars were detected above 1 GeV (with EGRET [56]), most of them showing an indication of a sharp cutoff in the spectrum at a few GeVs. Different theoretical models were proposed to explain the shape of the spectrum, namely polar cap, outer gap and more recently outer gap models. Prior the Fermi LAT satellite operation, IACTs were the only instruments that could access to the energy range below 100 GeV. Large reflectors and new detection techniques were developed to decrease the energy threshold as much as possible and try to understand the physics mechanisms producing pulsed γ-rays in the pulsar magnetosphere. A summary of the upper limits derived from VHE γ-ray observations is given in Table 2. Upper limits on later-detected pulsars such as Crab are not included. Unfortunately, the low energy cutoffs present in the pulsar spectra do not allow to further constrain emission models, although contributions from a second IC component predicted by outer gap models are challenged. The most prominent VHE target is the Crab pulsar and its nebula. The nebula spectrum shows an undisputed synchrotron nature of the non-thermal radiation from radio to low energy γ-rays, indicating the existence of relativistic electrons of energies up to 1016 eV. The Compton scattering of the same electrons leads to effective VHE emission while the synchrotron component is responsible for the radiation from radio to relatively low energy γ-rays (E104 yr), such as Vela X [15], HESS J1825–137 [14], HESS J1718-385 [20] and HESS J1809-193 [12]. The young systems show a good match with the morphology seen in X-rays, while in the latter group, very often the pulsar powering the TeV plerion is found offset with respect to the center of the TeV emission, with large size ratios between the X-ray and VHE γ-ray emission regions. The evolution of the SNR blast wave into an inhomogeneous ISM and/or the high velocity of the pulsar, together with a low magnetic field value ( ∼5 µG [36]), may explain these large offset as being the relic nebulae from the past history of the pulsar wind inside its host SNR. Since VHE-emitting electrons are usually less energetic than X-ray-emitting ones,


443

Table 3 TeV PWNe and PWNe candidates detected with IACT TeV Name J0534+220 J1514–591 J1747–281 J1813–178 J1833–105 J1846–029 J0835–456 J1303–631 J1825–137 J1119–6127 J1356–645 J1418–609 J1420–607 J1616–508 J1640–465 J1702–420 J1708–443 J1718–385 J1809–194 J1837-069 J1857+026 J1908+101 J1912+101 J1930+188 J2228+611 J1023+575 J2032+413

PWNe Fγ (c.u. at 1 TeV) Crab 1.00 MSH15–52 0.15 G0.9+0.1 0.02 G12.82–0.02 0.09 G21.5–0.9 0.01 kes75 0.02 VelaX 0.75 – 0.11 G18.0–0.69 0.17 G292.15–0.54 0.04 G309.92–2.51 0.07 Rabbit 0.07 Kookaburra 0.09 – 0.19 G338.3–0.0 0.09 G344.74+0.12 0.24 G343.10–2.69 0.07 G348.95–0.43 0.01 G11.09+0.08 0.12 G25.5+0.19 0.13 G36.01+006 0.16 G40.16–0.89 0.09 G44.48-0.17 0.09 G54.1+0.3 0.02 Boomerang 0.00 – 0.09 – 0.01

˙ 2 (erg/s/kpc2 ) d (kpc) Γ E/d 2.4 1.20e+38 2.0 2.3 6.66e+35 5.2 2.4 5.95e+35 8.5 2.1 3.08e+36 4.7 2.1 1.32e+36 5.0 2.3 2.31e+35 6.0 1.4 7.67e+37 0.3 2.4 3.90e+34 6.6 2.4 1.75e+35 4.0 2.3 3.26e+34 8.4 2.2 4.96e+35 2.5 2.2 1.96e+35 5.0 2.2 3.19e+35 5.6 2.4 3.79e+35 6.5 2.4 0.00e+00 0.0 2.1 1.36e+34 5.0 2.5 6.43e+35 2.3 0.7 8.13e+34 4.0 2.2 9.80e+34 3.5 2.3 1.12e+35 7.0 2.4 5.68e+34 9.0 2.0 2.73e+35 3.2 2.2 1.43e+35 4.5 2.4 3.12e+35 6.2 2.3 3.44e+37 0.8 2.6 1.72e+35 8.0 2.0 2.08e+34 3.6

τ (kyr) 1.2 1.7 5.3 4.6 4.7 0.7 11.0 11.0 21.0 1.6 7.0 16.0 13.0 8.1 0.0 55.0 17.0 89.0 51.0 23.0 21.0 19.0 170.0 2.9 10.5 4.6 120.0

ǫ (%) GeV/X-ray/Rad. 0.02 PS/Y/Y 0.60 PS/Y/Y 0.09 N/Y/Y 0.09 N/Y/Y 0.03 N/Y/Y 0.19 N/Y/Y 0.08 PS/Y/Y 7.06 N/N/Y 2.38 N/Y/Y 3.14 N/Y/Y 0.40 N/Y/Y 0.98 P/Y/Y 0.82 P/Y/Y 1.26 N/Y/Y 0.00 S/Y/N 54.85 N/N/N 0.27 P/N/N 4.51 N/N/N 3.44 N/Y/Y 3.11 N/N/N 7.03 N/N/N 1.04 P/Y/Y 1.79 N/N/Y 0.16 N/Y/Y 0.00 P/Y/Y 1.17 Y/N/N 1.90 P/N/N

they do not suffer from severe radiative losses and the majority of them may survive from (and hence probe) early epochs of the PWNe evolution. This interpretation has been further supported by the discovery of the spectral softening of the VHE nebula HESS J1825-137 as a function of the distance from the pulsar [14]. Further classification in four broad categories can be done (in table 3) • Unresolved Sources or TeV-X-ray/radio matching morphology, such as the Crab Nebula, MSH 15–52, G 21.5, etc. • Identified (evolved) PWNe; TeV plerions in which a cooling mechanism of leptonic emission has been clearly detected like in the case of HESS J1825–137 and HESS J1303–631 [33] and other candidates such as Vela X. • Unidentified sources very likely related with PWNe. • New PWNe candidates such as TeV J2032+413 and HESS J1023–575. Several counterparts were postulated to explain the VHE emission, such as open clusters, but the positional agreement with bright Fermi LAT pulsars recently discovered has questioned the association and opened new interpretation. Table 3 shows the parameters of the VHE PWNe detected with different IACTs, sorted by the above explained categories. The differential flux at 1 TeV in crab units (c.u) ranges from 0.01 to 0.75 c.u. and the photon indices (for a power law fit) vary from 2.0 to 2.6. In a few cases, the photon spectra are better described by a curved or power law with an exponential cutoff function, describing the IC component, like in the case of the Crab Nebula or HESS J1718–385. They show different efficiencies

444


ǫ, defined as the ratio between the VHE luminosity and the pulsar spin down luminosity. The VHE luminosity is defined as the integral flux in the 0.3 to 30 TeV range for the nominal distance quoted in the table [43]. The last column reports the pulsed (P) or steady (S) emission in the 100 MeV to 100 GeV energy range observed with the Fermi LAT satellite, the detection or not of X-ray counterpart, and the presence of a radio- nebula/pulsar associated to the VHE source. No clear correlation has been found so far between the observable parameters at VHE, due in part to the time-dependent evolution of the particle accelerated and the pulsar luminosity and magnetic field. Detailed MHD simulation carried on by for instance [36] and [37] are currently being investigated in order to understand the connection between the parameter of the pulsar and its relativistic wind producing non-thermal radiation, using VHE, HE and high resolution X-ray observations. In the next subsections some of the most prominent examples are discussed.

4.1 Young/Composite Pulsar Wind Nebula The prototype of this type of objects is the Crab Nebula, which has been extensively observed since 1989 [61] when first detected. The MHD model developed by [47]


−9

MAGIC

10

CANGAROO



−10

10

10−11

10−12 1

10

102

3

10

104

Energy [MeV]

5

10

6

10

107

8

10

Fig. 5 SED of the Crab Nebula at HE and VHE including several measurement of IACTs. The fit of the synchrotron component, using COMPTEL and LAT data (blue dashed line), is overlaid. The predicted inverse Compton spectra from [28] are overlaid for three different values of the mean magnetic field: 100 µG (solid red line), 200 µG (dashed green line) and the canonical equipartition field of the Crab Nebula 300 µG (dotted blue line) [2].

100

-0.4 PRELIMINARY

80

-0.6 HESS J1833-105

60

-0.8

40 -1 G21.5-0.9/ PSR J1833-1034

20 0

-1.2

Galactic Latitude (deg.)



445

200

0.2

PRELIMINARY

-0

HESS J1846-029

150

100

-0.2

-0.4

kes75/ PSR J1846-0258

-0.6

50

0

-20 22

21.5 21 Galactic Longitude (deg.)

30

29.5 Galactic Longitude (deg.)

Fig. 6 Smoothed excess maps (σ = 0.08◦ ) of the 0.5◦ × 0.5◦ field of view around the positions of HESS J1833–105 (left) and HESS J1846–029 (right). The white contours show the pre-trials significance levels for 4, 5, 6 σ, and 7, 8, 9 σ, respectively. The black triangle marks the position of the pulsars. The best-fit positions of the two sources are marked with an error cross (for HESS J1846-029 the latter overlaps with the triangle).

described satisfactorily the broad band emission of the Crab Nebula. The characteristic of the IC component explaining the VHE emission has been constrained by different IACT with high precision. At the highest energies, observations show that the photon spectrum can be fitted with a power law function plus an exponential cutoff at (14.3±2.1) TeV [16]. This energy cutoff implies acceleration of electrons in the nebula up to Ee ≃18×E0.5 γ ≃70 TeV (if neglecting the ∼30% drop in the cross section due to the Klein-Nishina effect). On the other extreme of the spectrum, observations down to 60 GeV [23] restricted the IC peak to (77±47) GeV. Finally, the combined measured of the spectral photon distribution (SED) by Fermi LAT and MAGIC/VERITAS has constrained the VHE emission from 100 MeV to 300 GeV with unprecedented sensitivity. The spectrum of the nebula below 100 GeV is well described by the sum of two power-laws of indices Γsync = (3.99 ± 0.12) and ΓIC = (1.64 ± 0.05), corresponding to the falling edge of the synchrotron and the rising edge of the inverse Compton components, respectively [2]. Fig. 3 shows the SED of the Crab Nebula, matching satisfactorily the Fermi LAT measurement with the IACT ones. The SED can be fitted using the broadband model by [28] for different values of the magnetic field (in Fig. 3 in solid red, dashed green and dotted blue lines for 300, 200 and 100 µG respectively). The SED is well described using a magnetic field between 100 and 200 µG, below the canonical equipartition field of the Crab Nebula of 300 µG [47]. However, this high magnetic field is not representative of other PWNe with similar characteristics to the Crab Nebula, such as the composite SNRs HESS J1833–105 (G 21.5–0.9) or HESS J1846–029 (kes 75). In both, the plerion is still embedded inside the shell of emission due to the SNR blast wave. This is evident from radio and X-ray observations. A magnetic field of 25 µG has been derived by detailed

−58.8

60

MSH 15−52 H.E.S.S.

−58.9

50

Excess (a.u.)

Emma de Oña Wilhelmi Dec (deg)

446

−59 40 −59.1 30

Fig. 7 Gaussian smoothed (σ=0.04◦ ) excess map from MSH 15-52. The white contour lines denote the X-ray (0.6–2.1 keV) count rate measured by ROSAT. The black point and black star lie at the pulsar position and at the excess centroid, respectively.

−59.2

20

−59.3

−59.4

10

−59.5 0 15h16m

15h14m

15h12m

RA (hours)

modeling of G 21.5–0.9 by [37], assuming IC scattering on CMBR photons only, and using the ratio of the X-ray to the γ-ray luminosities: L x /Lγ ∼30, which is 10 times smaller than the equipartition value of 0.3 mG. Similarly, kes 75 is related with PSR J1846–0258, which is one of the youngest (700 yrs) and most energetic pulsars (close to 1037 erg/s) known in the Milky Way. In the case of Kes 75, Lx /Lγ ∼ 10 yields also a lower than equipartition nebular magnetic field strength of ∼10 µG. These observations confirm that some of the observed PWNe can be particle dominated. Fig. 6 shows the sky maps for both PWNe. Magnetic fields of the order of a few µG is also found to fit well other young nebulae such as HESS J1747–281 (G 0.9+0.1). The VHE emission can be described by a simple leptonic model of IC on stellar photons, given its location in the central region of the Galaxy, with a magnetic field of 6 µG. The VHE luminosity is only 0.09% of the total spin down power of the associated pulsar PSR J1747–2809, which was recently discovered in G0.9+0.1 with the NRAO Green Bank Telescope at 2GHz [30]. In this case, the derived value of B is very close to the equipartition magnetic field (≈5 µG). Another example of young but extended, clearly identified PWN, is MSH 15–52. The VHE γ-ray image shows a clearly resolved structure (Fig. 7), with an elongated and slightly curved emission region, resembling in its morphology the X-ray jet detected by ROSAT [57]. The fact that the overall morphology is similar in X-rays and γ-rays demonstrates that the features seen in X-rays reflect the distribution of high-energy electrons rather than a peculiar structure of magnetic fields. X-ray and γ-ray spectra can be described as resulting from a single population of electrons, radiating in a 17 µG magnetic field and scattering infrared photons and starlight photons to TeV energies in the IC process.


447

Fig. 8 Three-colour image showing the γ-ray emission in different energy bands (0.2–0.8 TeV in red, 0.8–2.5 TeV in green and above 2.5 TeV in blue). The different γ-ray energy bands show a shrinking with increasing energy away from the pulsar PSR B182–13.

4.2 ”Relic” Pulsar Wind Nebula Middle age VHE PWNe are characterized by • very extended sources (few tens of pc), few orders of magnitude larger than the associated X-ray nebula. • VHE emission mostly displaced with respect to the pulsar position. • energy-dependent morphology as signature of cooling of particles suffering radiative energy losses as they flow away from the pulsar, resulting in the shrinking of the source towards the pulsar with increasing energy. In many of these objects the bulk of the γ-ray emission is not centered on the pulsar, and the displacement is too large to be explained in terms of a moving pulsar leaving behind a relic PWNe. Two possible explanations have been invoked: an offcenter compression by the reverse shock [16]; or the formation of a bow-shock tail [28, 62], where particle responsible for the inverse Compton emission in the γ-ray band can be advected to large distances from the pulsar. The large size of these VHE sources are usually explained by accumulation of relic electrons interacting via IC mechanisms scattering photon targets in the vicinity. The respective synchrotron lifetimes of electrons in a transverse magnetic field of strength B = 10−5 B−5 G, radiating synchrotron photons with mean energy EkeV (in units of keV) and IC scattered CMBR photons to a mean γ-ray energy of ETeV (in units of TeV), are given by −1/2 τ = 1.2 kyrB−3/2 E keV

and

τ = 4.8 kyrB−2 E T−1/2 eV

(2)

448


Fig. 9 H.E.S.S. significance image of the Galaxy as of 2009 (from [32]). The color transition from blue to red is set to 5σ. The Fermi LAT sources reported in the 1st catalog are overlaid in green.

the different cooling time is reflected on propagation effects as a result of the longer lifetime of TeV emitting electrons, compared to the relatively short lifetime of keV synchrotron emitting electrons. The prototype of this type of systems is HESS J1825–137 [14]. HESS J1825– 137 is associated with the pulsar PSR B1823–13, a 101 ms evolved pulsar with a characteristic age of τ=2.1×104 yr and located at a distance of 3.9 kpc. X-ray observations show an extended diffuse nebula of size ∼5′ (G 18.0–0.7). The very extended (∼35 pc, for a distance of 3.9 kpc) VHE emission (see Fig. 8) is ∼6 times larger than the X-ray size, and the analysis of its spectral feature shows a clear steepening on the photon spectrum away from the pulsar (i.e. decrease of γ-ray extension with increasing energy). The spectrum in HESS J1825–137 changes from a rather hard photon index ∼2 close to the pulsar to a softer value of ∼2.5 at a distance of 1o away from the pulsar. Fig. 8 shows the excess map around the position of PSR B1823–13 at different energy range [41]. Many of the extended dark sources discovered in the Galactic Plane Survey performed by H.E.S.S., which are sources without obvious counterpart at lower energies, are believed to be relic PWNe. They could be easily explained by considering old systems with large radio beaming, in which the evolved synchrotron nebula is too faint to be detected. The Fermi LAT satellite has proven to be a very efficient instrument for the detection of HE pulsars (∼60). Many of them are positionally coincident with some of the VHE unidentified sources and have been postulated as possible counterparts of a pulsar/PWNe system. Fig. 10 shows the H.E.S.S. significance image of the Scan Survey of the Galaxy with the HE sources detected by Fermi LAT and reported in the first catalog [3] overlaid. The HE pulsars are marked with green crosses. This is the case of i. e. HESS J1908+063 [9]. HESS J1908+63 was first discovered by the MILAGRO water Cherenkov detector [6] and confirmed as an extended source with a hard photon index spectrum with H.E.S.S. observations. Several counterparts were proposed although no clear identification could be done. Multi-wavelength studies performed by the Fermi LAT collaboration [5] triggered by the discovery of the 106.6 ms γ-ray pulsar PSR J1907+0.7 suggested that the TeV source is the PWN associated to the middle-age (19 kyr) and energetic (2.8×1036 erg/s) pulsar at a distance of 3.2 kpc (which translate in a size of the PWN of ∼40 pc). A peculiarity of this source is that the photon spectrum extends to very high energies, and no sign of cut-off has yet been detected. The H.E.S.S. observations [9] places a lower limit of 19.1 TeV on any exponential cutoff to the spectrum. This implies that either the spectrum is uncooled due to a very low nebular magnetic field(

80 SNR G40.5-0.5

-0.5

DSH J1907.5+0617

60

AX J1907.4+0549

40

-1 HESS J1908+063

-1.5

20

GRO J1908+0556

0

-2 -2.5

-20 42

41

40

39

Galactic Longitude (deg.)

10

-9

-10

)

100

0

10

1

0.5

120

2

3EG 1903+0550

449

10

-11

2

1

E dN/dE (erg cm s



10

10

-12

-13

10

-2

10

-1

10

0

10

1

E(GeV)

10

2

10

3

10

4

10

5

Fig. 10 On the left, Gaussian-smoothed (σ=0.11o ) excess map of the 3.6o ×3.6o field of view around the position of HESS J1908+063. The H.E.S.S. significance contours above 4σ are superimposed and marked in green (for the energy range between 0.7 to 2.5 TeV) and blue (for energies above 2.5 TeV) contours. The possible counterparts are also shown, including the Fermi LAT source in cyan bullet. On the right, the VHE spectrum is shown (blue bullets) together with the upper limits observed at HE by Fermi LAT and the pulsar contribution in green bullets.

B≃ 3µG, see, i. e. [38]), an age much less than the characteristic age of 19.5 kyr, or else there is a synchrotron cooling break below the HESS band.

4.3 Other PWNe candidates Finally, a number of VHE sources which remained unidentified or were associated with new type of particle accelerators have been found to be positionally coincident with energetic HE pulsars, and interpretation of the emission in light of the new discoveries has to be revised. The most prominent cases are the first unidentified source in the Cygnus region TeV J2032+4130 [22, 24, 4], associated with an outlying group of stars (from the Cygnus OB2 core), and HESS J1023–575 [11], for which the massive open cluster Westerlund 2 was proposed as possible counterpart. TeV J2032+4130 was discovered during observations with the HEGRA experiment [22] and later re-observed and confirmed by MAGIC and VERITAS [24, 60] as a slightly extended source with a hard photon index of 2. Later, the Milagro collaboration reported a very extended (3o ) VHE emission from the direction of TeV J2032+4130. Despite deep observations at other wavelength, the VHE source remained unidentified and only recently a radio and HE pulsar coincident with the position of the TeV source was reported [31, 1], located within the 1σ extent of TeV J2032+4130. If a PWN scenario is considered, the efficiency obtained (in table 3) is similar to the ones obtained for other PWNe candidates. Also typical for a PWN is the flux of the diffuse X-rays within 1′ of PSR J2032+4127, ∼1×10−13 erg cm−2 s−1 in the 0.5–10 keV band. Therefore, the ratio is roughly Lγ /Lx ∼50, which is comparable to the ratio for other older pulsars [49]. The positional agreement together with the characteristics of the pulsar makes it a plausible candidate to power the VHE source.

450


WR 20a PSR J1022-5746

-58°00’

60

E > 2.5 TeV

40 30 20 10

PSR J1028-5819

-57°00’

50

Excess/arcmin2

0.7 TeV < E < 2.5 TeV

0

Declination (J2000)

Declination (J2000)

-57°00’

Excess/arcmin2

HESS J1023–575 was discovered in 2007 [11] with the H.E.S.S. telescope array towards the direction of the massive stellar cluster Westerlund 2. The young open cluster was postulated as counterpart, powering the VHE emission with a γray luminosity Lγ (E > 380 GeV) = 1.5×1035 erg/s. Different mechanisms involving cosmic rays accelerated in expanding stellar wind or supernova blast waves interacting with the boundaries of the interstellar medium are among the possible scenarios to explain the VHE γ-ray emission. The origin of the observed emission was not unambiguously identified, and follow-up observations were performed to further investigate the nature of this γ-ray source. The new observations [8] unveiled a second source, HESS J1026–582 which is positionally coincident with the Fermi LAT pulsar PSR J1028–5819 [40], with a very substantial spin-down energy loss of ∼1036 ergs/s. The positional coincidence and radio/γ-ray characteristics of the LAT pulsar favors a scenario where the TeV emission originates from a PWN. A second 4.6 kyr old radio-quiet pulsar PSR J1022–5746 located well within the extended H.E.S.S. source (see Fig. 11) was also found, featuring a very high spin-down energy loss of ∼1037 ergs/s, ample to power an extended nebula of relativistic electrons giving rise to the VHE γ-rays, as opposed to the pulsed emission detected by Fermi and emitted in the direct vicinity of the pulsar. A PWN according to the model of [47] would nominally be consistent with a distance estimate for the pulsar/PWN of 6 kpc. No X-ray PWN counterpart has been found and a clear identification of the object responsible for the VHE emission from HESS J1023–575 is not yet possible. Contribution from the nearby high-energy pulsar and/or the open cluster remains a possibility

WR 20a PSR J1022-5746

-58°00’

PSR J1028-5819

10h25m 10h20m Right Ascension (J2000)

30 20 10

0 -10

-10 10h30m

40

10h30m

10h25m 10h20m Right Ascension (J2000)

Fig. 11 Gaussian-smoothed (σ=0.08o ) excess sky maps for Westerlund 2/RCW 49 and PSR J1028–5819 region. On the left, the low energy map (0.7 TeV <E < 2.5 TeV) is shown, while the high energy map (E > 2.5 TeV ) is displayed on the right. The H.E.S.S. significance contours (dashed black lines for the low energy map and solid green ones for the high energy map) are calculated using an oversampling radius of 0.1o and are shown above 4σ in steps of 1σ. The position of the Wolf Rayet star WR 20a and the two Fermi LAT pulsars are marked in cyan and white


451

5 Concluding Remarks The field of PWNe has overcame a fast development in the last years thanks to VHE observations with IACTs. The good angular resolution (∼0.1o) achieved with the third generation of Cherenkov telescopes, as well as their sensitivity (a few percent of the Crab Nebula flux) and wide field of view, allow a much better constrained of plausible counterparts of the VHE emission. The association with energetic pulsar powering PWNe is supported by a combination of positional and morphological evidence, multi-wavelength observations, and energy arguments. These currently constitute the most numerous class of identified Galactic VHE γ-ray sources. Several of these VHE PWNe exhibit a large extent of the order of a few tens of pc and are significantly offset from the pulsar position; MHD time-dependent models show that these are old PWNe, strongly affected by the passage of an asymmetric reverse shock in the parent SNR. In a leptonic interpretation of the VHE emission, the target photons for IC scattering have an approximately known and uniform density in individual PWNe, which allows direct inference of the spectral and spatial distribution of the energetic electrons, in contrast to observations of synchrotron emission at lower energies. VHE gamma-ray astronomy thus provides a new, independent observational window into the physics of PWNe. Pulsar observations on the contrary are still under development due to the presence of a sharp cutoff at a few GeV, where the effective area of IACTs decreases dramatically. Nevertheless, new techniques have been successfully tested, leading to the detection of the Crab Pulsar in good agreement with the Fermi LAT results. Further observations of other prominent candidates (high pulsed flux and high energy cutoff) are being carried on in order to firmly establish this pulsar technique.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 32.

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Lepton Acceleration in Pulsar Wind Nebulae Matthew G. Baring

Abstract Pulsar Wind Nebulae (PWNe) act as calorimeters for the relativistic pair winds emanating from within the pulsar light cylinder. Their radiative dissipation in various wavebands is significantly different from that of their pulsar central engines: the broadband spectra of PWNe possess characteristics distinct from those of pulsars, thereby demanding a site of lepton acceleration remote from the pulsar magnetosphere. A principal candidate for this locale is the pulsar wind termination shock, a putatively highly-oblique, ultra-relativistic MHD discontinuity. This paper summarizes key characteristics of relativistic shock acceleration germane to PWNe, using predominantly Monte Carlo simulation techniques that compare well with semi-analytic solutions of the diffusion-convection equation. The array of potential spectral indices for the pair distribution function is explored, defining how these depend critically on the parameters of the turbulent plasma in the shock environs. Injection efficiencies into the acceleration process are also addressed. Informative constraints on the frequency of particle scattering and the level of field turbulence are identified using the multiwavelength observations of selected PWNe. These suggest that the termination shock can be comfortably invoked as a principal injector of energetic leptons into PWNe without resorting to unrealistic properties for the shock layer turbulence or MHD structure.

1 Introduction Pulsar wind nebulae (PWNe) have fascinated astronomers ever since the discovery of the Crab Nebula. This source provides the template for PWN studies because of the excellent multiwavelength spectral information (de Jager & Harding 1992; Atoyan & Aharonian, 1996; Abdo et al. 2010b) and stunning spatial imaging afMatthew G. Baring Department of Physics and Astronomy, MS-108, Rice University, P. O. Box 1892, Houston, TX 77251-1892, USA, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_38, © Springer-Verlag Berlin Heidelberg 2011

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forded by radio (historic), optical (Hester et al. 1995 for Hubble) and X-ray (Weisskopf, et al. 2000 for Chandra) observations. Its unparalleled observational quality is driven by the exceptional powerhouse at its center, the high spin-down power Crab pulsar. The central pulsar fuels the dissipation in its surrounding PWN (exemplified in the seminal Rees & Gunn, 1974, and Kennel & Coroniti, 1984, models), with the nebula serving in a symbiotic relationship as the calorimeter for the pulsar over its entire spin-down history. Therefore, the interface between the central engine and the nebula must play a principal role in setting up the emission seen in PWNe. This boundary is the pulsar wind termination shock (PWTS), where the wind is abruptly slowed by the ram pressure of the circumstellar material; it forms the focus of this perspective on lepton acceleration in PWNe. This shock is a natural site for the acceleration of particles that spawn the nonthermal radiation in PWNe that we observe. It should possess turbulent electrodynamic fields that can energize and stochastically diffuse charges extremely efficiently. Yet, the PWTS is not the only possible site for leptonic acceleration. Field reconnection in and near the quasi-equatorial current sheet between the pulsar light cylinder and the termination shock is an alternative (e.g. Lyubarsky & Kirk 2001; Kirk & Skjæraasen 2003; Pétri & Lyubarsky 2007). In compact regions such as X-points in the striped wind, magnetic reconnection can release large amounts of energy as field tension is converted to heat of particles. Such a prospect needs fuller exploration from a theoretical standpoint. Reconnection theory needs to make robust predictions of distributions and injection efficiencies (from thermal gas) of accelerated populations in order to connect effectively to PWNe observations. The understanding of shock acceleration is more developed in this regard, and accordingly is the focus of this paper. We note that the solar corona may prove a powerful testing ground for honing models of reconnection in the same way that the solar wind has demonstrated the general viability of diffusive acceleration at non-relativistic shocks. It should also be remarked that all escaping pulsar wind leptons impact the surface of the termination shock, whereas perhaps only a minority of such thread the environs of the current sheet reconnection region. Notwithstanding, reconnection in the near wind zone may contribute significantly to the evolution of the global MHD structure and associated wind parameters, as well as generate some pre-acceleration, both of which in turn influence the cumulative contribution of the PWTS as an injector to a pulsar wind nebula over its active lifetime. This paper summarizes the key aspects of diffusive acceleration at relativistic shocks in general, and pulsar wind termination shocks in particular. As the injector of ultra-relativistic leptons, and ions, into PWNe, this process is only indirectly probed by radiation observations of nebulae. The volumetric extension of PWNe encompasses significant spatial stratification of both the nebular magnetic field and the fluid flow speed, the model template for which is the spherically symmetric Kennel & Coroniti (1984) contribution. Moreover, temporal evolution is significant, with high energy electrons cooling rapidly over the lifetime of a PWN like the Crab, driving synchrotron “burn-off” that is probed in the X-rays (see the review of Gaensler & Slane, 2006, for an extensive discussion of PWN observations and guiding interpretative material). Yet multiwavelength coverage, from radio to X-ray to high

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energy gamma-rays provides substantial constraints on the PWTS acceleration process. Presuming nebular fields in the range of B ∼ 0.1 mG implies pair Lorentz factors in the range γe ∼ 109 − 1010 for the Crab to enable γ-ray synchrotron emission. Since the pulsar is unlikely to generate such energetic particles, this demands efficient acceleration at the PWTS or elsewhere. Other PWNe impose similar requirements. The PWTS energy budget divides into three components: (i) thermal downstream heat, (ii) turbulent fields, and (iii) non-thermal shock-accelerated leptons, and perhaps ions. The balance between these is not yet fully understood, though indications from plasma simulations are that these components are not widely disparate in their energy densities. The central acceleration issue for PWN studies is whether a quasi-perpendicular termination shock can generate a sufficient injection efficiency ǫinj and the right spectral index in different energy ranges. In this paper, it becomes evident that the index issue can be satisfied in global terms using the current understanding of diffusive acceleration at relativistic shocks, while more work is needed to address the injection issue in a satisfactory manner.

2 Lepton Acceleration at Relativistic Shocks To understand the nature of relativistic lepton injection into the PWN, it is insightful to explore the general nature of particle acceleration at relativistic shocks. The key characteristic that distinguishes relativistic shocks from their non-relativistic counterparts is their inherent anisotropy of the phase space distribution function f (p) at any position. This is due to rapid convection of particles through and downstream away from the shock, since particle speeds v are never much greater than the downstream flow speed u2 ∼ c/3 : particle distributions never realize isotropy in either fluid or shock rest frames. This renders analytic approaches more complicated (Peacock 1981) than in non-relativistic systems. Early analytic offerings on particle acceleration at relativistic shocks focused on solutions of the diffusion-convection differential equation in the test-particle approximation (e.g., Kirk & Schneider 1987a; Heavens & Drury 1988; Kirk and Heavens 1989). These generally specialized to the limit of extremely small angle scattering (SAS, or pitch angle diffusion). In particular, the eigenfunction solution technique of Kirk & Schneider (1987a) was later successfully extended by Kirk et al. (2000) to the specific case of parallel, ultrarelativistic shocks, i.e. those with upstream fluid flow Lorentz factors Γ1 ≫ 1 in the shock rest frame. Kirk et al. demonstrated that as Γ1 → ∞ , the accelerated particle distribution power-law index σ (for dN/d p ∝ p2 f (p) ∝ p−σ ) asymptotically approached a constant, σ → 2.23 , a value realized when Γ1 & 10 . This result has been popularly invoked in astrophysics models of various sources, but is of very restricted applicability, as will become evident below. While diffusion-convection differential equation approaches are usually restricted to SAS that would be applicable to particle transport in quasi-linear field turbulence regimes, recently they have been generalized by Blasi & Vietri (2005) and Morlini, Blasi & Vietri (2007) to incorporate large angle deflections in MHD turbulence of larger amplitudes δB/B .

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The operating definition of such large angle scattering (LAS) is that the particle experiences momentum deflections on typical angles θscatt & 1/Γ1 in interactions with MHD turbulence in the shock environs. Clearly, for ultra-relativistic shocks, LAS can be realized with quite modest deflections. A central limitation of these analytic methods is that they are restricted to powerlaw regimes, which are only realized when there is no preferred momentum scale, i.e. far above the thermal injection momentum. Therefore they provide no probes of the injection efficiency ǫinj (defined to be the fraction of particles by number residing in the non-thermal tail of the distribution), how ǫinj connects key shock environmental parameters, and therefore how it correlates to the non-thermal distribution index σ . Hence the niche for Monte Carlo techniques for modeling diffusive transport in shocks. Such complementary simulation approaches have been employed for relativistic shocks by a number of authors, including test-particle analyses by Kirk & Schneider (1987b), Ellison, Jones & Reynolds (1990), and Baring (1999) for parallel, steady-state shocks, and extensions to include oblique magnetic fields by Ostrowski (1991), Ballard & Heavens (1992), Bednarz & Ostrowski (1998), Ellison & Double (2004), Niemiec & Ostrowski (2004), Stecker, Baring & Summerlin (2007) and Baring & Summerlin (2009). The Monte Carlo method successfully reproduced the asymptotic Γ1 → ∞ index value of σ ≈ 2.23 in work by different groups (Bednarz & Ostrowski 1998; Baring 1999; Achterberg, et al. 2001; Ellison & Double 2002). There are two main types of Monte Carlo simulation on the market: those that inject prescribed field turbulence to effect diffusion of charges (e.g. Ostrowski 1991; Bednarz & Ostrowski 1998; Niemiec & Ostrowski 2004), and those that describe the diffusion by phenomenological scattering parameters (e.g. Ellison, Jones & Reynolds 1990; Ellison & Double 2004; Baring & Summerlin 2009). It is this latter variety that will form the focus in this exposition, because of its ability to survey the parameter space of acceleration characteristics in an incisive fashion. Before outlining the essentials of the Monte Carlo technique used to generate many of the results presented here, it should be noted that there is a third popular approach to modeling particle acceleration at relativistic shocks: full plasma or particle-in-cell (PIC) simulations (e.g. Hoshino, et al. 1992; Nishikawa, et al. 2005; Medvedev, et al. 2005; Spitkovsky 2008). PIC codes compute fields generated by mobile charges, and the response of the charges to the dynamic electromagnetic fields. Accordingly they are rich in their information on shock-layer electrodynamics and turbulence, but pay the price of intensive demands on CPUs. This presently limits them to exploration of thermal and suprathermal energies, so that full plasma simulations generally exhibit largely Maxwellian distributions (Hoshino, et al. 1992; Nishikawa et al. 2005; Medvedev, et al. 2005). However, we note the isolated recent suggestion (Spitkovsky 2008; Martins et al. 2009; Sironi & Spitkovsky 2009) of non-thermal tails spanning relatively limited range of energies, generated by diffusive transport in PIC simulations, with the thermal population still dominating the high-energy tail by number. To interface with astrophysical spectral data, a broad dynamic range in momenta is desirable, and this is the natural niche of Monte Carlo simulation techniques.


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2.1 The Monte Carlo Method As informative background to the ensuing results on relativistic planar shocks, the structure of the simulation used to calculate diffusive acceleration is now described. It is a kinematic Monte Carlo technique that has been employed extensively in supernova remnant and heliospheric contexts, and is described in detail in numerous papers (e.g. Ellison, Jones and Reynolds, 1990, hereafter EJR90; Jones & Ellison 1991; Ellison & Double 2004; Baring & Summerlin 2009). It is conceptually similar to Bell’s (1978) test particle approach to diffusive shock acceleration, and essentially solves a Boltzmann transport equation for arbitrary orientations of the large scale MHD field B. The background fields and fluid flow velocities on either side of the shock are uniform, and the transition at the shock is defined by the standard relativistic MHD Rankine-Hugoniot conservation relations (e.g. Double et al. 2004) that depend on both the sonic and Alfvénic Mach numbers. Particles are injected upstream of the shock with a Maxwell-Boltzmann distribution of finite temperature, and convect and gyrate in the laminar electromagnetic field, with their trajectories being governed by a relativistic Lorentz force equation in the frame of the shock. The upstream fluid frame magnetic field is inclined at an angle ΘBf1 to the shock normal. Because the shock is moving with a velocity u(x) relative to the plasma rest frame, there is, in general, a u × B electric field in addition to the bulk magnetic field. Particle interactions with Alfvén wave and other hydromagnetic turbulence is modeled by using a phenomenological scattering of the charges in the rest frame of the plasma. The scattering precipitates spatial diffusion of particles along magnetic field lines, and to a varying extent, across them as well. The scatterings are also assumed to be quasi-elastic, an idealization that is usually valid because in most astrophysical systems the flow speed far exceeds the Alfvén speed, and contributions from stochastic second-order Fermi acceleration are small. The diffusion permits a minority of particles to transit the shock plane numerous times, gaining energy with each crossing via the coherent shock drift and diffusive first-order Fermi processes. A continuum of scattering angles, between large-angle or small-angle cases, can be modeled by the simulation. In the local fluid frame, the time, δt f , between scatterings is coupled (EJR90) to the mean free path, λ , and the maximum scattering 2 (i.e. momentum deflection) angle, θscatt via δt f ≈ λθscatt /(6v) for particles of speed v ≈ c . Here the mean fee path is that for turning the particles around along field lines. Usually λ is assumed to be proportional to a power of the particle momentum p (see EJR90 and Giacalone, Burgess and Schwartz, 1992, for microphysical justifications for this choice), and for simplicity it is presumed to scale as the particle gyroradius, rg , i.e. λ = ηrg ∝ p . Simulation results are fairly insensitive to this choice. Moreover, the scattering law is generally assumed to be identical in both the upstream and downstream fluids. Departures from this can easily be accommodated, but usually incur only a change in the spatial scales for diffusion either side of the shock. The parameter η in the model is a measure of the level of turbulence present in the system, coupling directly to the amount of cross-field diffusion, such that η = 1 corresponds to the isotropic Bohm diffusion limit, where the field fluctuations satisfy δB/B ∼ 1 . In the quasi-linear regime, δB/B ≪ 1 , one expects that η should scale

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inversely as the variance of the field, i.e. η ∝ (δB/B)−2 . In kinetic theory, η couples the parallel ( κk = λv/3 ) and perpendicular ( κ⊥ ) spatial diffusion coefficients via the relation κ⊥ /κk = 1/(1 + η2) (Forman, Jokipii & Owens 1974; Ellison, Baring & Jones 1995). In parallel shocks, where the B field is directed along the shock normal ( ΘBf1 = 0 ), η has only limited impact on the resulting energy spectrum, principally determining the frequency of scattering and hence the diffusive spatial scale normal to the shock. However, in oblique relativistic shocks where ΘBf1 > 0 , the diffusive transport of particles across the field (and hence through the shock) becomes critical to retention of them in the acceleration process. Accordingly, for such systems, the interplay between the field angle and the value of η controls the spectral index of the particle distribution (Ellison & Double 2004; Baring 2004), a feature that is central to the interpretation of PWN spectra. It should be remarked that this phenomenological description of diffusion in Monte Carlo techniques is most appropriate at high energies (where it is more or less commensurate with results from Monte Carlo codes that inject prescribed turbulence), and omits the details of microphysics present in plasma simulations such as PIC codes. In the injection domain at slightly suprathermal energies, the influences of complex turbulent and coherent electrodynamic effects become important, and will substantially modify the picture from that of pure diffusion that is presented here; such is the niche of PIC simulations. Note also that all subsequent simulation results presented here are obtained in the test particle approximation, where the accelerated population is not permitted to modify the overall MHD shock structure.

2.2 Results for Relativistic Shock Acceleration Representative particle differential distributions dN/d p ∝ p2 f (p) that result from the simulation of diffusive acceleration at mildly-relativistic shocks are depicted in Figure 2 (adapted from Baring 2009); the reader can survey Ellison & Double (2004), and Stecker, Baring and Summerlin (2007, hereafter SBS07) for Γ1 ≫ 1 simulation results that possess similar character to the parallel shock ( ΘBf1 = 0◦ ) examples in the Figure. These distributions are obtained just downstream of the shock and are measured in the shock rest frame. They are equally applicable to electrons or ions, and so the mass scale is not specified; presuming that the wind loss from pulsars is dominated by pairs, the mass scale is nominally me . A striking feature is that the slope and shape of the non-thermal particle distribution depends on the nature of the scattering. The often cited asymptotic, ultrarelativistic index of σ = 2.23 for dN/d p ∝ p−σ mentioned above is realized only for parallel shocks with ΘBf1 = 0◦ in the mathematical limit of small (pitch) angle diffusion (SAS), where the particle momentum is stochastically deflected on arbitrarily small angular (and therefore temporal) scales. As mentioned above, in practice, SAS results when the maximum scattering angle θscatt is inferior to the Lorentz cone angle 1/Γ1 in the upstream region. In such cases, particles diffuse in the region upstream of the shock only until their velocity’s angle to the shock normal exceeds around 1/Γ1 , after


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Fig. 1 Particle distribution functions dN/dp from mildly-relativistic shocks ( Γ1 β1 = 3 , i.e. β1 = u1 /c = 0.949 ) of upstream-to-downstream velocity compression ratio r = u1x /u2x ≈ 3.24 . Simulation results can be divided into two groups: parallel shock runs ( ΘBf1 = 0◦ , upper three histograms), and oblique, superluminal shock cases ( ΘBf1 = 20◦ , 40◦ , 60◦ , lower three histograms). Scattering off hydromagnetic turbulence was modeled by randomly deflecting particle momenta by an angle within a cone, of half-angle θscatt , whose axis coincides with the particle momentum prior to scattering; the ratio of the diffusive mean free path λ to the gyroradius rg was fixed at η = λ/rg = 5 . The heavyweight lines (two uppermost histograms) are for the large angle scattering cases (LAS: 1/Γ1 ≪ θscatt ≤ π ). All other cases constitute pitch angle diffusion (small angle scattering: SAS) runs, when θscatt ≪ 1/Γ1 and the distributions become independent of the choice of θscatt . All distributions asymptotically approach power-laws dN/dp ∝ p−σ at high energies. For the two cases bracketing the results depicted, the power-laws are indicated by lightweight lines, with indices of σ = 1.61 ( ΘBf1 = 0◦ , θscatt ≤ π ) and σ = 3.31 ( ΘBf1 = 60◦ , θscatt ≤ 10◦ ), respectively. Also displayed is an indication of the index required to match Fermi-LAT > 1 GeV observations for the Crab Nebula, assuming uncooled inverse Compton emission.

which they are rapidly swept downstream of the shock. The Figure indicates clearly that when the field obliquity ΘBf1 increases, so also does the index σ , with values greater than σ ∼ 3 arising for ΘBf1 & 50◦ for this mildly-relativistic scenario. This is a consequence of more prolific convection downstream away from the shock.

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Figure 2 also shows results for large angle scattering scenarios (LAS, with 4/Γ1 . θscatt . π ), where the distribution is highly structured and much flatter on average than p−2 . The structure becomes more pronounced for large Γ1 (see Baring 2004; Ellison & Double 2004; SBS07, for details), and is kinematic in origin, where large angle deflections lead to fractional energy gains between unity and Γ12 in successive shock crossings. Each structured bump or spectral segment corresponds to an increment of two in the number of shock transits (Baring 2004). For p ≫ mc , they asymptotically relax to a power-law, in this case with index σ ≈ 1.61 . Intermediate cases are also depicted in Figure 2, with θscatt ∼ 4/Γ1 . The spectrum is smooth, like for the SAS case, but the index is lower than 2.23. From the plasma physics perspective, magnetic turbulence could easily be sufficient to effect scatterings on this intermediate angular scale, a contention that becomes even more germane for ultrarelativistic shocks (SBS07). Note that there is a clear trend (e.g. see EJR90; Baring 2004; SBS07) of declining σ for higher Γ1 , the consequence of an increased kinematic energy boosting in collisions with turbulence. The plot in Figure 2 includes an indication of the particle distribution index required to match the Fermi observations of the Crab Nebula. The Fermi-LAT spectral index in the 1–20 GeV range, corresponding to a putative inverse Compton signal, is αγ = 1.64 (see Abdo et al. 2010a, and specifically Figure 5 therein). In the case where this corresponds to the in situ accelerated population (i.e. the population is uncooled on the relevant timescales), one finds that σ = 2αγ − 1 = 2.28 . Such a scenario is depicted by the “Crab 1–20 GeV” line in Fig. 2. In contrast, if inverse Compton cooling is sufficiently rapid as to define the total Fermi > 1 GeV spectrum, then σ = 2αγ −2 = 1.28 . Thus, strongly-cooled IC models would suggest large angle scattering is active in the Crab Nebula termination shock, if it is superluminal. Now for an important definition pertaining to the following discussion. The MHD phase space of relativistic shocks bifurcates neatly into two regimes. In general, Monte Carlo simulations “operate” in a shock rest frame named the normal incidence frame (NIF), where the upstream flow is directed along the shock normal (usually chosen to be the x -direction, a convention adopted here). In this frame, the upstream magnetic field is inclined to shock normal by an angle of ΘBs1 . Due to relativistic aberration effects, generally ΘBs1 , ΘBf1 , with equality arising only in truly non-relativistic shocks. For many systems, there is also a shock rest frame called the de Hoffman-Teller (HT) frame (identified by de Hoffman & Teller 1950), which is obtained by a boost u1HT ≡ β1HT c = u1x / cos ΘBf1 along the magnetic field so as to bring the shock to rest. In this HT frame, there are no static electric fields, implying no E × B drifts parallel to the shock plane. Subluminal shocks are defined to be those where the HT flow speed β1HT corresponds to a physical speed, less than unity, i.e. the upstream field obliquity satisfies cosΘBf1 < β1x ≡ u1x /c . When β1HT > 1 , the de Hoffman-Teller frame does not exist, and the shock is said to be superluminal. This division naturally demarcates a dichotomy for the gyrational characteristics of charges orbiting in the shock layer. Subluminal shocks permit many gyrational encounters of charges with the shock interface, and therefore also reflection of them into the upstream region. This implies efficient trapping (e.g see Baring & Summerlin 2009), and effective acceleration. In contrast, for super-


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Fig. 2 Particle distribution functions dN/dp from mildly-relativistic sub-luminal shocks ( Γ1x β1x = 0.577 , i.e. β1x = u1x /c = 0.5 ) of upstream-to-downstream velocity compression ratio r = u1x /u2x ≈ 4 . Simulation results are depicted for two upstream fluid frame magnetic field obliquities, labelled by their corresponding de Hoffman-Teller frame upstream flow speeds β1HT = β1x / cos ΘBf1 . These are in distinct groups of four: ΘBf1 = 48.2◦ ( β1HT = 0.75 , multiplied by 104 ) for the upper four histograms, and ΘBf1 = 59.1◦ ( β1HT = 0.975 ) for the lower four histograms. Scattering off hydromagnetic turbulence was modeled by randomly deflecting particle momenta by an angle within a cone, of half-angle θscatt , whose axis coincides with the particle momentum prior to scattering; four different ratios of the diffusive mean free path λ to the gyroradius rg were adopted for each ΘBf1 . All results were for small angle scattering (SAS), when θscatt ≪ 1/Γ1 and the distributions become independent of the choice of θscatt . A low sonic Mach number MS was chosen so as to effectively maximize the efficiency of injection from thermal energies. Adapted from Baring & Summerlin (2009).

luminal shocks, in the absence of deflections of particles by magnetic turbulence, the convective power of the flow compels particles to rapidly escape downstream (e.g. Begelman & Kirk 1990), thereby suppressing acceleration. In such cases, particles sliding along the magnetic field lines would have to move faster than the speed of light in order to return to the upstream side of the shock. Such dramatic losses from the acceleration mechanism can only be circumvented by strong cross field

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diffusion precipitated by large amplitude field turbulence fields (e.g. Jokipii 1987; Ellison, Baring & Jones 1995), i.e. essentially close to the Bohm limit. The focus now turns to displaying the array of expectations for subluminal relativistic shocks. Principally, we will explore how the distribution index σ and injection efficiency depend on the effective frequency λ/rg of scatterings, and the upstream field obliquity ΘBf1 . Representative particle (lepton or ion) differential distributions dN/d p that result from the simulation of diffusive acceleration at mildlyrelativistic shocks of speed β1x = 0.5 are depicted in Figure 2. These distributions were generated for θscatt . 10◦ , i.e. in the SAS regime. Results are displayed for two different upstream fluid frame field obliquities, namely ΘBf1 = 48.2◦ and ΘBf1 = 59.1◦ , with corresponding de Hoffman-Teller frame dimensionless speeds of β1HT = β1x / cos ΘBf1 = 0.75 and 0.975 , respectively. The distributions clearly exhibit an array of indices σ , including very flat power-laws, that are not monotonic functions of either the field obliquity ΘBf1 or the key diffusion parameter η = λ/rg . Fig. 2 also emphasizes that the normalization of the power-laws relative to the low momentum thermal populations (and hence the injection efficiency ǫinj ) is a strongly-declining function of λ/rg . Quantitatively, ǫinj drops from 0.1 − 0.2 in the Bohm limit cases to less than 10−4 for λ/rg = 102 when β1HT = 0.975 . This is a direct consequence of a more prolific convection of suprathermal particles downstream of the shock that suppresses diffusive injection from thermal energies into the acceleration process. Such losses are even more pronounced when λ/rg ≥ 104 , to the point that acceleration is not statistically discernible for β1HT > 0.98 runs with 104 simulated particles. This property is salient for the pulsar wind nebula context discussed below. A parameter survey for diffusive acceleration at a typical mildly-relativistic shock is exhibited in Figure 4, where only the pitch angle diffusion limit was employed. The power-law index σ is plotted as a function of the de Hoffman-Teller frame dimensionless speed β1HT = β1x / cos ΘBf1 . It is clear that there is a considerable range of indices σ possible for non-thermal particles accelerated in mildly relativistic shocks. A feature of this plot is that the dependence of σ on field obliquity is non-monotonic. When λ/rg ≫ 1 , the value of σ at first declines as ΘBf1 increases above zero, leading to very flat spectra. As β1HT approaches and eventually exceeds unity, this trend reverses, and σ then rapidly increases with increasing shock obliquity. This is the character of near-luminal and superluminal shocks evident in Fig. 2: it is caused by inexorable convection of particles away downstream of the shock, steepening the distribution dramatically. The only way to ameliorate this rapid decline in the acceleration efficiency is to reduce λ/rg to values below around 10 . Physically, this corresponds to increasing the hydromagnetic turbulence to high levels that force the particle diffusion to approach isotropy. This renders the field direction immaterial, and the shock behaves much like a parallel, subluminal shock in terms of its diffusive character. Charges can then be retained near the shock for sufficient times to accelerate and generate suitably flat distribution functions. This defines a second core property illustrated in Fig. 4: σ is only weakly dependent on ΘBf1 when λ/rg < 10 . Observe that the indication of the particle distribution index corresponding to Fermi-LAT observations in the 1–20 GeV range (for un-


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Fig. 3 Power-law indices σ for simulation runs in the limit of small angle scattering (pitch angle diffusion), for mildly-relativistic shocks of upstream flow speed β1x ≡ u1x /c = 0.5 , and an MHD velocity compression ratio r = 4 . The indices are displayed as functions of the effective de Hoffman-Teller frame upstream flow speed β1HT = β1x / cos ΘBf1 , with select values of the fluid frame field obliquity ΘBf1 marked at the top of the panel. The displayed simulation index results were obtained for different diffusive mean free paths λ parallel to the mean field direction, namely λ/rg = 1 (squares), λ/rg = 10 (triangles), λ/rg = 102 (pentagons), and λ/rg = 103 (triangles), as labelled. The short heavyweight line indicates the approximate spectral index σ that is appropriate to match Fermi-LAT > 1 GeV observations for the Crab Nebula, assuming uncooled inverse Compton emission is operable. Note that the indices for the β1HT = 0.75 , 0.975 cases correspond to those of the distributions exhibited in Fig. 2.

cooled inverse Compton models; same as in Fig. 2) suggests low values of λ/rg and proximity of the shock obliquity to the subluminal/superluminal boundary. This inference will be developed further below. It is appropriate to identify briefly the reason why the distribution indices approach σ ∼ 1 for subluminal shocks when λ/rg ≫ 1 , i.e. the field is almost laminar. The origin of the extremely flat distributions with σ ∼ 1 is in the coherent effect of shock drift acceleration at the shock discontinuity, discussed extensively in Baring & Summerlin (2009). This phenomenon is due to the energy gain of charges when

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they repeatedly encounter u × B electric fields (in frames other than the HT frame) in gyrations straddling the shock discontinuity. Such gains are experienced between episodic upstream excursions as charges more or less retain gyrophases that permit reflection from the shock for long periods of time. Reducing λ/rg , and thereby introducing extremely modest amounts of cross-field diffusion, disrupts this coherence, removes particles from the shock layer, and steepens the spectrum. It is not clear that astrophysical relativistic shocks can contain such low levels of turbulence as to access this academically interesting regime of phase space. In concluding this overview of particle acceleration characteristics at relativistic shocks, it is noted that the results from these Monte Carlo simulations are in good agreement with those from other techniques, such as semi-analytic numerical solutions of the diffusion-convection equation, and also other Monte Carlo research initiatives. In particular, the artificially high choice of the compression ratio r = 4 in Figures 2 and 4 was adopted to facilitate comparison with the semi-analytic work of Kirk & Heavens (1989). The reader is referred to Baring & Summerlin (2009) and Baring (2010) for more details on such simulation validation.

3 The Quasi-Perpendicular Pulsar Wind Termination Shock The discussion now turns to lepton acceleration in pulsar wind termination shocks. While it is clear that their upstream flow speeds should be ultrarelativistic, it is unclear how fast they are. The historical paradigm of upstream bulk Lorentz factors Γ1 ∼ 105 in the Crab Nebula has been promulgated from the seminal work of Kennel & Coroniti (1984). Pulsars can easily generate such bulk flows propagating out through the light cylinder, since the accelerating potentials in their gaps must energize primary electrons to at least γe ∼ 106 − 107 . This is true for both outer gap models (e.g. Cheng, Ho & Ruderman 1986; Romani 1996) or polar cap scenarios (e.g. Daugherty & Harding 1982; 1996) for the electromagnetic dissipation zone in gamma-ray puslars. If radiation reaction-limited curvature emission is what is principally responsible for the GeV emission seen in a host of Fermi-LAT pulsars (see the Fermi pulsar catalog compendium in Abdo et al. 2010b), then one can simply derive the relation γe3 λ –c /ρc ∼ 2εMAX /3 for emission turnovers εMAX ∼ 5 × 103 (in 2 units of me c ) in the GeV band. Here ρc is the magnetic field curvature radius, which is some fraction of the light cylinder radius Rlc = Pc/(2π) for pulsar period P seconds. Also, λ –c = h¯ /(me c) = 3.862 × 10−11 cm is the electron Compton wavelength over 2π . With 106 cm < ρc < 109 cm, it is inferred that primaries assume Lorentz factors 106 . γ0 . 107 in a broad array of young to middle-aged pulsars. However, pair cascading is rife in both the polar cap and slot gap/outer gap gamma-ray pulsar pictures. Much of the pair creation (magnetic one photon or conventional two-photon) occurs outside the gaps containing accelerating potentials. Several generations of pair production ensue, precipitating large pair multiplicities η± ∼ 10 − 104 (e.g. see Daugherty & Harding 1982 for polar cap realizations, and Muslimov & Harding 2003 for slot gap results). Furthermore, similar values are ob-


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tained by De Jager (2007), who used the TeV inverse Compton flux in PSR B150958 and PSR B1823-13 to infer the total electron deposition integrated over the ages of their nebulae, thereby acting as a calorimeter for their pulsar pair multiplicities (see also Bucciantini, Arons and Amato 2010 for generally higher estimates for η± ). Simple energy conservation in the cascading process trades multiplicity for Lorentz factor, so that most of the emergent pairs propagating outwards from the gap region assume typical Lorentz factors of γ± ∼ γ0 /η± . This then defines fiducial bulk Lorentz factors for the pair flow escaping towards the distant termination shock, so that for nebular modeling purposes Γ1 ∼ 102 − 104 may be more representative of the flow just upstream of the PWTS than the higher Kennel & Coroniti (1984) value. However, we note that since the wind is strongly magnetically-dominated at the light cylinder, mysteriously transitioning to a plasma-dominated flow at the termination shock (the so-called infamous σ problem), conversion of Poynting flux to bulk plasma kinetic energy is a distinct possibility for raising the value of Γ1 , perhaps taking advantage of magnetic reconnection in and near the current sheet. The obliquity of the PWTS is less subject to such debate. If the termination shock is a fairly regular spatial structure, it must be highly oblique or an essentially perpendicular shock ( ΘBf1 ∼ 90◦ ) in the equatorial wind zone, and also at much higher pulsar latitudes. Within the light cylinder, this follows from the winding up of the field in a classic Parker spiral, just like the solar wind termination shock (e.g. see Bogovalov, 1999, for a discussion of MHD structure in oblique rotators). Only directions outside the pulsar polar regions can possess more radial fields that permit the shock to be merely oblique, or even quasi-parallel. The actual solid angle (centered on the pulsar) portion of the PWTS that is quasi-perpendicular depends on the obliquity of the rotator, how the virtually rigid inner magnetospheric field morphology causally maps over to the field outside the light cylinder, and how the field geometry is modified by plasma loading. Yet it is in all probability large, regardless of whether Γ1 is as high as 105 or as low as 102 . From the MHD simulations of the Crab pulsar wind of Komissarov & Lyubarsky (2004), it is clear the the termination shock is non-spherical, being radially compressed in the polar zones. One can also entertain the possibility that the termination shock is slightly rippled, akin to what is an emerging paradigm for the solar wind shock based on the surprising magnetometer and energetic particle data acquired by the Voyager I and II spacecraft in the last few years. This can then permit localized regions of the PWTS to be subluminal or marginally superluminal. Or it can provide seeds for acceleration in a perpendicular shock zone from remote, but merely oblique shock environs. However, observational support for any such a conjecture is a long way off since it requires angular resolutions exceeding that of Hubble and Chandra to probe such PWTS geometry in bright PWNe like the Crab (see Hester et al. 1995 for Hubble and ROSAT images) and MSH 15-52 (see Gaensler et al. 2002 for Chandra imaging). The content of the PWTS is generally presumed to be an electron-positron pair plasma. This derives from the leading models for dissipation in the pulsar magnetosphere: pairs are rife therein due to the relative ease of leptons being stripped from the neutron star surface. Thermionic emission is possible in pulsars with higher surface temperatures. Moreover, if sufficiently intense parallel electric fields persist in

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the atmosphere, space-charge limited ion acceleration can proceed (Ruderman & Sutherland 1975; Arons and Scharlemann 1979). Such a prospect drove ideas that young neutron stars (Blasi, Epstein & Olinto 2000) and magnetars (Arons 2003) could act as accelerating sources of ultra-high energy cosmic rays. In the context of PWNe, baryonic loading of the wind that impacts the termination shock is possible, and inherently alters the character of the shock. Low energy charges then become subject to cross-shock potentials in the shock layer, since the inertial (i.e. gyrational) scales of the different species are widely disparate (e.g. see the discussion in Baring & Summerlin 2007). This can act to redistribute the thermal energy of the charges, possibly enhancing the injection and acceleration efficiency of leptons by tapping the inertia of the incoming thermal ions. Even if the pulsar wind is pair-dominated, it is still possible that the PWTS interface picks up ions from the proximate hydrogenic ejecta and feeds them into the acceleration process. Observational constraints on hadronic contributions to PWN gamma-ray emission are substantial. For example, the multi-zone models of multiwavelength emission in the Crab nebula of Atoyan & Aharonian (1996) indicate that pion decay emission from PWTS-accelerated protons colliding with cold ambient hydrogen lies comfortably below the inverse Compton signal in the 100 MeV – 1 TeV band, and is only likely to be detectable at energies > 10 TeV. The flat spectrum and absence of any pion decay feature in the Fermi-LAT spectrum of the Crab (Abdo et al. 2010a) strongly suggest that the pair component of the PWTS is the most relevant. Given that both environmental and neutron star-driven baryonic loading are uncertain, and the observational mandate for treating hadronic emission in PWNe is limited, the discussion below will focus on pure lepton models for wind nebulae.

4 Connecting to PWN Observations The emphasis now turns to making direct inferences on the pulsar wind termination shock environment and its lepton acceleration characteristics using the multiwavelength observations of nebular emission. This necessarily connects to the nonthermal power-law distribution indices σ . For the best known and most intensivelystudied case of the Crab, the radio spectral index is quite flat at αγ = 1.26 (e.g. Wright et al. 1979), the X-ray index is steeper at αγ ∼ 2.1 (see Weisskopf, et al. 2000; Atoyan & Aharonian 1996), the 1–20 GeV γ-ray spectrum has αγ = 1.64 (e.g. Abdo et al. 2010a) which slowly breaks to αγ ∼ 2.5 above 1 TeV. The radio spectrum is not flat enough for synchrotron self-absorption, and no low frequency turnover that would be a signature of a minimum lepton Lorentz factor is observed. Accordingly, injection of pairs into the acceleration process must take place at energies below around 3–10 GeV. These characteristics are more or less representative of other PWNe: the radio index generally lies around 1.3 (see Gaensler & Slane 2006), and is flatter than the X-ray and TeV gamma-ray spectra, a nice synopsis of which is provided in the recent review of Kargaltsev & Pavlov (2010). Even if effective radiative cooling is invoked at the maximum pair energies generating X-ray synchrotron


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emission, it becomes evident from these properties that the pair injection spectrum is convex, ranging from σ ∼ 1.5 below around 30 GeV to σ ∼ 2.3 well above 1 TeV (e.g. see Bucciantini, Arons & Amato 2010). As will become evident shortly, this is a significant constraint on diffusive acceleration at the PWTS. We now identify the shock conditions required to generate these detected spectral indices, by considering shocks of higher speeds than in the previous Section. Representative spectral index results from Monte Carlo simulation runs are exhibited in Figure 1 (from Summerlin & Baring, in preparation), the β1x = 0.71 portion of which mirrors those presented in Figure 4. When the Bohm limit of λ/rg = 1 is realized, the non-thermal distribution index is approximately independent of the field obliquity. When the shock is superluminal, the index σ is a rapidly increasing function of ΘBf1 . In subluminal regimes due to the powerful convective infleunces, when the field is laminar and λ/rg ≫ 1 , very flat spectra can be realized because particles can be trapped in the shock layer and shock drift acceleration is very effective. Note also, that inefficient injection from thermal energies is then operative, as is exhibited in Fig. 2. The β1x = 0.95 indices are those taken from Fig. 2 and indicate a moderate increase with obliquity in the superluminal regime. Such an increase is tempered relative to the β1x = 0.71 , λ/rg = 10 situation largely because λ/rg and the compression ratio are higher. The superluminal and ultra-relativistic Γ1 ≈ 10 , ΘBf1 = 60◦ results are possibly the most representative of the PWTS. They illustrate a significant sensitivity of σ to λ/rg , yet the indices are lower than those for the shocks of lower speeds β1x . This is caused by the increased kinematic energy gains in shock crossings for high Γ1 for quasi-elastic interactions between charges and MHD turbulence in the shock layer. The spectral indices observed for the Crab nebula in radio, X-ray and gammaray wavebands, as marked in Figure 1, offer clear constraints on the shock environment, if diffusive acceleration at the PWTS is the operable injection in PWNe. These can be taken to be more or less representative of the broader population of PWNe, though variations exist in the observational database. The flat radio (synchotron) spectra demand that the turbulence generate large mean free paths along B if the PWTS is subluminal. Shocks by their nature generate turbulence at levels that make this scenario unlikely (see the discussion in Baring & Summerlin 2009), disrupting the coherence that permits shock drift acceleration to operate prolifically. Given that the PWTS is very probably superluminal over most of its surface, the small angle scattering regime cannot supply flat enough acceleration distributions. Large angle scattering can though, as is evident in Fig. 2 and in Stecker, Baring & Summerlin (2007). This is not an unduly restrictive demand in ultra-relativistic shocks, since LAS is delineated by deflections θscatt & 1/Γ1 , and it is easy to envisage that MHD turbulence in such shocks can spawn scattering angles of the order of a degree or so. It is this scenario that is the one most probably pertinent to the 1–30 GeV leptons. The inverse Compton gamma-ray signal measured by the Fermi-LAT is probing leptons of energies in the TeV range. The spectroscopic demands are now different: the 1–20 GeV index can be supplied by either subluminal or superluminal shocks with SAS operating, provided that the turbulence is not far from the Bohm limit. LAS is also possible, but would require highly superluminal conditions to effect

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Fig. 4 Power-law indices σ for simulation runs in the limit of small angle scattering, for relativistic shocks of three different speeds. The indices are displayed as functions of the fluid frame field obliquity ΘBf1 (contrasting Fig. 4). Simulation data for the points connected by dotted lines were for an of upstream flow speed β1x ≡ u1x /c = 0.71 , and an MHD velocity compression ratio r = 3.02 ; for these runs, obliquities ΘBf1 > 45◦ constitute superluminal shocks. These index results were obtained for different diffusive mean free paths λ parallel to the mean field direction, namely λ/rg = 1 (squares), λ/rg = 10 (triangles), λ/rg = 102 (pentagons), and λ/rg = 103 (triangles), as labelled. Data for the higher shock speed ( Γ1 β1x = 3 ⇒ β1x ≡ u1x /c = 0.949 ) spectra displayed in Fig 2 (SAS only) are exhibited as circular points with dots centered therein. These are mostly superluminal and corresponded to λ/rg = 5 . The final subset of datapoints are the three filled squares grouped at ΘBf1 = 60◦ for runs with Γ1 β1x = 10 ( β1x ≈ 0.995 ) with r = 3.02 (Summerlin & Baring, in preparation). These were obtained for λ/rg = 1, 3, 6 ranging from the bottom to the top. As with previous Figures, short heavyweight lines are used to indicate the approximate spectral index σ that is appropriate to match Crab Nebula spectra in different wavebands: radio (presumed to be uncooled synchrotron), 10-100 keV X-ray (cooled synchrotron emission) and Fermi-LAT > 1 GeV observations (uncooled inverse Compton); see the text for a discussion.

the requisite balance between large kinematic gains in shock-layer scatterings and rapid convective losses downstream. The X-ray spectrum samples the highest energy electrons, in the super TeV range, that are subject to strong cooling (burn-off) over the nebular lifetime. Allowing for this modification, the inferences for the in-


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jected lepton spectrum at the PWTS are similar to those from the gamma-ray data. A broadband picture emerges that is highlighted in Atoyan & Aharonian (1996): the electron spectrum is convex (i.e. steepening) in the sense that σ is an increasing function of energy. This is not difficult to accommodate using the results from shock acceleration theory presented here, being modeled by a modest transition from LAS at low energies to Bohm-domain SAS at the highest pair energies. The portions of the PWTS driving this energization can be either superluminal or marginally subluminal. It is not hard to envisage turbulence that is slightly stronger at smaller scales than larger ones that might precipitate this LAS → SAS evolution with energy or Larmor radius in gyroresonant interactions. Yet in the near-term future, neither can observations resolve the angular scales to demonstrate such, nor can plasma simulations probe the wide dynamic ranges in lengthscales to validate such a scenario. The simulation results presented here are for species of a single mass, obviously applying to pure pair shocks. It is natural to ask whether they might differ if the abundance of ions is significant. The answer must be deferred to future explorations of diffusive acceleration in hydrogenic plasma shocks. Yet it is expected that the the index results should be the same unless the turbulence generation is different when massive species are present. At energies below 1 GeV, the gyrational scales of protons and electrons of a given energy differ because the protons are at most only mildly-relativistic. This must lead to significantly different gyroresonant interactions for e− and p . Furthermore, at these energies, charge separation cross shock potentials are anticipated to play a profound role in energy exchange between the two species (e.g. Baring & Summerlin 2007). These two contributions should provide substantial differences in injection efficiency between pair shocks and hydrogenic or electron-ion ones. This injection issue is clearly salient for the overall prediction of fluxes in different bands for PWNe. However, at energies well above 10 GeV, the gyro-scale of a charge of a given energy is independent of its mass, so that to leading order, turbulence generation and diffusion characteristics should be similar in this domain for relativistic e± and e − p shocks. Another question is whether or not the well-known non-linear spectral concavity encountered in non-relativistic shocks that efficiently accelerate charges (see Jones & Ellison 1991; Ellison & Double 2002; Baring 2004, and references therein) might compete with and preclude the spectral convexity that is demanded by the multiwavelength observations. Such non-linear enhancements of high energy particles arise for distributions that have indices σ . 2 , where these particles supply a sizeable portion of the total energy flux through the shock, and thereby modify the global MHD shock structure. While the radio observations in PWNe access this domain, the distribution convexity demanded by the gamma-ray and X-ray data must mute possible non-linear modifications, so that they should play a more minor role than in the non-relativistic shocks that illuminate supernova remnant outer shells.

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5 Conclusions This paper has outlined the key features of relativistic shock acceleration that pertain to lepton injection at termination shocks into pulsar wind nebulae. This shock is the most popular site for such injection, because (i) all pairs emanating from the pulsar that travel to the nebula must transit through this interface, (ii) it should be turbulent and therefore an efficient injector/accelerator, and (iii) the main characteristics of diffusive acceleration theory at shocks are fairly well understood. While it is quite possible that pre-acceleration can arise in magnetic reconnection zones between the pulsar light cylinder and the PWTS, such seed particles can be further energized at the shock to the point of masking the signatures of pre-acceleration. The historical models that developed the paradigm of the PWTS as an injector predate refined studies of relativistic shock acceleration over the last decade. As is evident here, these more recent studies support such a paradigm in being able to generate the requisite distribution indices to match the multiwavelength PWN observations without appealing to unlikely situations concerning turbulence in the shock layer. The key issue that remains unresolved by theory is how efficient injection arises from thermal energies in the PWTS. Does it occur for pure pair shocks, or is some baryonic loading necessary to precipitate prolific energization? Or, is a pre-acceleration seed required to set the diffusive processes at the shock active all the way to super-TeV energies? Addressing such questions will require more advanced simulations and theoretical analyses. The answer will illuminate the overall particle budget in pulsar wind nebulae, balancing radiation luminosity, non-thermal particle energetics, and the wind power from the pulsars that drives these fascinating systems. Acknowledgements This research was supported in part by National Science Foundation grant PHY07-58158 and NASA grant NNX10AC79G.

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MHD models of Pulsar Wind Nebulae Niccolò Bucciantini

Abstract Pulsar Wind Nebulae (PWNe) are bubbles or relativistic plasma that form when the pulsar wind is confined by the SNR or the ISM. Recent observations have shown a richness of emission features that has driven a renewed interest in the theoretical modeling of these objects. In recent years a MHD paradigm has been developed, capable of reproducing almost all of the observed properties of PWNe, shedding new light on many old issues. Given that PWNe are perhaps the nearest systems where processes related to relativistic dynamics can be investigated with high accuracy, a reliable model of their behavior is paramount for a correct understanding of high energy astrophysics in general. I will review the present status of MHD models: what are the key ingredients, their successes, and open questions that still need further investigation.

1 Introduction When the ultra-relativistic wind from a pulsar interacts with the ambient medium, either the SNR or the ISM, a bubble of non-thermal relativistic particles and magnetic field, known as Pulsar Wind Nebula or “Plerion” (PWN), is formed. The Crab Nebula is undoubtedly the best example of a PWN, and it is often considered the prototype of this entire class of objects, to the point that models of PWNe are, to a large extent, based on what is known in this single case. The first theoretical model of the structure and the dynamical properties of PWNe was presented by Rees & Gun [90], further developed in more details by Kennel & Coroniti [66, 67] (KC84 hereafter), and is based on a relativistic MHD description. The MHD paradigm is based on three key assumptions:

N. Bucciantini NORDITA, Roslagstullsbacken 23, 106 91 Stockholm, Sweden, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_39, © Springer-Verlag Berlin Heidelberg 2011

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• That the Larmor radii of the particles is much smaller than the typical size of the nebula, and particles are simply advected with the magnetic field. This is true up to energies of order of the pulsar’s voltage, where the Larmor radius becomes comparable with the typical size of the system. • That radiative losses are negligible, or at least that they can be accounted for by renormalizing the pulsar spin-down luminosity. This again can be proved to be true in the case of Crab Nebula (and to some extent also in other systems with good spectral coverage), where the synchrotron spectrum shows that the particles carrying the bulk of the energy have a typical lifetime for synchrotron cooling longer than the age of the nebula. • That we are dealing with almost pure pair plasma, and dispersive or hybrid effects (separation of scales) due to the presence of heavier ions are absent. While there is no direct evidence for the absence of ions, standard pulsar wind theory, and the success of the MHD model of PWNe suggest that, from a purely dynamical point of view, there is no need for this extra component. In it simplest form [90] the MHD model of PWNe can be summarized as follow (see left panel of Fig. 1): the ultra-relativistic pulsar wind is confined inside the slowly expanding SNR, and slowed down to non relativistic speeds in a strong termination shock (TS). At the shock the plasma is heated, the toroidal magnetic field of the wind is compressed, and particles are accelerated to high energies. These high energy particles and magnetic field produce a post-shock flow which expands at a non relativistic speed toward the edge of the nebula.

1

a

b c

de

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Fig. 1 Left picture: schematic representation of the global structure of the PWN in the first phase of its evolution inside a SNR. From the center the various regions are: 1- the relativistic pulsar wind, 2- the hot magnetized bubble responsible for the non thermal emission, 3- the free expanding ejecta of the SNR, 4- the ISM. These regions are separated by discontinuities: a- the wind termination shock, b- the contact discontinuity between the hot shocked pulsar material and the swept-up SNR ejecta, c-the front shock of the thin shell expanding into the ejecta, d- the reverse shock of the SNR, e- the contact discontinuity separating the ejecta material from the compressed ISM, f- the forward SNR shock. Right picture: evolution of the PWN size, from free-expansion to sedov phase (from [25]).

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Despite its simplicity the MHD model can explain many of the observed properties of PWNe, and until now no observation has been presented that could rule it out. The presence of an under-luminous region, centered on the location of the pulsar, is interpreted as due to the ultra-relativistic unshocked wind. Polarization measures [114, 108, 95, 59, 84, 43, 72, 55] show that emission is highly polarized and the nebular magnetic field is mostly toroidal, as one would expect from the compression of the pulsar wind, and it is consistent with the inferred symmetry axis of the system. The pressure anisotropy associated to the compressed nebular toroidal magnetic field [11, 103], explains the elongated axisymmetric shape of many PWNe (i.e. Crab Nebula, 3C58). The MHD flow from the TS to the edge of the nebula also leads to the prediction that PWNe should appear bigger at smaller frequencies: high energy X-rays emitting particles are present only in the vicinity of the TS, having a shorter lifetime for synchrotron losses, compared to radio-emitting particles which fill the entire volume, having negligible losses on the age of the nebula. This increase in size at smaller frequencies is observed in the Crab Nebula [107, 14, 7]. However one must bear to mind that not all properties of PWNe can be explained within the MHD framework, which, ultimately, only provides a description of the flow dynamics. For example, the acceleration of particles at the TS that accounts for the continuous, non-thermal, very broad-band spectrum, extending from Radio to Xrays [107, 8, 112, 113, 85], is usually assumed as given. The MHD model provides no hint to the reason why the injection spectrum looks like a broken power-law, with no sign of a Maxwellian component at lower energies. Moreover the MHD description might prove faulty if applied to particles responsible for the emission in the 10-100 MeV band, whose Larmor radii are comparable to the size of the TS, and can lead to wrong conclusion on their expected behavior. The MHD model of PWNe has been used, by comparing observations with the predictions of numerical simulations, to constrain some of the properties of the pulsar wind, at least at the distance of the TS. While it is not possible to derive the Lorentz factor of the wind, or its multiplicity, it is possible to constrain the ratio between Poynting flux and kinetic energy, the latitudinal dependence of the energy flux, and the presence of a dissipated equatorial current sheet. This shows that nebular properties can be used to derive informations on the conditions of the pulsar wind at large distances.

2 Jet-Torus structure and Inner flow properties Let us start our discussion from young objects. The Crab Nebula, 3C58, MSH 1552, G21.5 all belong to this group. Younger objects are the most well studied and perhaps the ones for which the MHD models have provided the greatest insight. These systems are characterized by a simple interaction with the confining SNR, they are bright, we have broad band data, and the pulsar proper motion can be neglected. Older systems are often subject to a much more complex interaction with the SNR, they are affected by the pulsar proper motion, and usually lack the deep

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observational coverage of the younger counterparts. For these reasons, models of old objects have also progressed far less than for young ones, and the agreement with observations is mostly qualitative. We will leave a description of MHD models of the evolution of PWNe to Sec. 3. The KC84 model has been for a long time the reference for the understanding of young PWNe, with only minor theoretical developments. Things have changed recently thanks to high resolution optical and X-rays images from HST, Chandra and XMM-Newton, that have have shown that the properties of the emission at high energy cannot be explained within a simplified one dimensional model. This refers not just to the geometrical features that are observed, but in practice to all aspects of X-ray emission. These new data show that the inner region of young PWNe is characterized by a complex axisymmetric structure, generally referred as jet-torus structure (see right panel of Fig. 2 and Fig. 4). First observed in Crab Nebula [56, 112], it has subsequently been detected in many other PWNe [51, 45, 54, 89, 46, 76, 93, 97, 35, 94], to the point that the common consensus is that, with deep enough observations, it should always be detected. This structure is characterized by an emission torus, in what is thought to be the equatorial plane of the pulsar rotation, and, possibly, a series of multiple arcs or rings, together with a central knot, almost coincident with the pulsar position, and one or two opposite jets along the polar axis, which seem to originate close to the pulsar itself. Even if the existence of a main torus could be qualitatively explained as a consequence of a higher equatorial energy injection [20] it is not possible to reproduce quantitatively the observed luminosity. Shibata et al. [96] were the first to point that, the difference in brightness between the front and back sides of the torus in Crab Nebula, requires a post-shock flow velocity ∼ 0.4 − 0.5c, much higher than what expected for subsonic expanding flows. The same conclusion applies to all the other systems where a torus is observed. The existence of an inner ring, detached from the torus, and of the knot which seemed to be located inside the wind region, are incompatible with the assumption of a smooth flow from the TS. From a theoretical point of view however, the most interesting feature is the jet [80], because theoretical [12, 13] and numerical [34, 19, 52, 70, 30] studies of relativistic winds from pulsars have shown no presence of collimated energetic outflows. To this, one must add other observed properties, like the X-ray photon index maps of Crab Nebula, Vela and Kes 75 [85, 63, 87], which harden moving from the inner ring toward the main torus, while steepening due to synchrotron losses is expected, and the relatively large size of the X-ray nebula in Crab compared to the radio [4]. The fact that the symmetry axis of the jet-torus corresponds to the major axis of the nebula, leads immediately to the conclusion that the toroidal magnetic field is paramount in shaping the inner flow. The keys in understanding the jet-torus structure are the magnetization and energy distribution in the pulsar wind. It has been known for a long time [83], and has been recently confirmed with numerical simulations [19, 70, 30], that far from the light cylinder a higher equatorial energy flux is expected. It is this particular latitudinal distribution of the pulsar spin-down luminosity which naturally produces an oblate TS with a cusp in the polar region [20, 21], giving rise to a complex post-


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Fig. 2 From left to right: structure of the post shock flow in PWNe [22], the funneling of the wind (A) into an equatorial flow (B/C) is clearly evident. Same structure showing the complex flow dynamics that develops downstream of the shock and the corrugation of the shock surface which manifests itself as time variability at high energy [33]. Numerical result of the internal dynamics in the body of the PWN [22] where the flow is diverted back toward the axis by the magnetic hoop stresses, and is collimated into a jet.

shock dynamics. The obliquity of the TS at higher latitudes, forces the flow in the nebula toward the equator with speeds ∼ 0.3 − 0.5c. Hoop-stresses are more efficient in the mildly relativistic flow, and the collimation of a jet occurs in the post shock region [77, 65]. The evident complexity of this scenario makes clear that the only possible way to proceed requires the use of efficient and robust numerical schemes for relativistic MHD [69, 40, 49]. Thanks to numerical simulations this qualitative picture has been developed into a quantitative model which has been successfully validated against observations. The starting point of the MHD model is the structure of the force-free pulsar wind: the energy flux in the wind has a strong latitudinal dependence of the form L(θ) = Lo (1 + α sin (θ)), where α is a measure of the pole-equator anisotropy, while the magnetic field in the wind B(θ) ∝ sin (θ). Various numerical simulations of the interaction of such wind with the SNR ejecta have been presented [71, 22, 22, 23, 111, 33]: the result of the anisotropic energy distribution in the wind is that almost all of the downstream plasma is deflected toward the equatorial plane, and flow channels with velocity ∼ 0.5c can form (fig. 2), the value expected in order to justify the luminosity distribution in the torus of the Crab Nebula [96]. Shear and instabilities tend to destroy this collimated equatorial flow before it reaches the edge of the nebula, however a bulk equatorial motion survives to distances corresponding to the location of the torus. It is this flow inside the nebula, with a speed in excess of c/3 that advects freshly injected particles to larger distances, giving rise to a more extended X-ray nebula, than the simple 1D model would predict [4]. The post shock flow is independent on the specific values of Lorentz factor or density distribution, but it is only determined by the puslar spin-down energy distribution, and the nebular dynamics cannot be used to constrain the value of the wind Lorentz factor or the multiplicity in the wind. As the flow expands away from the TS, toward the edge of the nebula, the magnetization increases, until equipartition is reached. Due to the magnetic field distri-

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Fig. 3 Upper panel: left - simulated X-rays synchrotron map based on numerical MHD simulations of the flow [33]; right - Chandra image of the central region of Crab Nebula. The two images have similar scaling. Lower panel: left - simulated optical synchrotron map based on numerical MHD simulations of the flow (different from the above one); right - HST image of the wisp region in Crab Nebula [58]. Note the agreement between the observed features and the results of MHD models.

bution in the wind, equipartition is first reached closer to the equator than at higher latitudes. The magnetic pressure prevents further compression beyond equipartition, hoop stresses in the mildly relativistic postshock flow become efficient, and the flow is diverted back toward the axis. This is the process that causes the formation of a collimated jet along the axis itself (Fig. 2). The wind magnetization regulates the formation and properties of the jet: for low values σ < 0.001, where σ is the ratio of Poynting flux to total energy flux in the wind, equipartition is not reached inside the nebula, and no jet is formed. At higher magnetizations equipartition is reached in the close vicinity of the TS, and most of the plasma ends in a jet. The plasma speed in the jet is ∼ 0.7c, in agreement with observation of the jet in Crab Nebula and


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MSH 15-52 [112, 58, 74, 39], for magnetization values σ ∼ 0.1. Associated with this collimated back-flow there is a global circulation inside the nebula, with typical speeds ∼ 0.1c that might lead to mixing with cold ions [82]. Numerical models offer the possibility to investigate different distributions of magnetic field in the wind. In particular, for oblique rotators, while the energy distribution in the wind is identical to the aligned case [18, 98], the magnetic field is supposed to give rise to a striped equatorial region, with alternating polarities. If this striped wind region is dissipated, and this can happen either in the wind [81, 68] or at the termination shock itself [78, 79], then a low magnetization equatorial flow is expected, which adds complexity to the flow structure inside the nebula. One of the main success of the MHD model is that emission maps based on the results of numerical simulations give different observational signatures if an unmagnetized equatorial sector, corresponding to the striped wind region, is present or not: a large striped region is needed to explain the observed inner-ring outer-torus structure of many PWNe, while models without it lead to single ring nebulae. When comparing observations with emission maps based on the fluid structure derived from relativistic MHD simulations we clearly see that, within the MHD regime, it is possible to recover almost all of the observed features, with correct size and luminosity. However, until now, little work has been devoted to investigate if it is possible to discriminate among various particle injection mechanism. Work has mostly focused on X-rays, and a uniform injection in the form of a single powerlaw distribution has been assumed [23, 111, 71, 33]. Moreover one should be aware that even today, with better computational facilities, it is not possible to conduct an exaustive sampling of the entire parameter space characterizing the interaction of PWNe with SNRs. Works has mostly focused on reproducing Crab Nebula, where many parameters are constrained by a rich set of observations. In Fig. 2, Chandra and HST images of the Crab Nebula are compared to maps based on a simulations with striped wind in X-rays and optical. The knot and the inner ring are both present, and they are due to the high velocity flow in the immediate post shock region, at intermediate latitudes. The main torus is visible at larger distances, as well as features like the anvil which corresponds to the backward side of the nebula. X-ray maps of the spectral index based on simulations also agree with the main observed properties of the Crab Nebula [85] and with recent results about Vela [63] and Kes 75 [87]: in particular the spectrum appears to flatten moving away from the pulsar toward the main torus, without the need to assume any re-acceleration. All this rich emission pattern is ultimately related to Doppler boosting effects: at high speed, the emission is enhanced (rings) and the spectrum is harder. There are still problems to recover the correct luminosity/spectrum in the jet. This might be indicative of some form of dissipation and re-energization along the axis, possibly associated with local instabilities in the toroidal magnetic field [9] which present axisymmetric simulations cannot address, but for which there are many observational evidences [89, 86, 74, 39]. Preliminary results [33] show that, to realistically respoduce the X-ray emission from Crab Nebula, σ ≃ 0.1 is required (about two orders of magnitude higher than the 1D estimate by KC84) in conjunction with a large (∼ 45◦) striped zone.

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Fig. 4 Variability in the wisps region in MHD [33]. Left figure: variability at a selected point on axis, note the typical 2-years long cycle and also the shorter timescale variations. Right figure: variability of the nebula obtained by subtracting two images at 2-year distance. The outgoing wave pattern is easily seen. Compare with optical images from [58].

Perhaps the most promising clues to investigate the flow dynamics inside PWNe in the future might come from polarization, and possibly X-ray polarization: while emission maps mostly trace the flow velocity inside the nebula, they have little sensitivity to the presence of a small scale disordered component of the magnetic field. There are several indications from optical polarimetry in the Crab Nebula [55], as well as indication from recent MHD simulations [33, 111], suggesting that turbulence might be present, in the body of the nebula, leading to a partial randomization of the field. The effect of the flow velocity on the polarization angle has been discussed by [29] and [23], and the results generally agree with available optical polarization measured in Crab [114, 108, 95, 59, 55].

2.1 Time variability It is known that, close to the supposed location of the termination shock, PWNe show a short time variability mainly detected in optical and X-ray bands. This however does not affect the global properties of the main observed features belonging to the jet-torus structure (i.e. the inner ring, torus and jet) which appear to be quite persistent on long time-scales. Variability of the wisps in the Crab Nebula has been known for a long time[58, 15]. Recent observation have shown that the jet in Vela appears to be strongly variables [88, 89], together with the main rings [63]. Variability is also observed in the jet of Crab [86, 74], and have recently been detected in MSH 15-52 [39].


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In the strongly toroidal field of these nebulae, the jet variability, which usually has time-scale of years, is likely due to kink or sausage mode, or even to fire-hose instability [102]. On the other hand the wisps show variability on shorter time-scales of months: the variability takes the form of an outgoing wave pattern, with a possible year-long duty cycle. For a long time the only model capable of reproducing the observed variability was the one proposed by Spitkovsky & Arons [99], based on the assumption that ions are present in the wind. The idea of ions was also supported by kinetic simulations of acceleration in a strong shock [3]. The presence of particles with Larmor radii, of order of the size of termination shock, introduces kinetic effects related to the separation of scales, leading to compression of electrons. The model however requires a large fraction of pulsar spin-down energy in the ion component, which contrast the basic idea of leptonic dominated systems, and in general is not supported by spectral model of PWNe. The most recent achievement of the MHD nebular models have been the ability to reproduce the observed variability [33, 31, 10, 111]. It is the fundamental multidimensional nature of the problem that allows for variability of the flow pattern. It was already noted in early simulations [22] that the synchrotron emissivity inside the nebula varies. There were also evidences [71] suggesting that the nebular flow might have a feedback action on the TS, causing it to change shape, and thus inducing a change in the appearance of the wisps. This picture has been confirmed recently [33, 111]: within the MHD regime it is possible to recover the variability, the outgoing wave patter, its typical speed, and luminosity variations (Fig. 4). It is found indeed that a SASI like instability is present. Waves injected at the termination shock can propagate toward the axis, feeding back on the termination shock and triggering the injection of new waves. Simulations show that there is a typical duty-cycle of about 1-2 year; more generally the duty-cycle will be of the order of the radius of the termination shock divided by the typical propagation speed ∼ 0.5c.

2.2 Gamma rays At the moment the most promising observational avenue in PWNe research is the study of gamma-ray emission. HESS has shown that many extended gamma-ray sources are associated with PWNe both young ones in the free expansion phase and older ones undergoing reverberation [37, 48]. New results from the FERMI satellite are just arriving [1, 2], with data extending from the high energy MeV synchrotron part of the spectrum, to the 100 GeV IC part. The emission at MeV energy observed from young objects should enable us to put constraints on the acceleration mechanism. It seems that an exponential cutoff in energy can explain the observed data. The more interesting question centers on how the observed variability of the wisps manifests itself at higher energies. Naively one might expect that the emission at high energies should show similar variability,

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on comparable time-scales, but with amplitudes of order unity. On the other hand preliminary results [75] suggest that in the 100MeV range no variability is detected. This has important implications in term of acceleration: particles responsible for the 100MeV emission have typical Larmor radii of order of the size of the TS. Coincidentally this is also the coherent length of the turbulence that is at the base of the MHD variability [33]. In this sense high energy particles are decoupled from the MHD flow, and their response to the MHD turbulence is incoherent. This of course deserves further investigation. In particular one would like to know at what energy variability reaches a maximum, where the particles start to decouple form the MHD flow, and to what degree this incoherent interaction with turbulence can induce variability. The emission at GeV energies is assumed to be from Inverse Compton (IC) scattering on background radiation, and in the case of Crab Nebula the IC selfsynchrotron. Interestingly the spectral properties of the comptonized radiation can be used to derive information about particles which are supposed to emit synchrotron in the UV, and are usually not directly accessible given the high UV absorption in the ISM. In the case of MSH 15-52 [2] Fermi results, have ruled out previous EGRET data, and shown that the undetected high energy part of the particle distribution function must be harder than previously assumed. Similar results could be expected for Kes 75. GeV emission could in principle help provide an independent constraint on the magnetization in the nebula. An alternative contribution to the gamma ray emission, if protons are present in the pulsar wind, is the p-p scattering and related pion decay [5, 61]. However uncertainties on the target number density and the spin-down energy in protons, make this channel hard to constrain. At present IC scattering can fit most of the objects, if one allows for fluctuations of the local background of order unity with respect to the Galactic average. Recently a series of simplified evolutionary models for the high energy emission from PWNe have been developed extending beyond the free expansion [38, 50, 32]. This is quite important given that the majority of the gamma-ray PWNe are supposed to be post-reverberation objects, where the interaction with the SNR shell can play a major role For example in many of these objects the bulk of the gamma emission is not centered on the pulsar, and the displacement is too large to be explained in term of a moving pulsar leaving behind a relic PWN. Two possible explanations have been invoked: an off-center compression by the reverse shock [16]; or the formation of a bow-shock tail [28, 64], where particle responsible for the inverse Compton emission in the gamma-ray band can be advected to large distances from the pulsar.

3 Evolution of PWNe In the previous section we have devoted our attention to the successes of the fluid/MHD model regarding the emission properties observed in young systems.


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Numerical simulations also offer a way to follow the evolution of a PWN and its interaction with the SNR at later ages. At the moment, however, the study of old objects has been limited to a qualitative analysis of the interaction in an attempt to recover the main phases of the evolution and understand how the observed multi-wavelength morphology depends on the interaction itself. In the analytic model developed by KC84 the SNR has only a passive role, providing the confinement of the PWN. Given the complexity of the PWN-SNR interaction, a detailed study of the evolution of the system, has been possible only recently, thanks to the improvement in computational resources [44, 16, 25, 106, 44]. By comparing the energy in the SNR (∼ 1051 ergs) to the total energy injected by the pulsar during its lifetime (∼ 1049 ergs) it is easy to realize that a PWN cannot significantly affect the SNR, while the evolution of the SNR can have important consequences for the PWN. There are three main phases (for a more complete discussion of PWN-SNR evolution see [91] and [47]), in the PWN-SNR evolution (see right panel of Fig. 1). At the beginning the PWN expands inside the cold SN ejecta. The SN ejecta are in free expansion, so this phase is generally called free expansion phase. This phase lasts for about 1000-3000 yr, and during this period the pulsar luminosity is high and, given the weak dependence of the expasion rate on the pulsar luminosity, it can be approximated assiming that it is almost constant. This is the present phase of the Crab Nebula, 3C58, MSH 15-52, G21.5, and PWNe in this phase are expected to shine in high energy X-rays emission. The expansion velocity of PWNe in this early stage is typically few thousands kilometer per second. For this reason one can neglect the pulsar kick (velocities in the range 50-300 km/s) in modeling young objects, and assume the pulsar to be centrally located. As the system expands inside the high density, cold, supersonic ejecta of the SNR, a thin shell of swept-up material is formed. Given that the density of the shell is much higher than the the inertia of the relativistic plasma (the enthalpy), the shell is subject to Rayleigh-Taylor instability. This is supposed to be at the origin of the filamentary network of the Crab Nebula [57, 62, 27], and 3C58 [17]. In the thin-shell approximation, it has been shown that it is possible to derive an analytic self-similar solution [27], describing the expansion of the nebula in this phase. The PWN will expand until eventually it will come into contact with the reverse shock in the SNR shell. In the absence of a central source of energy, like a pulsar, the reverse shock is supposed to recede to the center of the SNR in a time of order of 5000-10000 yr [101]. From this moment on the evolution of the PWN is modified by the more massive and energetic SNR shell: the PWN undergoes a compression phase generally referred as reverberation phase, that can last 5000-10000 yr. In the simple 1D scenario the pressure in the compressed PWN will rise to balance the compression and to push back the ejecta, and the nebula might undergo several compression and rarefaction cycles. This is however an artifact of the 1D geometry, and conclusions based on the existence of these oscillations are not reliable. More appropriate multidimensional studies have shown that the SNR-PWN interface is highly Rayleigh-Taylor unstable during compression [16], which can

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Fig. 5 Upper part: images of various evolutionary phases of PWNe (see also Gaensler & Slane [47]). From Left to right, up to down: X-ray image of the composite remnant G21.5-0.9, free expansion phase; X-ray image of Vela SNR (insert is TeV emission [53]), displacement of the nebula due to the compression of the reverse shock during reverberation; SNR G 327.1-1.1 in radio (red) and X-rays (blue), relic PWN phase; W44 in radio, transition to the internal bow-shock phase [36]; PSR B1957+20 in Hα (green) an X-rays (red), ISM bow-shock nebula. Lower part: numerical hydrodynamical simulations of the various phases of the PWN-SNR evolution (from [106, 23]). Each figure of the lower part corresponds to systems shown in the upper one.


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cause efficient mixing of the pulsar wind material with the SNR. This mixing will most likely prevent any oscillation and the system might rapidly relax to pressure equilibrium. This reverberation phase is supposed to last about 104 years. Even if energy injection from the pulsar at these later times is negligible, PWNe can still be observed, due to the re-energization during compression. The interaction with the reverse shock can lead to a variety of different morphological structures if one considers also the pulsar proper motion [105, 106, 28, 44]. The most likely outcome of the interaction is that the nebula can be displaced with respect to the location of the pulsar (Fig. 3). At the beginning this might result in a system where the pulsar is not located at the center of the radio non thermal emission, analogous to what is observed in Vela. As the system evolves the reverse shock will completely displace the body of the PWN, creating a relic nebula. The relic PWN will mostly contain low energy particles, and will be visible in radio, while high energy particles, observable in X-rays will be seen only close to the pulsar. G327.1-1.1 shows indeed this kind of morphology [47]. Depending on projection effects one might also end up with very small X-ray nebulae centered on vast and large radio nebulae. In this regard polarization might prove essential to disentangle the structure. In particular, if the Rayleigh-Taylor instability is efficient and the radio nebula is disrupted and mixed with the ejecta, one expects to find a low level of polarization and no evidence for a global toroidal field. To this one must add the possibility that the ISM magnetic field might be dragged inside the PWN, or the nebular field inside the SNR shell. Given the importance of magnetic configurations for particle (cosmic ray) diffusion, one understands how important a proper model of older objects is. At later time the SNR ejecta starts cooling and the pulsar will eventually become supersonic. Once this happens the pulsar will form around itself a bow-shock PWN, and one expects an emission tail to form connecting the pulsar to the relic PWN (Fig. 3). This model applies to the morphology and structure of W44 [47], or possibly IC443. Interestingly, the location with respect to the SNR where this happens does not depend on the pulsar proper motion, and turns out to be ∼ 70% of the radius of the forward shock. An obvious question is if the jet-torus structure, that is observed in young and relatively undisturbed systems, can survive the later interaction with the SNR shell and the reverse shock. We know that in Vela the jet-torus is visible and does not appear to be distorted. This suggest that, as long as the evolution is subsonic, in the pulsar vicinity the dynamic of the nebula flow will still be regulated by the pulsar wind. On the other hand bow-shock simulations have shown that the typical size of the nebula in the head of the bow-shock and the flow dynamics do not allow the formation of collimated structures [24, 28, 109]. In the case of SNR G327.1-1.1 [100] have suggested the presence of a jet-torus, but photon counts and resolution are not high enough to make a definite statement. Deeper observation of transitional objects are needed. The ultimate phase of a PWN evolution depends on the pulsar kick. For slow moving pulsars the PWN will expands adiabatically inside the heated SNR, now in Sedov phase. Given the absence of energy injection, a PWN in this stage is probably only observable as a faint extended radio source, or possibly as a large TeV nebula due to IC from the relic leptons. To some extent this relic particle population might

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contribute to the diffuse gamma-ray background. On the contrary a fast moving pulsar can escape from the SNR, and will give rise to a bow-shock nebula due to the interaction with the ISM, through which it is moving at supersonic speeds [24, 28, 109]. These objects are observed both in Hα emission, due to ionization of ISM neutral hydrogen, and as long extended cometary-like source of non thermal radio and X-ray emission, due to the shocked pulsar wind, now forced to flow in the direction opposite to the pulsar motion (Fig. 3). These nebulae might constitute one of the primary sources of positrons in the galaxy. Bow-shock PWNe, constitute a very interesting class among PWNe, and have recently received some attention, in particular regarding their X-ray emission. MHD models predict that the outflow in the tail of the bow-shock should have high speeds, of order of 0.5c, and that the tail should form a very well collimated channel, with cross section comparable with the bow-shock size [24, 28, 109]. However observations have shown that in general the tail is wider than expected and that typical flow speeds are high but of order 10000 km/s. It has been suggested that some form of mixing with the ISM, either via shear instability between the fast relativistic tail and the surrounding slower ISM, or via some particle contamination by ionized neutrals coming from the ISM, might be at play. A more detailed study of the fate of pairs injected in the tails of bow-shock nebulae, is essential, to assess the importance of pulsar as contributor to the pair CR background.

4 Conclusion In the last few years, the combination of high resolution observations, and numerical simulations, has improved our understanding of the evolution and internal dynamics of PWNe. We can reproduce the observed jet-torus structure and we can relate the formation of the jet in the post shock flow to the wind magnetization. Simulated maps can reproduce many of the observed features, including the details of spectral properties. Results suggests that the best agreement is achieved in the case of a wind with a large striped zone, even if MHD simulations are not able to distinguish between dissipation of the current sheet in the wind or at the TS. Results also suggest that it is possible to use X-ray imaging to constrain the pulsar wind properties; already the rings and tori observed in many PWNe have been used to determine the spin axis of the pulsar [94]. Interestingly in the Crab Nebula the inner ring appear less boosted in X-rays than the optical wisps (which should trace the same flow structure) are. Despite the undeniable successes of the MHD model, which are universally recognized within the community, and the fact that there is general agreement that the observed X-ray properties are strongly dependent on the internal dynamic at the termination shock, for reasons unknown to the author, the old KC84 model is still used as a canonical reference for interpreting observations. While this might be understandable for Radio or Optical data (where emission is quite homogeneous), it is completely unreasonable in X-ray. The fact that KC84 model is analytic and simple,


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is no excuse for its use, when it is clear that it is both qualitatively and quantitatively wrong, to the point that it basically fails to explain almost every single aspect of X-ray data. Moreover application of KC84 to observation can easily lead to misinterpretation of the results. For example, in KC84 the relative radius of inner ring and outer torus can be used to infer the magnetization σ of the wind; however 2D models show that such ratio only depends on the pulsar wind energy distribution and on the inclination angle of the pulsar spin axis on the plane of the sky. Similar arguments apply for the hardening of the X-ray spectrum in the vicinity of the pulsar, or the relative size of the nebula at radio vs X-ray energies. Moreover numerical tools and facilities are today widely available to conduct a correct study. Interestingly, even when data are unreasonably averaged over spherical shells (even if imaging shows no hint of sphericity), they cannot be modeled using the original KC84 structure, and arbitrary velocity profiles are often assumed to reproduce the data. So one trades a model (KC84) which is wrong (nebulae are far from spherical), but at least dynamically consistent (the correct solution of MHD equations), for models which not only are wrong but also dynamically inconsistent. These models are usually tuned to fit a single object, with no attempt at validating them against a larger sample, and rely on the presence of extra free paramanters, which often rises the question of how significative are the fit from a statistical point of view. Information derived in this way have almost no scientific value, and the entire analisys is nothing more than a fit to the data. There are still however unsolved questions, and possible future developments for research in this field. All present simulations are axisymmetric, and none is able to address the problem of the stability of the toroidal field, nor can they reproduce the observed emission from the jet. It is not clear if small scale disordered field is present in the inner region: maybe a residual of the dissipation in the TS of the striped wind, or an outcome of the turbulence injected by the SASI-like instability of the TS. A combination of simulations and polarimetry might help to answer this question. Perhaps the more interesting developments might come from either the study of old systems, or from the investigation of particle energy distribution signatures in young ones. For the former, what is really needed is a large parameter study, where the various effects of pulsar proper motion and SNR reverberation are taken into account together with some simplified treatment of the spectral properties of these nebulae, in order to go beyond the simple qualitative morphological agreement, and provide templates for emission and spectral properties to be compared with observations. For the latter, a study of possible signature of different injection mechanism at the TS, either as a function of shock properties, latitude or time, should be carried on by following the full particle distribution function in the nebula, instead of the simple power-law assumption. This will allow us to verify if observable signatures should be expected, in what band, and provide some constraint on the physics at the TS, and more important, on relativistic shock acceleration in general. Acknowledgements N.B. was supported by a NORDITA Fellowship grant.

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TeV Gamma Ray Survey on the Direction of Fermi-LAT Pulsars with the Tibet Air Shower Array M. Amenomori, X. J. Bi, D. Chen, S. W. Cui, Danzengluobu, L. K. Ding, X. H. Ding, C. Fan, C. F. Feng, Zhaoyang Feng, Z. Y. Feng, X. Y. Gao, Q. X. Geng, Q. B. Gou, H. W. Guo, H. H. He, M. He, K. Hibino, N. Hotta, Haibing Hu, H. B. Hu, J. Huang, Q. Huang, H. Y. Jia, L. Jiang, F. Kajino, K. Kasahara, Y. Katayose, C. Kato, K. Kawata, Labaciren, G. M. Le, A. F. Li, H. C. Li, J. Y. Li, C. Liu, Y.-Q. Lou, H. Lu, X. R. Meng, K. Mizutani, J. Mu, K. Munakata, H. Nanjo, M. Nishizawa, M. Ohnishi, I. Ohta, S. Ozawa, T. Saito, T. Y. Saito, M. Sakata, T. K. Sako, M. Shibata, A. Shiomi, T. Shirai, H. Sugimoto, M. Takita, Y. H. Tan, N. Tateyama, S. Torii, H. Tsuchiya, S. Udo, B. Wang, H. Wang, Y. Wang, Y. G. Wang, H. R. Wu, L. Xue, Y. Yamamoto, C. T. Yan, X. C. Yang, S. Yasue, Z. H. Ye, G. C. Yu, A. F. Yuan, T. Yuda, H. M. Zhang, J. L. Zhang, N. J. Zhang, X. Y. Zhang, Y. Zhang, Yi Zhang, Ying Zhang, Zhaxisangzhu, and X. X. Zhou (The Tibet ASγ Collaboration)

M. Amenomori · H. Nanjo Department of Physics, Hirosaki University, Hirosaki 036-8561, Japan X. J. Bi · L. K. Ding · C. Fan · Zhaoyang Feng · Q. B. Gou · H. H. He · H. B. Hu · J. Huang · L. Jiang · H. C. Li · C. Liu · H. Lu · Y. H. Tan · B. Wang · H. Wang · Y. Wang · H. R. Wu · H. M. Zhang · J. L. Zhang · Y. Zhang · Yi Zhang · Ying Zhang Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China D. Chen · K. Kawata (e-mail: [email protected]) · M. Ohnishi · M. Takita Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582, Japan S. W. Cui · H. C. Li Department of Physics, Hebei Normal University, Shijiazhuang 050016, China Danzengluobu · X. H. Ding · H. W. Guo · Haibing Hu · Labaciren · X. R. Meng · A. F. Yuan · Zhaxisangzhu Department of Mathematics and Physics, Tibet University, Lhasa 850000, China C. Fan · C. F. Feng · M. He · A. F. Li · J. Y. Li · Y. G. Wang · L. Xue · N. J. Zhang · X. Y. Zhang Department of Physics, Shandong University, Jinan 250100, China Z. Y. Feng · Q. Huang · H. Y. Jia · G. C. Yu · Ying Zhang · X. X. Zhou Institute of Modern Physics, SouthWest Jiaotong University, Chengdu 610031, China X. Y. Gao · Q. X. Geng · L. Jiang · J. Mu · X. C. Yang Department of Physics, Yunnan University, Kunming 650091, China K. Hibino · T. Shirai · N. Tateyama · S. Udo · T. Yuda Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Japan N. Hotta Faculty of Education, Utsunomiya University, Utsunomiya 321-8505, Japan N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_40, © Springer-Verlag Berlin Heidelberg 2011

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Abstract We search for steady TeV γ-rays from 18 pulsars in the Fermi-LAT pulsar catalog using the Tibet air shower array. We observe 8 sources including the Crab against expected 0.41 sources at a significance of 2σ or more among the 18 pulsars. The chance probability from Poisson statistics is estimated to be 1.4×10−8. With the Crab excluded, it is estimated to be 1.8×10−7. These low chance probabilities clearly show that the Fermi pulsars have a statistically significant correlation with TeV γ-ray excesses observed by the Tibet air shower array. F. Kajino · M. Sakata · Y. Yamamoto Department of Physics, Konan University, Kobe 658-8501, Japan K. Kasahara · K. Mizutani · S. Ozawa · S. Torii Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan Y. Katayose · T. K. Sako · M. Shibata Faculty of Engineering, Yokohama National University, Yokohama 240-8501, Japan C. Kato · K. Munakata Department of Physics, Shinshu University, Matsumoto 390-8621, Japan G. M. Le National Center for Space Weather, China Meteorological Administration, Beijing 100081, China Y.-Q. Lou Physics Department and Tsinghua Center for Astrophysics, Tsinghua University, Beijing 100084, China K. Mizutani Saitama University, Saitama 338-8570, Japan M. Nishizawa National Institute of Informatics, Tokyo 101-8430, Japan I. Ohta Sakushin Gakuin University, Utsunomiya 321-3295, Japan T. Saito Tokyo Metropolitan College of Industrial Technology, Tokyo 116-8523, Japan T. Y. Saito Max-Planck-Institut für Physik, München D-80805, Deutschland A. Shiomi College of Industrial Technology, Nihon University, Narashino 275-8576, Japan H. Sugimoto Shonan Institute of Technology, Fujisawa 251-8511, Japan H. Tsuchiya RIKEN, Wako 351-0198, Japan C. T. Yan Institute of Disaster Prevention Science and Technology, Yanjiao 065201, China S. Yasue School of General Education, Shinshu University, Matsumoto 390-8621, Japan Z. H. Ye Center of Space Science and Application Research, Chinese Academy of Sciences, Beijing 100080, China

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1 Introduction The Tibet air shower (AS) array has been successfully operated at Yangbajing (4,300 m above sea level) in Tibet, China. The array consists of 533 plastic scintillation detectors of 0.5 m2 placed at grid point 7.5 m apart, and its coverage area is approximately 22,050 m2 [1]. We have successfully observed TeV γ-ray sources, such as the Crab Nebula [2, 3], Mrk 501 [4], and Mrk 421 [1] using the Tibet AS array. The advantage of this technique is that it enables us to operate 24 hours every day, regardless of weather, and to observe almost half of the celestial sphere with a higher energy threshold, compared with the Cherenkov telescopes. In earlier research, the Milagro experiment observed many γ-ray sources in the Fermi bright source list at 35 TeV [5]. The Tibet AS array also found statistically significant correlation between the Fermi bright sources and TeV γ-ray excesses at 3 TeV [6]. Besides, all excesses are associated with pulsars. Recently, the number of γ-ray pulsars increases by the first pulsar catalog of the Fermi Large Area Telescope (LAT) [7]. In this paper, we survey on steady TeV γ-rays from 18 Fermi pulsars in this catalog within our field of view (FOV) using the Tibet AS array.

2 Results & Discussion The Tibet AS array observation of the 18 Fermi pulsars within our FOV is summarized in Table 1. We found no significant excess of TeV γ-rays from individual sources except for the Crab. Subsequently, the distribution of the observed significance is examined for statistical consistency with the normal Gaussian. Figure 2 (a) shows the significance distribution of the 18 Fermi pulsars observed by the Tibet AS array. One can see that this distribution obviously deviates from the normal Gaussian. On the other hand, Figure 2 (b) shows the significance distribution of dummy sources randomly selected from our FOV. This is consistent with the normal Gaussian. It should be emphasized that we observe 8 sources at a significance of 2σ or more in this distribution, against an expected 0.41 sources (upper probability of 2σ multiplied by 18 sources) from the normal Gaussian. The chance probability from Poisson statistics is estimated to be 1.4×10−8. With the Crab excluded, it is estimated to be 1.8×10−7. These low chance probabilities clearly show that the Fermi pulsars have statistically significant correlations with the TeV excesses. These might be bright and extended TeV pulsar wind nebulae [6]. Acknowledgements The collaborative experiment of the Tibet Air Shower Arrays has been performed under the auspices of the Ministry of Science and Technology of China and the Ministry of Foreign Affairs of Japan. This work was supported in part by a Grant-in-Aid for Scientific Research on Priority Areas from the Ministry of Education, Culture, Sports, Science and Technology, by Grants-in-Aid for Science Research from the Japan Society for the Promotion of Science (JSPS) in Japan, and by the Grants from the National Natural Science Foundation of China, the Chinese Academy of Sciences, and the Ministry of Education of China. K. Kawata is supported by Grant-in-Aid for JSPS Fellows 21·9437.

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Table 1 Summary of the Tibet-III array survey on the direction of Fermi pulsars Pulsar Name

Period γ-ray Tibet-III Pulsar [ms] selecteda Sig. [σ] Name

J0030+0451 J0218+4232 J0357+32 J0534+2200(Crab) J0631+1036 J0633+0632 J0633+1746(Geminga) J0659+1414 J0751+1807 a

4.9 2.3 444 33.1 288 297 237 385 3.5

1.6 -0.2 -1.2 7.1 -0.0 2.4 2.3 0.7 1.3

Yes Yes Yes

J1836+5925 J1907+06 J1952+3252 J1958+2846 J2021+3651 J2021+4026 J2032+4127 J2043+2740 J2238+59

Period γ-ray Tibet-III [ms] selecteda Sig. [σ] 173 107 39.5 290 104 265 143 96.1 163

Yes Yes

-0.3 2.6 -0.2 0.1 2.2 2.2 2.9 -0.1 2.4

Yes Yes Yes Yes

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Fig. 1 Histograms show significance distribution observed by the Tibet-III array. (a): In the case of 18 Fermi pulsar directions. The dashed curve is the expected normal Gaussian. (b): In the case of ∼2000 dummy sources randomly selected from the FOV of the Tibet AS array. The solid curve is the fitted curve by the normal Gaussian

References 1. Amenomori, M., et al.: Multi-TeV gamma-ray flares from Markarian 421 in 2000 and 2001 observed with the Tibet air shower array. Astrophys. J. 598, 242–249 (2003) 2. Amenomori, M., et al.: Observation of multi-TeV gamma rays from the Crab Nebula using the Tibet air shower array. Astrophys. J. 525, L93–L96 (1999) 3. Amenomori, M., et al.: Multi-TeV gamma-ray observation from the Crab Nebula using the Tibet-III air shower array finely tuned by the cosmic-ray Moon’s shadow. Astrophys. J. 692, 61–72 (2009) 4. Amenomori, M., et al.: Detection of multi-TeV gamma rays from Markarian 501 during an unforeseen flaring state in 1997 with the Tibet air shower array. Astrophys. J. 532, 302–307 (2000) 5. Abdo, A.A., et al.: Milagro observations of multi-TeV emission from Galactic sources in the Fermi bright source list. Astrophys. J. 700, L127–L131 (2009) 6. Amenomori, M., et al.: Observation of TeV gamma rays from the Fermi bright galactic sources with the Tibet air shower array. Astrophys. J. 709, L6–L10 (2010)

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7. Abdo, A.A., et al.: The first Fermi Large Area Telescope catalog of gamma-ray pulsars. Astrophys. J. Supplement 187, 460–494 (2010)

Fermi results on γ-ray binaries Adam B. Hill, Richard Dubois, and Diego F Torres for the Fermi-LAT collaboration

Abstract The past decade has presented a revolution in the field of observational high energy γ-ray astrophysics with the advent of a new generation in ground-based TeV telescopes and subsequent GeV space telescopes. The Fermi Large Area Telescope (LAT) was launched in August 2008 and has offered unprecedented sensitivity and survey capabilities in the 30 MeV - 300 GeV energy range. Presented here are the results from the first two years of LAT observations of galactic binary systems including the definitive detections of LS I +61◦ 303, LS 5039 and Cyg X-3. These sources and others are discussed in context with their known TeV and X-ray properties. The LAT data provides new understandings and pose new questions about the nature of these objects. The identification of an exponential cutoff in the spectra of both LS I +61◦ 303 and LS 5039 was unexpected and poses challenges for explaining the emission mechanisms and processes which are in operation within these systems.

A. B. Hill Université Joseph Fourier, LAOG, UMR 5571, BP 53, 38041 Grenoble Cedex 09, France e-mail: [email protected] R. Dubois W. W. Hansen Experimental Physics Laboratory, KIPAC, Department of Physics and SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94305, USA e-mail: [email protected] D. F. Torres Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_41, © Springer-Verlag Berlin Heidelberg 2011

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1 Introduction To date there are only five X-ray binaries that have reported detections of high energy (HE; 0.1-100 GeV) or very high energy (VHE; >100 GeV) γ-ray emission: LS I +61◦ 303 [13, 1]; LS 5039 [8, 2]; PSR B1259−63 [2]; Cyg X-3 [15, 3]; Cyg X-1 [12, 34]. Whilst there were theoretical predictions that these systems may be capable of emitting such high energy radiation and some reports of high energy sources that may be associated with some of the above systems the first definitive detections and identifications have only occurred within the past five years due to the current generation of sensitive HE and VHE telescope facilities. PSR B1259−63 was long known to be the only millisecond pulsar in orbit around a main-sequence star. It was a known hard X-ray source and was predicted to produce γ-rays through the interaction of the pulsar wind with the disk of the Be companion; VHE radiation was discovered by the H.E.S.S. experiment [2] confirming this theoretical prediction. LS I +61◦ 303 and LS 5039 are both persistent, well known X-ray binaries which were spatially consistent with HE sources detected by the Energetic Gamma-Ray Experiment (EGRET) in the 1990s [25], however the lack of detection of periodic flux modulation and the size of the error box meant it was impossible to definitively claim a detection of γ-rays from these sources. This all changed with first the detection of these sources at VHE by the MAGIC, VERITAS and H.E.S.S. Cherenkov radiation telescopes and subsequently the detections at HE by the Fermi Gamma-Ray Space Telescope. Cyg X-1 and Cyg X-3 are examples of microquasars, accreting black holes or neutron stars in binary systems which have associated relativistic jets. A key tool for identifying binary systems is their orbital modulation, due to the regular pattern of emission as the orbit is traversed. Typically the zero phase of the orbit may be assigned from radio data, the time of periastron or some other marker, but is arbitrary. Until 2009, there had been no unambiguous detection of γ-ray emission from a microquasar system. The identification became conclusive with the confirmation of modulation at the orbital period. We present here the latest results on the HE and VHE γ-ray emission from this population of sources, with an emphasis on the results and discoveries from the Fermi-LAT.

2 LS I +61 303 2.1 The original discovery, and further TeV observations: flux, spectrum, periodicity The very-high energy (VHE) spectrum derived from MAGIC data between 200 GeV and 4 TeV at orbital phases between 0.4 and 0.7 was fitted by a power law function: F γ = (2.7 ± 0.4 ± 0.8) × 10−12(E/TeV)−2.6±0.2±0.2 cm−2 s−1 TeV−1 , with the

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errors quoted being statistical and systematic, respectively [13]. All further reports of LS I +61◦303 at very-high energies would produce compatible spectra with this measurement, within errors. These first MAGIC measurements showed that the very-high energy γ-ray emission from LS I +61 303 was variable. The maximum flux corresponded to about 16% of that of the Crab Nebula, and was detected around phase 0.6 with a significance of 8.7σ. The source is no longer detected near periastron and only upper limits were therein imposed. The VERITAS array carried out independent observations and soon confirmed these results [1]. These early MAGIC/VERITAS observations occured at a number of different orbital phases but the source was only ever detected at similar phases; this hinted at a periodic nature of the emission. Further MAGIC observations showed that this emission is indeed periodic [4], with the system showing regular outbursts at TeV energies in phases around 0.65 and no significant signal elsewhere. The periodicity was tested using the LombScargle perodogram both on a set of OFF data and on the source of choice. Whereas the former produced no periodicity, the periodogram analysis of the latter did. The maximum peak in the periodogram is seen at frequency ν = 0.0373d−1 which had a post-trial chance probability of 2 × 10−7 . Other peaks (although less significant) were seen in the signal analysis and not seen in the background sample. When folding the data with the frequency obtained, the data did not seem at first sight to be described by a simple sinusoidal shape (in part, perhaps due to spacing and quality). In fact, fitting a sine function and subtracting it from the power analysis removes the peak related to the orbital period but not the others, something that is improved when a sine plus a gaussian function is fitted to the data, and subsequently subtracted from the analysis. Thus, whereas further MAGIC observations succeeded in bracketing the periodicity of LS I +61◦ 303 in TeV γ-rays to be very close to the orbital period (26.8±0.2) days, as well as to other wavelength estimates (e.g., at 1.5σ from the best estimate, coming from radio of 26.4960±0.0028 days [23]), with the error determined by Monte-Carlo simulations, they also reveal a new mystery for the flux evolution of LS I +61◦ 303 at these energies. Is there an average (sinusoidal) emission along the orbit, plus an extra component associated with the turn on of a different process (the Gaussian) that only appears at the TeV maximum phase range?

2.2 TeV and X-ray simultaneous observations The first strictly simultaneous observations at TeV and X-rays of LS I +61◦ 303 have been recently presented by the MAGIC collaboration [28]. Using observations by XMM-Newton, Swift, and MAGIC during 60% of an orbit, it was found that there is a correlation between the X-ray and TeV emission at the time of the TeV maximum. A linear fit to the six MAGIC/XMM-Newton pairs of observations that trace the outburst yielded a correlation coefficient of r = 0.97. A linear fit to all ten simultaneous pairs (including Swift data) provides a high correlation coefficient of −3 to be produced from inder = 0.81+0.06 −0.21 (which has a probability of about 5 × 10

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pendent X-ray and TeV fluxes). Due to strong variability of the X-ray emission of LS I +61◦ 303, of about 25% in hour scales, other previous campaigns with contemporaneous, but not strictly simultaneous data, as for instance the previous MAGIC campaign [11]. 2008, or the VERITAS campaign [5] come short in reaching such a result, which, nevertheless, would not suffer from adding further statistics and confirmation. Therefore, the X-ray/TeV correlation found for LS I +61◦303 points to emitting processes happening at the same time in both wavelengths, and being the result of the same physical population of particles; especially, since at the TeV maximum one would not expect the TeV photons to be subject to significant absorption due to gamma-gamma processes.

2.3 The Fermi results on LS I +61◦ 303 With the launch of the Fermi Gamma-ray Space Telescope on 11 June 2008 and the beginning of operations in its survey mode [14], coverage of the full sky above 100 MeV is available through its main instrument, the Large Area Telescope (LAT). There are two main results to extract out of the Fermi observations of LS I +61◦303 using the data collected in the first 9 months after launch [1]: 1. The unambiguous detection of a source co-located with the position of LS I +61◦ 303 which is seen to be periodic (too) at GeV energies (the first such periodicity ever detected) and anti-correlated with the TeV emission. 2. The discovery of a cutoff in the spectrum of the Fermi (GeV) source. LS I +61◦ 303 is detected at significance of ∼70σ at a position consistent with the optical location of the source. The LAT light curve was constructed using aperture photometry of 100 MeV – 20 GeV events. From a 3.2 hour binned light curve the weighted Lomb-Scargle periodogram [20] was calculated. The periodogram exhibits a clear peak at 26.6 ± 0.5 days (1σ errors obtained though Monte-Carlo) consistent with the known orbital period. The binned LAT light curve folded on the nominal orbital period [23] with the usual zero phase at MJD 43, 366.2749 [24] shows a large modulation amplitude with maximum flux occurring slightly after periastron passage (where there is no TeV emission detected, neither by MAGIC nor by VERITAS). The folded light curve and the Lomb-Scargle periodogram are shown in Figure 1. The overall light curve can be reasonably well fit by a simple sine wave. Fitting a sine wave to each of the individual 9 orbits observed finds that the best fit amplitude varies between 6.8±0.9 and 2.2±0.9 ×10−7 photons cm−2 s−1 [1], which might be indicative of some orbit-to-orbit variability. The LAT data was well fit by a power-law plus exponential cutoff returns; the chance probability that a simple power-law was incorrectly rejected is 1.1×10−9. The photon index was found to be Γ =2.21 ± 0.04 (stat) ± 0.06 (syst); the flux above 100 MeV is (0.82 ± 0.03 (stat) ± 0.07 (syst)) ×10−6 photons cm−2 s−1 and the cutoff energy is 6.3 ± 1.1 (stat) ± 0.4 (syst) GeV. Reduced statistics in a phasebin of 0.1 of the orbit precluded us from finding a statistically significant cutoff in


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Fig. 1 The power spectrum (left) and phase folded light curve (right) of LS I +61◦ 303 at 100 MeV – 20 GeV. Left: The weighted Lomb-Scargle periodogram of the LAT light curve. The vertical dashed line indicates the known orbital period [23]; the horizontal dashed lines indicate the marked significance levels. Right: The phase folded 100 MeV – 20 GeV light curve of LS I +61◦ 303. The dashed lines indicate periastron and apastron of the system.

each of the bins, and so a simple power law was fitted. No significant variation of this photon index with phase was found. During part of the Fermi measurements, there was a VERITAS campaign [27] observing at higher energies (100 GeV – 30 TeV), and no detection was found even when part of the TeV maximum phase region was covered. The lack of strong emission from LS I +61◦ 303 during these observations is at face value somewhat surprising, especially if one looks at the light curve in the orbit where all are upper limits, but does not contradict (yet) previous measurements. The TeV maximum has happened around phase 0.6 with excursions down and up in phases of about 0.2 of the orbit. The apastron coverage during this campaign was limited, with large data gaps, e.g., the coverage between phases 0.72 and 0.82 consists of only 40 minutes. Consequently the low statistics of the VERITAS measurements during this campaign do not allow firm conclusions to be drawn regarding the disappearance of the signal or on its deviation from the usual periodic behavior. It is clear, however, that any future ground-based LS I +61◦303 campaign will benefit from automatic Fermi coverage. At the same time, a strictly periodic behavior would be easy to rule out by subsequent MAGIC/VERITAS observations of the TeV maximum, and the problem of understanding the origin of the γ-ray emission would be even more complex if this were so.

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Fig. 2 High and very-high energy spectral data points of LS I +61◦ 303 (left) and LS 5039 (right). Left: Fermi data points are red; MAGIC data are blue (high state phases 0.5-0.7); VERITAS data are black (0.5-0.8). Right: The red data points show the spectrum at inferior conjunction (TeV maximum, GeV minimum, phases 0.45–0.9; the blue data points show the spectrum at superior conjunction (TeV minimum, GeV maximum, phases < 0.45 and > 0.9). Higher energy data come from H.E.S.S. Note that the data from the different telescopes are not contemporaneous, though they do cover multiple orbital periods.

3 LS 5039 3.1 The original discovery, and further TeV observations: flux, spectrum, periodicity LS 5039 was discovered by the H.E.S.S. experiment to be a γ-ray source[8] and soon afterwards, periodicity in the TeV γ-ray flux, consistent with the known orbital period [18], was also reported [3]. Unlike LS I +61◦303 H.E.S.S. observations of LS 5039 have detected this source at all orbital phases observed. The authors of [3] define two broad phase intervals, the inferior conjunction (0.45 < ϕ < 0.9) and superior conjunction ( ϕ > 0.9 and ϕ < 0.45), for which different (averaged) H.E.S.S. spectra were produced. The differential photon energy spectrum (0.2 to 10.0 TeV) for inferior conjunction is consistent with a hard power-law with an exponential cutoff, where the slope is Γ = 1.85±0.06 (stat) ± 0.1 (syst) and the exponential cutoff energy is at E 0 = 8.7 ± 2.0 TeV (for the fitted function dN/dE ∼ E Γ exp(−E/E 0 )). In contrast, the spectrum for superior conjunction is consistent with a relatively steeper (Γ = 2.53 ± 0.07 (stat) ± 0.1 (syst)) pure power-law (0.2 to 10 TeV). The statistics collected along the orbit actually allowed to find that the parameters of power-law fits to the γ-ray data obtained in 0.1 phase binning already displayed significant variability. Because of low statistics, and presumably too, of different statistics at the higher end of the spectrum in each of these bins, more complicated functions such as a power-law with exponential cutoff provided no better fit than that of a pure power-law. These results, together with the H.E.S.S. light curve and averaged spectra are shown below, where we make a comparison with various models.


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3.2 The Fermi results on LS 5039 The dataset for the analysis reported by Fermi spanned the period from 4 August 2008, through 29 April 2009, and thus covered multiple orbits of the system [2]. Like LS I +61◦303 this system is also found to be periodic in GeV γ-rays (3.903±0.005 days) and anti-correlated with the TeV emission. The periodicity is thus also consistent with the orbital period. The SED also presents a cutoff at a few GeV and is well fitted by a similar function: E −Γ exp(−E/Ecutoff ), with the photon index being Γ = 1.9± 0.1(stat) ± 0.3 (syst); a 100 MeV–300 GeV flux of (4.9 ± 0.5 (stat) ± 1.8 (syst)) ×10−7 photons cm−2 s−1 , and a cutoff energy at 2.1 ± 0.3 (stat) ± 1.1 (syst) GeV. The energy spectra of both LS 5039 and LS I +61◦303 are shown in Figure 1. Fermi observations were able to further separate into superior and inferior parts of the orbit, in phase ranges as defined by H.E.S.S.: GeV observations also pinpoint this (GeV / TeV – anti-correlated) flux variability. The fact that H.E.S.S. did not find long-term variability makes it reasonable to directly compare non-simultaneous H.E.S.S. and Fermi observations. Using the same phase intervals, the inferior conjunction slope was found to be Γ = 2.25 ± 0.11 with no exponential cutoff energy required to provide a better fit; whereas at superior conjunction, a Γ = 1.91 ± 0.16 with a cutoff energy of 1.9 ± 0.5 GeV was found. The spectral shape in Fermi is softer around periastron (near superior conjunction) and is harder around apastron as shown in Figure 3.

4 Cygnus X-3 4.1 Historical observations at high energies Cyg X-3 is a well known, powerful high-mass X-ray binary with a short orbital period of 4.8 hours [15]. The system comprises of a compact object, the nature of which is still subject to debate, accreting matter from a Wolf-Rayet companion star [36]. The source was discovered in 1966 and has been widely observed across the electromagnetic spectrum. It regularly becomes the brightest radio source amongst the known binary systems with large flares attributed to its relativistic jets. Emission had been detected up to ∼300 keV whilst the system shows a complex X-ray spectrum which transitions between two main states; ‘soft’ and ‘hard’, the source is known to flare in radio when entering the ‘soft’ state with associated relativistic plasma ejection events [22]. Historically there were reported detections at MeV–PeV energies in the 1970s and 1980s. These observations came from 30 MeV – 5 GeV sensitive balloon and satellite borne experiments such as SAS-2 and COS-B, from atmospheric Cherenkov experiments at 0.1–500 TeV and extensive air shower experiments at 0.1–10 PeV [15]. However, the detections were typically of low significance and although some experiments claimed detections, others could not confirm them. These

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Fig. 3 Fermi average phase folded light curves for LS 5039. Top: 0.1–10 GeV flux variations with orbital phase. Bottom: Changes in the hardness ratio, flux(1–100 GeV)/flux(0.1–1 GeV), across the orbit.

detections remained doubtful when the next generation of more sensitive ground based telescopes failed to confirm the TeV and PeV detection of Cyg X-3 [33, 16] and the CGRO-EGRET failed to detect any GeV emission [32]. Hence, claims of HE and VHE emission from this microquasar were controversial and highly contested.

4.2 The Fermi results on Cygnus X-3 The analysis of Fermi-LAT observations of Cyg X-3 [3] spans data taken from 4 August 2008 to 2 September 2009. The Cygnus region is challenging to analyze due to the high levels of diffuse emission combined with the presence of 3 bright γ-ray pulsars [4]: PSR J2021+4026; PSR J2021+3651; PSR J2032+4127. In fact, PSR J2032+4127, lies very close to the location of Cyg X-3 (∼30′ ) and contributes significantly to the large number of photons detected by the LAT at the location of Cyg X-3. The impact of this pulsar was minimized by only using photons which


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Fig. 4 Gamma-ray light curves of two of the flaring events observed by Fermi. The LAT fluxes > 100 MeV (filled circles) are calculated from a likelihood analysis of 4-day long segments of data; a power-law with index of 2.7 is assumed in the analysis. The vertical dashed lines indicate the periods the LAT detects flaring activity. In the top of each panel the 15 GHz radio flux as measured by the AMI and OVRO 40-m radio telescopes is presented; an offset of 0.124 Jy has been removed from the OVRO data to compensate for the effect of extended nearby sources that are resolved by the AMI interferometer. It is clear that a number of radio flares are detected coincident with the γ-ray activity detected by the LAT.

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arrive during the off-pulse phase. This preserves approximately 80% of the live time and produces a significantly cleaner data set. The LAT data yield a detection of a point source at the level of 29σ at a location consistent with that of Cyg X-3. The 4-day binned γ-ray light curve of the source flux >100 MeV (sections of which are shown in Figure 4) clearly indicates that the source is highly variable. The LAT detects Cyg X-3 during two specific active periods: 11 October to 20 December 2009 (MJD 54750–54820); 8 June to 2 August 2009 (MJD 54990–55045). These active phases comprises one or more flares with a peak flux of up to ∼2 × 10−6 photons cm−2 s−1 above 100 MeV. The average spectrum over the two active periods is represented by a single power-law model with a spectral index Γ = 2.70 ± 0.05 (stat) ± 0.20 (syst) and an average flux above 100 MeV of [4.0 ± 0.3 (stat) ± 1.3 (syst)] × 10−10 erg cm−2 s−1 . Assuming a distance of 7 kpc this gives a luminosity, Lγ ∼ 3 × 1036 erg s−1 , comparable to what was reported by SAS-2 [29]. The AGILE mission also reported detecting γ-ray activity coincident with the location of Cyg X-3 during these epochs as well as activity from 16-17 April 2008 (MJD 54572–54573), prior to the launch of Fermi [35]. The AGILE team report a 5.5σ detection with a comparable average flaring flux to that reported by the Fermi-LAT. The association of the γ-ray flaring source was definitively confirmed though the detection of the 4.8 hour orbital period in a finely binned (1000s) aperture photometry light curve. The periodicity was found using the Lomb-Scargle periodogram and weighting the input flux data points by their relative exposure. No orbital periodicity is evident when using the entire data set, however restricting the data set to the periods of LAT detected enhanced emission discussed above yields a strong detection with a nominal false detection probability of 3.6×10−5. Comparing the folded 0.1-100 GeV light curve with the 1.5–12 keV X-ray light curve taken from RXTE/ASM data shows that both have the same asymmetric shape with a slow rise and faster decay. However, the LAT minimum trails the X-ray minimum by 0.3–0.4 in phase. The relationship between the γ-ray and radio emission was confirmed through a discrete cross-correlation analysis which indicated a positive correlation between the two wavebands with a significance of > 3σ. The lag of the radio light curve to the γ-rays is not well constrained and is estimated to be 5 ± 7 days. This specifically links the γ-ray activity to periods of relativistic ejection events. The LAT flux is compatible with extrapolations of the hard X-ray tail observed above 30 keV, reportedly up to several 100 keV [26], in instances of the ‘ultrasoft’ state. In this case the Fermi emission could be explained by inverse Compton scattering of UV photons from the WR star off of high energy electrons. However this scenario requires that the emission region is not too close to the accretion disk otherwise the γ-ray emission will be absorbed through pair production on soft X-ray photons coming from the disk. If inverse Compton scattering is the dominant γ-ray production method then it is expected that the peak in the γ-rays would correspond to the time of superior conjunction when the electrons are seen behind the WR star and hence the energetic electrons directed towards the Earth undergo head-on collisions with the stellar UV


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Fig. 5 Left: The Fermi power spectrum using only the data during the periods of enhanced emission (top) and for the entire LAT data set (bottom). The vertical arrows indicate the frequencies of the orbital period and the second harmonic. Right: The average orbital phase folded light curve of the LAT data during the periods of enhanced emission (top) and of the RXTE ASM X-ray data taking during the RXTE mission lifetime. Phase zero is set to be at the point of superior conjunction.

photons. This would correspond to the X-ray minimum assuming the X-ray modulation is produced through Compton scattering in the WR wind which is approximately what is observed in the average folded light curves. A proposed model to explain the observed behavior of Cyg X-3 at high energies is that of a jet launched around a black hole oriented not too far from the line of sight, which interacts with the WR stellar wind to produce a shock at a distance of 1-10 times the orbital separation from the system [21]. This shock is the location where electrons are accelerated to GeV energies and upscatter star photons.

5 Cygnus X-1 Cyg X-1 is an exceptionally bright, well studied high-mass X-ray binary and is believed to host a stellar mass black hole. It is located at a distance of ∼2.2 kpc and comprises of a O9.7 Iab donor star in a 5.6 day orbit with the compact object [37]. Cyg X-1 is another example of a microquasar, it is believed to be principally powered by accretion and is seen to transition between ‘soft’ and ‘hard’ X-ray spectral states. The radio emission is observed to be relatively stable during the ‘hard’ state except for rarely observed radio flares [22] and is undetected in the ‘soft’ state.

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5.1 Reports of high energy and very high energy emission Between June and November 2006 the MAGIC telescope observed Cyg X-1 for a total of 46.2 hours. The MAGIC team searched the entire data set and found no significant persistent VHE γ-ray source at the location of Cyg X-1 and reported a 95% flux upper limit in the 150 GeV – 3 TeV band of the order of 1–5% of the Crab [12]. Searching for faster time-varying signals within any given night resulted in the detection an excess of 4.9σ (4.1σ after correcting for trials) resulting from 79 minutes of effective on-time on September 24 2006 UTC 22:17 – 23:41. The observed excess is reported to be consistent with a point source at the location of Cyg X-1 and excludes a nearby radio nebula. The spectrum was fitted by a power law function: Fγ = (2.3 ± 0.6) × 10−12(E/TeV)−3.2±0.6 cm−2 s−1 TeV−1 , with the errors quoted being statistical only; the systematic uncertainty is estimated to be 35% on the overall flux normalization and 0.2 in the determination of the spectral index [12]. The TeV flare was coincident with a hard X-ray flare detected by INTEGRAL, Swift-BAT and RXTE-ASM. The TeV detection was observed at the rising edge of the first hard X-ray peak and the MAGIC non-detection the following night coincided with the decay of the second hard X-ray peak and hypothesize that the hard X-ray and γ-rays may be produced in regions linked by the collimated jet [12]; these processes would have different physical timescales explaining the shift in time between the TeV and X-ray peaks. Recently the AGILE satellite has reported the detection of transient γ-ray activity from Cyg X-1 above 100 MeV [34]. They used ∼315 days of data from July 2007 – mid October 2009 giving a net exposure of ∼13 Ms. Performing a likelihood analysis over the entire integrated dataset does not yield a significant detection of Cyg X-1 and places a 2σ upper limit on the γ-ray flux (0.1–3 GeV) of 3× 10−8 photons cm−2 s−1 . The AGILE team searched for variability on day timescales and reported a single flaring episode corresponding to 15 October 2009 UTC 23:13:36 – 16 October 2009 UTC 23:02:24, with a 5.3σ pre-trial (4σ post-trial) significance level. The location of the flare is consistent with the location of Cyg X-1 and corresponds to a 0.1–3 GeV γ-ray flux of (2.32 ± 0.66) × 10−6 photons cm−2 s−1 . At the time of the flare Cyg X-1 was in the ‘hard’ X-ray spectral state, however, unlike the instance of the MAGIC flaring event there was no simultaneous flare seen in the X-ray (or any other) waveband. In March 2010 the AGILE team reported new transient activity in the Cygnus region which was compatible with the Cyg X-1 location [17]. They reported a 5σ detection integrating from 24 March 2010 UTC 02:24 to 25 March 2010 UTC 01:01 with a corresponding flux above 100 MeV of (2.0 ± 0.9) × 10−6 photons cm−2 s−1 . A search of the Fermi-LAT data for signs of the October 2009 flare yielded no significant detection. Extracting data from the exact period reported by AGILE the LAT places a 95% upper limit on the γ-ray flux (0.1–3 GeV) of ∼4× 10−7 photons cm−2 s−1 (assuming a power-law spectral shape with photon index, Γ=2.2) [30]. Similarly the LAT did not detect any flaring emission during March 2010.


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6 Conclusion The first couple of years of Fermi-LAT operations have been highly fruitful in expanding our understanding of the high energy γ-ray emission properties of Galactic γ-ray binaries. In fact the availability of sensitive telescopes spanning the MeV–TeV energy range in the past decade have opened up this entire field of study and the LAT is the latest instrument to add to and expand this field of study. Gamma-ray binaries have now been definitively detected in the GeV energy range; both LS I +61◦ 303 and LS 5039 are strong detections which have been identified through their spatial location and the clear signs of orbital modulation in the LAT observed flux. The orbital modulation of the GeV flux was found to be anticorrelated with the modulation observed at TeV energies with the GeV flux peaking around periastron in both cases. The identification of an exponential cut-off powerlaw shape to the spectrum of both sources was not expected. It has been noted that the spectral shape observed in both γ-ray binaries is reminiscent of that seen in the large family of γ-ray pulsars now detected by the LAT [2] (i.e. a hard power-law spectrum with an exponential cutoff at ∼2.5 GeV). It has been proposed that this may indicate that the emission in the Fermi energy range from both LS I +61◦303 and LS 5039 may therefore be magnetospheric in origin, however, this raises a new problem as it is not clear how such emission would be modulated by the orbital period of the binary. A clear indication of magnetospheric emission would come from the detection of pulsations in the Fermi emission of these sources whilst simultaneously confirming for the first time the nature of the compact object. PSR B1259−63 is the only known millisecond pulsar in a binary system with a main-sequence star. It has been detected at TeV energies by H.E.S.S. [2] during periastron passages of its 3.4 year orbital period. Fermi has yet to report any detection of pulsed magnetospheric emission from this source however, the upcoming periastron passage in December 2010 will offer the first opportunity for Fermi to observe the expected GeV emission resulting from the pulsar wind interacting with the stellar wind of the companion. Observations of this periastron passage will provide a key dataset to compare and contrast with those of the persistent γ-ray binaries in which the nature of the compact object is still unknown. The detection of transient γ-ray activity from Cyg X-3 by both Fermi and AGILE during multiple epochs of soft-state transitions has confirmed this microquasar as a source of high energy emission. Furthermore, it has been seen that the γ-ray emission is correlated with radio flare events. The clear signature of orbital flux modulation detected by the LAT removes any doubt that Cyg X-3 is the source of the emission whilst also suggesting that the emitting region is likely bounded by the orbital separation of the system. The recent reports by AGILE of γ-ray activity from another microquasar, Cyg X-1, have not been confirmed by Fermi. The potential to discover flaring events from this source and other microquasars remains a real possibility through future observations with the LAT. Indeed with the upcoming periastron passage of PSR B1259−63, the detection of a symbiotic binary undergoing a nova outburst [19] and

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the ever present possibility of detecting a new γ-ray binary the future is very bright for Fermi-LAT observations of binary systems. Acknowledgements The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat a` l’Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Spanish CSIC and MICINN, the Istituto Nazionale di Astrofisica in Italy and the Centre ´ National d’Etudes Spatiales in France. ABH ackowledges funding by contract ERC-StG-200911 from the European Community.

References 1. 2. 3. 4. 5. 1. 3. 8. 2. 4. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

Abdo A. A., et al., 2009, Astrophys. J., 701, L123 Abdo A. A., et al., 2009, Astrophys. J., 706, L56 Abdo A. A., et al., 2009, Sci., 326, 1512 Abdo A. A., et al., 2010, ApJS, 187, 460 Acciari V. A., et al., 2009, Astrophys. J., 700, 1034 Acciari V. A., et al., 2008, Astrophys. J., 679, 1427 Aharonian F., et al., 2006, Astron. Astrophys., 460, 743 Aharonian F., et al., 2005, Sci., 309, 746 Aharonian F., et al., 2005, Astron. Astrophys., 442, 1 Albert J., et al., 2009, Astrophys. J., 693, 303 Albert J., et al., 2008, Astrophys. J., 684, 1351 Albert J., et al., 2007, Astrophys. J., 665, L51 Albert J., et al., 2006, Sci., 312, 1771 Atwood W. B., et al., 2009, Astrophys. J., 697, 1071 Bonnet-Bidaud J. M., Chardin G., 1988, Phys. Rep., 170, 325 Borione A., et al., 1997, Phys. Rev. D, 55, 1714 Bulgarelli, A., et al., 2010, Astron. Telegr., 2512 http://www.astronomerstelegram.org/?read=2512.Cited25May2010 Casares J., Ribó M., Ribas I., Paredes J. M., Mart´ı J., Herrero A., 2005, Mon. not. R. Astron. Soc., 364, 899 Cheung, C. C., et al., 2010, Astron. Telegr., 2587 http://www.astronomerstelegram.org/?read=2487.Cited25May2010 Corbet R. H. D., Kerr M., 2010, in Proceedings of the 2009 Fermi Symposium., eConf Proceedings C091122, arXiv:1001.4718 Dubus G., Cerutti B., Henri G., 2010, MNRAS, 404, L55 Fender R. P., Stirling A. M., Spencer R. E., Brown I., Pooley G. G., Muxlow T. W. B., MillerJones J. C. A., 2006, Mon. not. R. Astron. Soc., 369, 603 Gregory P. C., 2002, Astrophys. J., 575, 427 Gregory P. C., et al., 1979, Astron. J. , 84, 1030 Hartman R. C., et al., 1999, Astrophys. J., Suppl. Ser., 123, 79


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26. Hjalmarsdotter L., Zdziarski A. A., Szostek A., Hannikainen D. C., 2009, Mon. not. R. Astron. Soc., 392, 251 27. Holder J., for the VERITAS Collaboration, in Proceedings of the 31 st ICRC, Łód´z 2009, arXiv:0907.3921 28. Jogler T., et al., in Proceedings of the 31 st ICRC, Łód´z 2009, arXiv:0907.0992 29. Lamb R. C., Fichtel C. E., Hartman R. C., Kniffen D. A., Thompson D. J., 1977, Astrophys. J., 212, L63 30. the LAT Collaboration, in Fermi Gamma-ray Sky blog, http://fermisky.blogspot.com/2010/03/lat-limit-on-cyg-x-1-during-reported. html.Cited25May2010 31. Miller-Jones J. C. A., Blundell K. M., Rupen M. P., Mioduszewski A. J., Duffy P., Beasley A. J., 2004, Astrophys. J., 600, 368 32. Mori M., et al., 1997, Astrophys. J., 476, 842 33. O’Flaherty K. S., et al., 1992, Astrophys. J., 396, 674 34. Sabatini S., et al., 2010, Astrophys. J., 712, L10 35. Tavani M., et al., 2009, Nat., 462, 620 36. van Kerkwijk M. H., et al., 1992, Nat., 355, 703 37. Ziółkowski J., 2005, Mon. not. R. Astron. Soc., 358, 851

Cherenkov Telescope results on gamma-ray binaries Juan Cortina

Abstract In the past ten years of regular operations, a new generation of Cherenkov telescopes have established binary systems as a new class of Very High Energy γray (VHE) emitters. Particle acceleration in these systems may occur either in an accretion-powered jet (“microquasar”) or in the shock between a pulsar wind and a stellar wind (“wind-wind”). This paper describes the phenomenology of the three VHE binaries PSR B1259-63, LS 5039 and LS I+61◦ 303. Two other objects may belong to this new class: HESS J0632+057 is a point-like variable VHE source whose multiwavelength behaviour resembles that of the other binaries, whereas Cyg X-1 is a well-known accreting system which may have been detected in VHE during a flaring episode. The paper concludes with a review of the latest searches for other binaries with Cherenkov telescopes, with special emphasis on Cyg X-3.

1 Introduction The VHE (or TeV) band covers photon energies in excess of a few tens of GeV and it is mainly studied with ground-based Imaging Atmospheric Cherenkov Telescopes (IACTs). Results presented here mostly refer to the latest generation instruments HESS, MAGIC and VERITAS. A recent review of this young field of astronomy can be found here[1]. High Energy γ-ray (HE) detectors on board satellites such as EGRET, AGILE and Fermi/LAT are sensitive to photon energies from tens to MeV up to tens of GeV and are reviewed elsewhere in this conference[2]. We will not dwell in this paper on the physics interpretation of the observational results, but refer the reader to other contributions to this conference[3, 4, 5, 6, 7, 8] and references within. Let us shortly mention however that theoretical models fall into two possible scenarios for the production of VHE γ-rays in binary systems. In Juan Cortina Institut de Fisica d’Altes Energies (IFAE), Edifici CN, Campus UAB, Cerdanyola del Valles, E08193, Spain, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_42, © Springer-Verlag Berlin Heidelberg 2011

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the “microquasar” scenario, particle acceleration takes place at a jet which originates at an accretion disk. This scaled-down version of an active galactic nucleus may provide significant insights into the mechanism of jet production and particle acceleration since all processes take place at significantly shorter time scales. In the “wind-wind” scenario, particle acceleration happens at the interaction region between a pulsar wind and the wind of the companion star. We will start by describing the VHE results on the three well established γ-ray binaries PSR B1259-63, LS 5039, LS I+61◦303. The compact object in the first system is a pulsar and the VHE emission can be well understood within the wind-wind scenario. The physical interpretation for the other two systems is still controversial. We will then deal with the X-ray binary Cyg X-1, for which the only evidence for VHE emission comes from a short flare marginally detected by MAGIC, and with another object, HESS J0632+057, which is an established source of VHE emission, but whose association to a binary system is still uncertain. We will close the paper with a review of several X-ray binaries which have been actively searched for at VHE energies, but which remain undetected.

2 Detected in VHE: PSR B1259-63, LS 5039 and LS I+61◦ 303 2.1 PSR B1259-63/SS2833 PSR B1259-63/SS2833 was the first binary established at VHE. It was discovered using the HESS telescope array in 2004[9]. The binary system is formed by a 48 ms pulsar and a B2Ve star at a distance of 1.5 kpc (for a summary of the system parameters, see [10]). There is no evidence for jets, so particle acceleration most certainly takes place at a shock between the pulsar wind and the wind of the stellar companion. In fact VHE emission through Inverse Compton of shock-accelerated leptons had been predicted well before the detection[11] and PSR B1259-63/SS2833 had already been classified as a binary system with a plerionic component in [10]. The orbit is highly eccentric (e=0.87) and has a period of 3.4 years. Periastron takes place at a distance of 0.7 A.U., while apastron happens at around 10 A.U. Close to periastron, the pulsar travels through the stars circumstellar disk, which is inclined 10-40◦ to the ecliptic. The radio pulse vanishes from around 15 days before to around 15 days after periastron due to absorption in the disk. The long and eccentric orbit complicates the VHE observations, as the source is only bright in VHE for a few months every 3.4 years and observational constraints further limit the coverage during this period. In fact the source could never be observed in the 2-3 days around periastron. The first HESS campaign during the periastron passage in 2004 revealed a complex light curve (see black points in Fig. 1). Observations could only start when the source was already 10 days before periastron. The VHE flux was actually decreasing from a maximum of ∼10% of the

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Fig. 1 VHE integrated flux from PSR B1259-63 above 1 TeV as a function of the true anomaly. The corresponding orbital phases (mean anomaly) are shown on the upper horizontal axis. The red vertical line indicates the periastron passage. Shown are data from the years 2004 to 2007: the black points are the daily fluxes as measured in 2004. The green empty triangles show the overall flux level as seen in 2005 and 2006. The blue filled squares represent the monthly fluxes taken from the campaign in 2007. From [14].

crab nebula flux on the first nights of observation. It followed a gap during periastron and the source was found to be brightening again up to another maximum at ∼10% of crab. The flux then decreased steadily for the following three months. This peculiar behaviour has been linked to the influence of the Be star disc on the emission process[12, 13]. The spectrum could be fitted to a power law with Γ=2.7±0.2 (stat) ±0.2 (sys) with no indication of index variability. The VHE flux corresponds to a luminosity of 8×1032 erg/s, which represents only 0.1% of the pulsar’s spindown luminosity. Figure 1 shows the VHE flux of the source as a function of the true anomaly for both the 2004 periastron passage and the next passage in 2007[14]. It was again impossible to observe strictly during periastron. In general terms the source displays the same level of VHE emission, but the two light curves show different shapes, even if there are no observations at exactly the same true anomalies: the VHE seems to be brighter at θ=-0.3 in 2004, but dimmer after periastron, at θ=+0.2. This different behaviour in 2007 challenges models where the double-hump structure is associated to the pulsar crossing the disc.

2.2 LS 5039 This binary system consists of a compact object and an O6.5V star of 23 M⊙ . It is located a distance of ∼2.5 kpc. The orbit has a small eccentricity e=0.337 with a period of 3.9061±0.0001 days. The two objects are 0.1 A.U. away at periastron (φ=0) and 0.2 A.U away at apastron. More details about the latest orbital parameters and phase definition can be found at [15] The nature of the compact object is unknown: it may range from a 1.4 M⊙ neutron star to a 3.7 M⊙ black hole. No pulsar has been found in radio or X-ray searches,

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although any pulsations would probably be diluted by Compton scattering for all orbital phases. As mentioned above, no pulsations are observed when the two components of the PSR B1259-63/SS2833 system approach periastron and the two components of LS 5039 are a comparable distance for all orbital phases. VLBA shows complex extended morphology which may look at first sight like a jet, but changes orientation as the two objects progress along the orbit[17]. This argues in favor of acceleration at the region where the pulsar wind and the companion star’s wind interact, rather than acceleration in a jet. LS 5039 was discovered in VHE by HESS [16] during their first Galactic Plane Survey. In fact it was the only point-like source found in the survey and its position was consistent with a bright unidentified EGRET source which had been proposed as a counterpart to a binary system[18]. The spectrum could be fitted to a power law with photon index 2.12±0.15 and a flux of ∼5% crab. The VHE luminosity was similar to the X-ray luminosity. Further HESS observations in 2005 allowed to establish variability and periodicity consistent with the orbital period[19]. The phase-folded flux of the source is shown in figure 2 along with the evolution of the photon index with phase. The VHE


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2.3 LS I+61◦ 303 LS I+61◦ 303 is a binary system formed by a compact object and a B0Ve star of 12M⊙ at a distance of 2.0±0.2kpc. It has an eccentricity e=0.54 with 26.4960 ± 0.0028 day period (from radio observations). At periastron the two system components are separated by 0.2 A.U. (φ= 0.275, see [15] for the orbital elements of the system and the definition of the phase), while at apastron they are 1 A.U apart. Orbital phase 0.4

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Historically this object has drawn much interest due to its periodic outbursts in radio and X-rays. The radio outbursts are well correlated with the orbital period[29], although the phase of maximum emission moves from φ=0.45 to 0.95 over a period of 1667 days. This superorbital variability is probably related to changes in the speed of the circumstellar wind[30]. Even if extensively studied, we do not know the nature of the compact object: it could be anything from a 1.4M⊙ neutron star to a 4M⊙ black hole. No pulsar has been found in radio or X-ray searches, but the aforementioned considerations about absorption for LS 5039 apply here as well. Also similarly to LS 5039, VLBA observations reveal a complex morphology which is coupled with the orbital period[21], once again pointing to wind-wind interaction. This binary system was discovered in γ-rays by MAGIC in 2006[22] after following the source for a good fraction of the orbital phases over six orbital periods. The VHE emission was significantly variable: there was no detection at periastron or at inferior conjunction (i.e. when the compact object is between the companion star and the Earth, the phase for which LS 5039 reaches a maximum); the emission peaks at ∼15% crab before apastron (φ=0.6-0.7). The spectrum is Crab-like, with a photon index of 2.6 ± 0.2 (stat) ± 0.2 (syst). The source was confirmed by the VERITAS telescope array during the next season [23]. The light curve and spectrum were found to be consistent with MAGIC results. A second MAGIC campaign in 2006[24] combined with previous 2005 data allowed to establish that the VHE emission has a significant periodic component with a period of 26.8±0.2 days, compatible with the orbital period and the period found in other wavelengths. Contrary to what happens in LS 5039, the phaseogram follows no simple sinusoidal shape. MAGIC observations showed evidence for a second peak of VHE emission in December 2006 at φ=0.8-0.9 but for only one orbit. No evidence was found for intranight variability in searches down to 15 min time scales, or for spectral variability, although it must be said that the spectral index could only be measured for phases φ=0.5-0.6 and φ=0.6-0.7[24]. Multiwavelengh observations with VERITAS, Swift and RXTE in 2007[26]) showed large X-ray variability with flux values typically varying between 0.5 and 3.0×10−11 erg cm−2 s−1 over a single orbital cycle, but the TeV sampling was not dense enough to detect a correlation between the two bands MAGIC organized two multiwavelength campaigns. During the first campaign in 2006, with VLBA, MERLIN, e-EVN and Chandra[25], the gamma-ray and radio bands were found not to be correlated. The radio interferometers confirmed that the shape of the extended emission follows orbital period. No VHE/X-ray correlation could be established. In 2007, MAGIC followed the source along with the X-ray detectors XMM and Swift[27] for most of a single orbit. Around the maximum of the VHE emission (φ = 0.6-0.7), the energy flux in X-rays E·Flux X − ray was measured to be about two times larger than the energy flux in VHE E·Flux V HE, and, as can be seen in figure 3, both bands are significantly correlated: the correlation factor is r = 0.81, corresponding to a random probabilty ∼ 5×10−3.


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The phenomenology of the source in VHE has become even more complex after the latest observations of VERITAS in the 2008/09 and 2009/10 seasons[28, 31]. These are actually the only reported observations after Fermi started operations in 2008. LS I+61◦ 303 has not been detected for any of the orbital phases. In fact making use of the full VERITAS array with nominal sensitivity has allowed to set stringent upper limits at the level of 2% crab for the phase of the maximum VHE emission. The drop in VHE emission may be correlated with the super-orbital variability of 1667 days, which, as already mentioned, is probably associated to changes in the circumstellar disk and may hence have an impact on the efficiency of the particle acceleration or γ-ray absorption processes.

3 Uncertain VHE binaries: Cyg X-1 and HESS J0632+057 3.1 Cyg X-1 Cygnus X-1 is a High Mass X-ray Binary at 2 kpc distance. It represents the best established candidate for a stellar mass black hole, with a mass of more than 13 M⊙ . Its optical companion is an O9.7 super-giant with a mass of 30 M⊙ and a strong stellar wind[32]. The orbit is low-eccentric with radius 0.2 AU and 5.6 days period. The source belongs to the microquasar class because it displays a single-sided jet resolved at milli-arcsec scales with VLBA during the X-ray hard state. The jet’s opening angle is less than 2◦ and the bulk velocity is >0.6c. Some authors[33] have suggested that Cygnus X-1 is a “microblazar”, where the jet axis is roughly aligned with the line of sight. 1.4 GHz radio observations show a 5 pc (8 arcmin) diameter ring structure of bremsstrahlung emitting ionized gas at the shock between the jet and the interstellar medium. The power released by the (dark) jet is of the same order or the bolometric X-ray luminosity and two orders of magnitude higher than that inferred from the radio spectrum[34]. The results from observations in the soft γ-ray range with COMPTEL [35] and INTEGRAL [36] strongly suggest the presence of a non-thermal component extending beyond the hard X-ray band. In addition, fast episodes of flux variation by a factor between 3 and 30 have been detected at different time scales, ranging from milliseconds in the 3-30 keV band [37] to several hours in the 15-300 keV band [38]. MAGIC observed this microquasar for 40 h in 2006[39]. No VHE emission was found either at the microquasar or at the interaction point between the jet and the interstellar medium. Cyg X-1 however showed evidence for emission for around 1 hour in September 24th with a pre-trial significance of 4.9σ. Given the number of observed hours, this corresponds to a post-trial significance of 4.1σ. The observation stopped at sunset and could only be resumed on the following night, so the high level of VHE emission may have extended for as long as one day.

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Fig. 4 From top to bottom: MAGIC, Swift/BAT and RXTE/ASM measured fluxes from Cygnus X1 as a function of the time. The left panels show the whole time spanned by MAGIC observations. The vertical, dotted blue lines delimit the range zoomed in the right panels. The vertical red line marks the time of the MAGIC signal. From [39].

During the 79 minutes when the VHE signal was found (MJD 54002.928 and 54002.987) the VHE spectrum could be fitted to a power law with a rather soft spectral index of 3.2±0.6 and a differential flux of roughly 10% crab at 1 TeV.


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Figure 4 shows the VHE, soft X-ray (RXTE/ASM) and hard X-ray (Swift/BAT) light curves of the source during the MAGIC observation campaign in 2006. It is especially suggestive that the VHE signal was correlated with an increase both in soft and hard X-rays, although it must be said that Cyg X-1 was in a similarly high level of X-ray emission in the following night and MAGIC did not detect it in VHE. INTEGRAL also reports a historically high ux around the same time (∼1.5 Crab between 2040 keV and ∼1.8 Crab between 4080 keV). The long exposure also allowed to set stringent upper limits to the low-hard state of the binary system: any steady VHE flux due to the persistent jet associated to this X-ray state is below the present IACTs sensitivity. For the time being, this remains the only evidence for VHE emission in an accreting binary system. Detection of such an object would allow to determine the maximum particle energy which can be achieved in the jet of a stellar-mass black hole, a fact which may help to understand the general mechanism of jet acceleration.

3.2 HESS J0632+057 HESS J0632+057 is one of very few point-like (100 MeV)x10 [photons cm-2 s-1 ]

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the source is in the HS state and last for several days, Cyg X-3 reveals the presence of collimated relativistic jets[68, 69], a fact which grants it access to the microquasar class.

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Cyg X-3 has also historically drawn a great deal of attention, and in fact strongly contributed to the development of the field, due to numerous claims of detection at TeV and PeV γ-rays. However, a critical analysis of these observations raised doubts on their validity (we refer the reader to [70] and references within for all the reports of detection). In recent years, more sensitive instruments have failed to confirm those claims for energies above 500 GeV [71, 72]. Nevertheless, the fact that this object is a microquasar with the aforementioned strong X-ray and radio emission makes into a good candidate for VHE emission (see e.g. [73, 74, 75]). This radiation could have either an episodic nature due to the ejection of strong radio-


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emitting blobs[76] in the HS state, or a quasi-stationary character if it is originated in the persistent compact jet present during the LH state[75]. The source has been very recently detected at high energy γ-rays by AGILE[77] and Fermi/LAT[78, 2]. AGILE found five γ-ray flares above 100 MeV, which were temporally correlated with transitional spectral states of the radio and X-ray emissions, whereas Fermi/LAT detected an orbital modulation of the flux during periods of GeV high-activity which lasted for several weeks and coincided with the source being in the HS state. Fermi/LAT has found to source to be variable with peaks as high as ∼2.0×10−6 photons cm−2 s−1 above 100 MeV, which are comparable and simultaneous with the AGILE detections. The emission during the HE active period is periodic with the orbital period of the system.

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Fig. 7 Cyg X-3 spectral energy distribution in the HE and VHE bands. The lines indicate the power-law spectra derived from Fermi/LAT and AGILE integral fluxes and photon indices. The corresponding errors are shown as shadowed areas. The arrows correspond to the 95% CL MAGIC differential flux upper limits and their slope indicates the assumed power-law spectrum (photon index 2.6). The black color corresponds to the general period of Fermi/LAT enhanced GeV activity, which is simultaneous to the X-ray High Soft state, whereas, the red color corresponds to the highest HE peak (MJD 55031–55034). From [79].

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MAGIC observed Cyg X-3[79] for about 70 hours between 2006 March and 2009 August in different X-ray/radio spectral states and also during one of the active HE periods reported by Fermi/LAT. No evidence was found for a VHE signal from the direction of the microquasar. An upper limit to the integral flux for energies higher than 250 GeV has been set to 2.2×10−12 photons cm−2 s−1 (95% confidence level). It corresponds to 1.3% of the Crab Nebula flux at these energies and is most stringent limit so far to the persistent VHE emission of this source. A search for emission was performed separately for each year of observations, on a daily basis and for each orbital phase. No significant VHE emission was found in any of the three searches (for more details and differential flux upper limits, see [79]). The VHE data sample was also split according to the X-ray state of the source. The upper limit to VHE emission during the HS state corresponds to 2.5% of the Crab Nebula flux. In the LH state, the VHE emission is expected to be produced inside the compact and persistent jets, whose total luminosity is estimated to be at least 1037 erg s−1 [80]. The MAGIC upper limit corresponds to a VHE luminosity of 7×1033 erg s−1 for a distance of 7 kpc. Thus, the maximum conversion efficiency of the jet power into VHE γ-rays is 0.07% which is similar to that of Cygnus X-1 for the upper limit on the VHE steady emission, but one order of magnitude larger than that of GRS 1915+105. MAGIC pointed at Cyg X-3 during the second period of HE enhanced activity detected by Fermi/LAT in 2009, as shown in figure 6. In particular, MAGIC carried out observations simultaneous with a GeV emission peak on 2009 July 21 and 22 (MJD 55033–55034), but did not detect VHE emission. The corresponding integral flux UL above 250 GeV is lower than 6% of the Crab Nebula flux. As can be seen in figure 7, this flux UL is roughly at the level of a power-law extrapolation of the HE flux measured by Fermi/LAT, assuming the photon index Γ=2.6 which Fermi/LAT has measured for both the low and high state of the source, but it is significantly below the extrapolation of the Fermi/LAT flux but assuming the photon index measured by AGILE only during the high state (Γ=1.8). Both results point to a cutoff in the energy spectrum of the source at energies in the range between a few GeV and 250 GeV.

5 Conclusions VHE binaries may be powered by the interaction between a pulsar wind and the wind of its companion star, or by an accretion-driven jet. Three binary systems have been recently established at the VHE band: PSR B1259-63, LS 5039 and LS I+61◦303. Emission in the first binary stems from pulsar wind/stellar wind interaction, and the other two objects are consistent with the same scenario. All three sources display a complex phenomenology. Even if there is a significant component of the VHE emission which is associated to the orbital period, variations from orbit to orbit are observed. LS I+61◦303 significantly dropped in brightness over the past two years and recent observations have in fact failed to


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detect it for any orbital phase, a fact which may be linked to superorbital variability observed at other wavelengths. Its variability at VHE and lower energies, its point-like character and its SED make HESS J0632+057 into a plausible candidate to become the fourth VHE binary. On the other hand, a black hole X-ray binary, Cyg X-1, has shown a marginal episodic signal at VHE, which may eventually make it into the first VHE microquasar. Searches for other well-known X-ray binaries have proved unfruitful. Recent observations of Cyg X-3 in a wide variety of X-ray and radio states and during a high energy γ-ray flare detected by Fermi/LAT have not shown evidence for simultaneous VHE emission.

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γ-ray binaries as non-accreting pulsar systems Diego F. Torres

Abstract The γ-ray binaries LS 5039 and LS I +61◦ 303 have been detected by Cerenkov telescopes at TeV energies, exhibiting periodic behavior correlated with the orbital period. These γ-ray binary systems have also been recently detected by the Fermi Gamma-ray Telescope at GeV energies, and combination of GeV and TeV observations are providing both, expected and surprising results. We summarize these results, also considering the multi-frequency scenario, from the perspective of pulsar systems. We discuss similarities and differences of models in which pulsar wind/star wind shocks, or pulsar wind zone processes lead to particles accelerated enough to emit TeV photons. We discuss in detail the caveats of the current observations for detecting either accretion lines or pulsations from these objects. We also comment on the possibility for understanding the GeV to TeV emission from these binaries with a 2-components contribution to their spectrum. We show that it would be possible to accommodate both, normal pulsar emission and GeV / TeV fluxes that vary with orbital phase. We point out several aspects of this idea that are subject to test with data being currently taken.

1 Prologue Four massive binaries have been discovered as variable very-high-energy (VHE) γray sources. They are PSR B1259-63 (Aharonian et al. 2005a), LS 5039 (Aharonian et al. 2005b, 2006), LS I +61◦ 303 (Albert et al. 2006, 2009, Acciari 2008,2009), and Cyg X-1 (Albert et al. 2007). HESS J0632+057 was found by the H.E.S.S. experiment (Aharonian et al. 2007) as one of the very few point like sources. Its positional association with the massive star MWC 148 led to the suggestion that its nature is Diego F. Torres Institució Catalana de Recerca i Estudis Avançats (ICREA), Catalunya, Spain; and Institut de Ciències de l’Espai (IEEC-CSIC), Campus UAB, Fac. de Ciències, Torre C5, parell, 2a planta 08193 Barcelona, Spain. e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_43, © Springer-Verlag Berlin Heidelberg 2011

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that of a gamma-ray binary system, albeit this has not yet been confirmed (Hinton et al. 2009). PSR B1259-63 is obviously a system formed with a pulsar whereas Cyg X-1 is most likely formed with a black hole compact object. The nature of the two remaining systems (LS I +61◦303, and LS 5039, recently detected by Fermi, see below) is not yet settled. Variable gamma-ray emission was also reported from Cyg X-3, but it is only detected at GeV energies (Abdo et al. 2009c, Aleksić et al. 2010). The phenomenology presented by the systems that have been detected both at TeV and GeV energies can be distinguished in two classes: there are those presenting recurrent TeV emission correlated with the orbit (the case of LS I +61◦ 303, LS 5039, and PSR B1259-63) and there is also one case (Cyg X-1) that was hinted at in a flaring episode that has not been found to repeat yet. Cyg X-1 and the three other TeV sources also differ in their SEDs. In Cyg X-1, the transient VHE luminosity was less than 1% of the X-ray luminosity. This Chapter analyzes some aspects of the high-energy and multi-wavelength phenomenology, especially of LS I +61◦303 and LS 5039, in what concerns to their possible interpretation as non-accreting pulsar systems. In this same volume, contributions by R. Dubois et al. (Fermi collaboration) and J. Cortina give account of the observations at high and very-high energies of these sources. We shall only make notice of the spectral energy distribution, referring to the work of the former authors for details. Figure 1 shows the high and VHE spectrum for both LS 5039 and LS I +61◦303. For LS I +61◦ 303, the data plotted at the two energy bands are not corresponding to the same part of the orbit, with the Fermi data being an average. In the case of LS 5039, two broad band spectra –corresponding to the inferior and superior conjunction phase intervals– are shown for both energy bands, and although not contemporaneous, they cover multiple orbital periods.

2 Why is a non-accreting pulsar system a tenable alternative? In this section, we put some important aspects of the multi-wavelength information on LS 5039 and LS I +61◦303 in context of the highest energy detection. We list the main reasons by which one can in principle sustain that a non-accreting pulsar system is a tenable alternative for these binaries (see also Dubus 2006, and Zdziarski, Neronov & Chernyakova 2008). 1) The mass function does not provide definite constraints to the mass of the compact object, with a pulsar being an acceptable (if not preferred) alternative: Combining Newton’s laws of gravitation and motion, the mass function is f (m1 , m x ) = (4π2/G)((a sin i)3 /P2b ) = (m x sin i)3 /(m1 + m x )2 , where m1 and m x are the masses of the star and companion respectively, G is Newton’s gravitational constant and i is the inclination angle of the binary orbit (defined so i = 900 is edge on). The mass function has then units of mass, and is the minimum mass of the

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Fig. 1 Summary of GeV to TeV observations of the two γ-ray binaries detected with Fermi. High and very-high energy spectral data points of LS I +61◦ 303 (left) and LS 5039 (right). Left: Fermi (integrating the whole orbit) data points are triangles; MAGIC data are lighter circles (high state phases 0.5-0.7); and VERITAS data are black circles (0.5-0.8). Right: Circles show the spectral data at INFC (TeV maximum, GeV minimum, phases 0.45–0.9; triangles show the spectral data at SUPC (TeV minimum, GeV maximum, phases < 0.45 and > 0.9). Higher energy data comes from H.E.S.S. Note that the data from the different telescopes are not contemporaneous, though they do cover multiple orbital periods.

x-companion corresponding to a zero-mass m1 = 0 and inclination angle i = 900 : m x > f (m1 , m x ). This means that the determination of the inclination and companion mass is mandatory to determine the type of the compact object. If m1 = 10 − 15 M⊙ , and f (m1 , m x ) ∼ 0.01 the companion would be a neutron star if i > 250 . The mass function values found for LS 5039 and LS I +61◦ 303 (see e.g., Casares et al. 2005a,b; or Aragona et al. 2009) are low (∼ 0.01). To constrain the compact object mass from the mass function, the orbital inclination and mass of the optical primary must be known, which are subject to their own uncertainties. The parameter space derived by Casares et al. (2005a,b), by Grundstrom et al. (2007), and by Aragona et al (2009) all allow for both a neutron star or a black hole in LS 5039 and LS I +61◦ 303 the inclination of the orbit being poorly constrained (limits are not strict) 100 < i < 60, or even higher. It is interesting to note that the assumption of a neutron star in both objects, of 1.4 M⊙ would imply a large inclination: the compact object would be a neutron star if i > 250 and a black hole otherwise. If ignorance of the orbital inclination can be represented by a random distribution of i, the likelihood for the system to be formed by a neutron star is greater than if it is formed by a black hole compact object. 2) There is no clear sign of an on-going accretion process: The X-ray and radio properties of LS 5039 and LS I +61◦303 distinguish them from other X-ray binaries, and particularly for LS I +61◦ 303, set it apart from other Be X-ray binaries (XRBs) (see below), since they both present no conclusive signs of accretion. If these systems accrete, given the sizes of their orbits, accretion would have to be wind-fed. Periodic ellipsoidal variations are also a common phenomenon

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among high-mass X-ray binaries (HMXBs), provided that the optical companion fills its Roche lobe, due to tidal distorsions of the optical star. These are also not ˙ w /(2ra /d s )2 observed (Mart´ı et al. 2004). The Bondi mass accretion rate is M˙ ∼ M 7−8 ˙ where Mw is the stellar wind mass loss rate (typically about 10 M⊙ yr−1 ), d s is 2 the orbital separation, and ra = 2GMc /vw is the Bondi capture radius, with Mc the mass of the compact object and vw the wind speed. This implies average values, e.g., for LS 5039 and assuming a polar flow of 2000 km s−1 , of 5 × 1014 g s−1 . This value of mass accretion, when transformed into power, is close to, or even lower than the GeV luminosity of the system, implying unrealistic efficiencies (see, e.g., Dubus 2006). In order to avoid disc or magnetospheric accretion, the relativistic wind of the pulsar must be able to stop the infall of stellar matter, implying an upper limit to its putative period. Writing the spin-down power as a function of the pulsar ˙ −1/4 ms, with M˙ 15 being the magnetic field B and period P, it results P < 230B1/2 M 15 15 g s−1 . Thus, if a fast millisecond pulsar is present in these systems, ˙ scale M/10 accretion onto it is not expected. As e.g., Zhang et al. (2010) confirmed with the analysis of deep INTEGRAL observations of LS I +61◦ 303, there is no high-energy cut-off at energies below 100 keV, as it would be common in conventional accretion scenarios. Indeed, if the system is an accreting neutron star or black hole, one expects to find a cut-off powerlaw spectrum in the hard X-ray band with a cut-off energy normally at 10 – 60 keV for neutron stars (e.g., Filippova et al. 2005) and at ∼100 keV for black holes (McClintock & Remillard 2003). See also the LS 5039 Suzaku observations by Takahashi et al. 2009, where the X-ray spectral data up to 70 keV are described by a hard power-law with a phase-dependent photon index which varies within 1.45–1.61). Regarding spectral lines due to accretion, RXTE spectra of LS 5039 did appear to show a strong, broad Fe line (Ribó et al., 1999), although it was not confirmed by other X-ray missions (see, e.g., the XMM-Newton observations by Martocchia et al., 2005). Several authors argued that being LS 5039 in the Galactic Plane, the Fe line is very likely due to Ridge emission sampled by the large RXTE field of view (e.g., Bosch-Ramon et al., 2005; Dubus 2006a, Zdziarski, Neronov, Chernyakova 2008). We discuss the prospects for line detection from these systems in greater detail below, where we put forward a note of caution given the relatively limited observation times that have been granted compared with the amount of time needed to detect accretion lines from these systems under some assumptions. 3) If there is a pulsar, non-detection of radio pulses is expected: Zdziarski, Neronov & Chernyakova (2008) have already shown in detail why radio pulses would be absorbed in these compact binaries. We follow their derivation in what follows: The free-free absorption coefficient due to ions with the atomic charge, Z, is given by −3/2 2 αff = (25/2 π1/2 e6 )/(33/2m3/2 Z ne nZ ν−2 g¯ , e c)(kT )

(1)


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where ν is the frequency, nZ is the Z-ion density, ne is the electron density, and g¯ is the average Gaunt factor.1 Using Z = 1, T = 105 K and ν = 5 GHz, and averaging over Z, αff ≃ 0.12T −3/2 (µ2i /µe )n2i ν−2 cm−1 ≃ 0.175T −3/2n2i ν−2 cm−1 , where T and ν are in units of K and Hz, respectively, and µe = 2/(1 + X) ≃ 1.2 is the mean electron molecular weight. For the equatorial disc, the density can be expressed as nd,i (D) ≃ nd,0 (D/R⋆ )−γ , where nd,0 ∼ 1013 cm−3 , γ ≃ 3.2, and D is the distance from the center of the Be star (see, e.g., Waters et al. 1988, and the discussion below). The optical depth perpendicular to the disc plane is subject to a disc thickness of 2D tan θ0 , with θ0 the half-inclination angle. Thus, n 2 T −3/2 ν −2 −5.4 τd,ff D w,0 ≃ 1GHz 1013cm−3 3 × 1012cm 6 × 106 105 K

(2)

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(3)

where 3 × 1012 cm corresponds to the periastron separation of LS I +61◦303. Thus, the equatorial disc is optically thick to radio emission, including of course, pulsations. This is consistent with the suppression of pulsed radio emission observed close to periastron in the system PSR B1259-63 (Johnston et al. 1992, Melatos et al. 1995). To calculate the radial optical depth of the fast polar wind from infinity down to a given value of D we can consider a clumpy wind (free-free absorption would still provide a high opacity even for smooth polar flows) where the wind density inside the clumps is 1/ f times that of the smooth wind, hni i ≃ ni f and

In a clumpy medium, τff is an integral over the square of the density within the clumps times f , i.e., n2i f (or equivalently, an integral over hni i2 f −1 ). The opacity then results, " #2 −2 " f #−1 τw,ff M˙ w v∞ ≃ 0.1 5 × 103 10−8 M⊙ yr−1 108 cm s−1 ν −2 T −3/2 −3 D × . 1GHz 105 K 3 × 1012cm

(4)

Thus, according to the orbital solutions found for the systems, the neutron star would move in the optically thick region, explaining the absence of observed radio pulsations. In addition of the high opacity, one can always entertain the possibility for the radio emission cone to be emitted off our line of sight, thus missing it entirely as in the case of any undetected-in-radio, bright GeV pulsars, even if at some portion of the orbit, radio pulses could escape. Pulsed emission in the X-ray or GeV band would be as important as those in radio to pinpoint a pulsar component, and we come back to these possibilities below.

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The Gaunt factor for hν ≪ kT and ν ≫ νp (where νp is the plasma frequency) equals g¯ = (31/2 /π)[ln((2kT )3/2 )/(πe2 Zme ν)) − 5γE /2], where γE ≃ 0.5772 is Euler’s constant.

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4) There are no clear signs of jets and the radio morphology is consistent with a pulsar component: From ∼50 mas resolution radio images of LS I +61◦ 303 obtained with MultiElement Radio Linked Interferometer (MERLIN), extended, apparently precessing, radio emitting structures at angular extensions of 0.01 − 0.05 arcsec have been reported by Massi et al. (2001, 2004). However, recent Very Long Baseline Array (VLBA) imaging obtained by Dhawan et al. (2006) over a full orbit of LS I +61◦303 has shown the radio emission to come from angular scales smaller than about 7 mas (which is a projected size of 14 AU at an assumed distance of 2 kpc). This radio emission appeared cometary-like, and interpreted to be pointing away from the high mass star and thus being the smoking gun of a pulsar wind. A careful analysis of the images and phases, however shows that this interpretation is not straightforward: The tail is not always seemingly pointing in the right direction, at least when the polar flow of the Be star is considered. Nevertheless, there are some unambiguous results of these observations: a) No large features or high-velocity flows were noted in any of the observing days, which implies at least its non-permanent nature. b) The changes within 3 hours were found to be insignificant, so the velocity of the outflow can not be much over 0.05c. The MAGIC collaboration also conducted a radio campaign (in concurrence with TeV observations) to test these results using again MERLIN in the UK, the European VLBI Network (EVN), and the VLBA in the USA (Albert et al. 2008). In this campaign, radio observations at different angular resolutions were conducted at the same time. It is then interesting to focus on the day where all these facilities observed at the same time (October 25-26, 2006). The results obtained by radio imaging at different angular scales show that the size of the radio emitting region of LS I +61◦ 303 is constrained to be below ∼6 mas (∼12 projected AU), and the presence of persistent jets above this scale is therefore excluded. As in the case of Dhawan et al. (2006), these observations have shown a radio-emitting region extending east-southeast from the brighter, unresolved emitting core. The outflow velocity implied by these observations is ∼ 0.1c. The comparison between Dhawan et al. (2006) and Albert et al. (2008) images at the same orbital phase (but obtained 10 orbital cycles apart) show a high degree of similarity on both its morphology and flux, which suggests periodicity and stability of the physical processes involved in the radio emission. These would be hard to attain if, for instance, the radio emission is the result of the random interaction of a steady flow with wind clumps. On the other hand, if the radio emission is produced by a milli-arcsecond scale jet, the required stability and periodic behavior of such a jet in order to produce the same radio map across many orbital cycles would be difficult to reconcile with the non-persistent nature of a larger scale (∼100 mas) relativistic jet. Figure 2 shows that no jet can be seen at any scale. A similarly changing milli-arcsecond radio morphology was found for LS 5039 (Ribó et al. 2008). In fact, early detection of elongated asymmetric emission in highresolution radio images obtained with VLBA and EVN was interpreted as evidence of its microquasar nature, and suggested that the source was persistently producing


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5) A young age of the system is consistent with observations: If the compact object is a young and energetic millisecond pulsar (necessary to avoid accretion onto it), the system should then be similarly young. Ribó et al. (2002) have put an upper limit to the age of LS 5039 by tracing back the proper motion of the system to the plane. LS 5039 is a runaway system, with a total systemic velocity of about 150 km s−1 and a component perpendicular to the galactic plane larger than 100 km s−1 . This is probably the result of an acceleration obtained during the supernova event that created the compact object in this binary system. Nitrogen enrichment in the atmosphere of the companion star also suggests a young age in LS 5039 (McSwain et al. 2004; rotational-mixing could also explain the enrichment, Casares et al. 2005b, see Dubus 2006). Note too that radio searches of supernova remnants have also failed for PSR B1259-63, which has a measured spin-down age of 3 × 105 years (Johnston et al. 1992). 6) Pulsar systems would be consistent with population predictions of Be XRBs: The Be XRBs, like LS I +61◦ 303 are the most numerous class of XRBs known. At present, 64 Be XRBs are known in the Galaxy, and in 42 the compact object was confirmed to be a neutron star (NS) by the presence of the X-ray pulsations; in not a single one of them, a black hole was confirmed (Belczynski & Ziolkowski 2009). Recent population synthesis made by the latter authors are consistent with 0-2 black hole Be XRB in the Galaxy, which can perhaps be understood as a result of an evolutionary effect. The rotation of Be stars could be achieved during a period of Roche-lobe overflow mass transfer from its initially more massive companion, and if it looses most of the mass in the early pre-SN phase process, becoming a He star with mass of only a few M⊙ , when exploding as a supernova it can only leave a neutron star behind (see e.g., Tauris & van den Heuvel 2006). One has to bear in mind, however, that most of these Be XRBs are accreting systems, hosting pulsars with long periods (older spin-down systems) and only a few are expected to have a young age at any given moment. Spectral-wise, then, e.g., LS I +61◦ 303 is very different from most of these objects above 10 keV, with the latter being cut off in hard X-rays (typically with ∼20 keV bremsstrahlung-like spectra) with only very weak emission above ∼100 keV as measured, e.g., by INTEGRAL.

3 Caveats in the search for X-ray spectral lines The apparent absence of spectral lines in the X-ray spectra of TeV binaries has been often used as a proof of their non-accreting nature. However, a word of caution is useful in this respect. The X-ray continuum spectra of accretion dominated HMXBs are often described by a power law with photon index α ∼ 1 − 2 (modified at higher energies by an exponential cutoff between ∼30-100 keV). A spectrum of this form can be produced by inverse Compton scattering of soft X-rays by hot electrons in


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the accretion column near the compact object, and a part of this emission is scattered by the stellar wind of the massive companion. This results in a further non-thermal spectral component, but with a different absorption column depending on the orbital phase of the system. Furthermore, in some HMXBs a soft excess at ∼ 0.1 − 2 keV is detected, very common in systems hosting pulsars (Hickox et al 2004). In luminous systems this soft component can be explained by reprocessing of hard X-rays from the neutron star by optically thick, accreting material. For less luminous sources the soft excess is probably due to other processes, e.g. emission from photoionised or collisionally heated diffuse gas or thermal emission from the surface of the neutron star. On top of the continuum model, several spectral lines are usually present in these systems, neutral and ionized, such as Fe, Si, Mg, Al, N, Ca, mainly produced in the stellar wind or in the accretion disk (if any) illuminated by the strong X-ray emission of the compact object. One clear example of such a system, showing all the above mentioned spectral components is the HMXB 4U1700-37 (composed by an O type star in a ∼4 days orbit around a compact object of unknown nature: see e.g. Clark et al. 2002; van der Meer et al. 2005; see e.g. Figure 3). Note that in 4U170037 as well as many other binaries, the presence of spectral lines is highly dependent on the continuum spectrum and on the orbital phase of the system. So far a detailed high-resolution spectral analysis has been missing for the two debated TeV binaries: LS 5039 and LS I +61◦ 303. The best data available for these kind of studies come from the XMM-Newton satellite, thanks to its large collecting area, spectral resolution, as well as the availability of its grating spectrometer. However, at a given orbital phase, only very short observations have been taken (mainly aiming at monitoring the continuum spectral variability over the orbits). In the past XMM-Newton spectra of, e.g, LS 5039, an EW ∼ 60 eV is the current 1σ limit on the presence of Fe Kα (and only in a small part of the orbit), while in the available Suzaku observations, the limit on the detection of lines is 40 eV (see Takahashi et al. 2009). Furthermore, with the current short pointings (at a given orbital phase) there are not enough counts to use anyhow the high-resolution spectral capabilities of the grating cameras, making impossible to answer any question about the presence of narrow lines. To understand what does this mean, one can consider the binary 4U 1700-37, a very similar HMXB to LS 5039 (i.e., similar companion star and orbital period, but no TeV emission, and clearly accreting) located at ∼ 1.5 kpc rather than 3 kpc. Fig. 3 shows the XMM-Newton spectrum of 4U 1700-37 during an eclipse (van der Meer et al. 2005), and how would these accretion lines look, assuming all are present, in the available data for LS 5039. As a result of this simulation, one can see that none of the lines present in 4U 1700-37 would be detectable by the current data. In Figure 3 we also show the limits for the presence of lines derived from a 95 ks long Chandra recent observation of LS I +61◦ 303 (Rea et al. 2010).

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4 Caveats in the search for pulsations The detection of pulsations is the only unambiguous tracer for a secure determination of the pulsar nature of the compact objects hosted in LS 5039 and LS I +61◦ 303. Deep searches for pulsations have been performed in the radio band at several frequencies, with the hope of detecting a fast spinning radio pulsar as in the case of the other TeV binary PSR B1259–63 (Johnston et al. 1999, 2005). However, no radio pulsation have detected so far from any of these two sources. As it has been discussed earlier, this is anyway not surprising. In particular, note that at periastron, PSR B1259–63 does not show radio pulsations, and that its periastron (given the large orbit, 3.4 year period) has about the same dimension of the major axis of the orbit of LS I +61◦ 303 and it is way larger than that of LS 5039’s. On the other hand, searches for pulsations in the X-ray band have many more chances of success than in the radio band. In fact, the X-ray pulsar beam is usually larger than the radio one, and the strong companion wind does not influence much the X–ray pulsed emission if present. However, what limits the X-ray pulsation search is the pulsed fraction sensitivity that current instruments can achieve. Until not long ago, archival observations which could give reliable upper limits on pulsations for fast spinning pulsars (P ≤ 100 ms) hosted in LS 5039 and LS I +61◦ 303 were not very constraining, coming mainly from RXTE and XMMNewton observations. In particular the high background of these instruments (especially RXTE) limited the pulsed fraction sensitivity of these observations. For LS I +61◦ 303 the deepest pulsed fraction limit was derived from a 41 ks XMMNewton observation (Sidoli et al. 2006), which was < 28% (if not otherwise specified, all pulsed fraction limits here are calculated assuming a sinusoidal profile and are reported at 90% confidence level in the 2–10 keV energy range), in the 12– 200 ms period range.3 Similarly, for LS 5039 the deepest limits for the presence of a 3

Note that the RXTE monitoring observations performed in 1996 gave an upper limit of only 32% in the 1–200 ms range, in fact, even though RXTE’s timing resolution and collecting area was much larger than XMM-Newton, the much higher background contamination is a killer for


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fast pulsar were derived from a 50 ks RXTE observation performed in 2003, giving an upper limit of P f < 30%. Very recently, to increase the pulsed fraction sensitivity reducing the background contamination, long Chandra observations have been performed for both LS I +61◦303 and LS 5039 (Rea et al. 2010). The results of these observations in the case of LS I +61◦ 303 are summarized in very deep limits on the presence of X-ray pulsations, with an average limit of < 10% in the 6 ms – 10 s period range (Rea et al. 2010). Isolated rotational-powered pulsars emitting pulsed X-rays are all characterized by X-ray pulsed fraction much larger than the limits derived by Chandra for LS I +61◦ 303. However, the presence of the strong stellar wind of the companion, and in particular the shock between the possible pulsar and the stellar wind, is a source of strong X-ray emission. This unpulsed X-ray emission coming from the shock can be responsible in diluting the pulsed X-ray emission proper to the pulsar, which then might easily end up to represent only < 10% of the total X-rays emitted by the systems. Of course, geometry and beaming can also be claimed for missing the pulsations at all. The possible detection of pulses could also come from observations of the Fermi telescope. Blind search pulsations of faint γ-ray sources require very long observation times, which implies the calculation of very large fast Fourier transforms (FFT). In addition, the significant frequency derivatives ( f˙) typical of the γ-ray pulsars require that the FFT be repeated many times over a scan of f˙. Specifically, in order to keep the signal power within a single bin of the FFT, the frequency step should be ∆ f = 1/T obs, where T obs is the total observation time, and the steps size 2 , which means an enormous number of of f˙ would have to be no larger than 1/T obs f˙ trials for observation periods as long as ∼1 year. Atwood et al. (2006) proposed the time-differencing technique, that reduces the number of f˙ trials with a modest reduction in sensitivity. This method is based on the application of the FFT on the differences of the photon arrival times, rather than on the time series itself. In order to be efficient, only the time differences shorter than a predefined time window T w , that is significantly shorter than the whole observation, are considered in the FFT. In this way the number of required steps in f˙ is reduced by a factor T w /T obs . But unless the binary parameters are exactly known, they should also be scanned (like the f˙) to search for a solution. The correction of the photon arrival time series from the solar system reference frame to the pulsar reference frame is mostly affected by the Roemer delay in the binary system. To evaluate it, five binary parameters are necessary: the orbital period (P B ), the epoch of the periastron (T 0), the argument of the periapsis (ω), the projected semi-major axis (A1), and the eccentricity (e). For LS 5039 and LS I +61◦ 303, the first two parameters are know with relatively good precision, but the uncertainties on A1, e, and ω are larger than a few percent (e.g, see Casares et al. 2005; worse for LS I +61◦ 303, see Aragona et al. 2009 and references therein). Thus, without detecting weak signals, resulting in a larger pulsed fraction limit. For that observations, Harrison et al. (2000) claims a limiting pulsed fraction of ∼6%. However they considered the total count rate without correcting for the cosmic and instrumental background, which if corrected increases substantially the upper limit on the detectable pulsed fraction.

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better knowledge of the binary system parameters, the computational difficulties in running a blind search make the detection of γ-ray pulsations very challenging.

5 Notes on the theoretical models based on pulsar systems High energy emission from pulsar binaries have been subject of study for a long time (e.g., Bignami et al. 1977, Maraschi and Treves 1981; Protheroe and Stanev 1987, Arons and Tavani 1993, 1994; Tavani & Arons 1997; Bednarek 1997; Kirk et al. 1999, Ball and Kirk 2000; Dubus 2006a,b; Sierpowska-Bartosik 2008a,b and others). In most of these studies high-energy primaries are assumed to be accelerated at the shock formed by the collision of the (sometimes, putative) pulsar and the massive star winds. This generic feature allows them to be classified as wind-wind or inter-winds models. In other works the initial injection is assumed to come directly from the pulsar (the interacting particle population can be a result of equilibrium between this injected distribution and the losses to which it is subject, just as in the case of shock-provided electron primaries; and can also be the result of topof-magnetosphere or inner-pulsar-wind shocks). In this case, and when opacities to γ-ray production are high due to geometrical and physical characteristics, the pulsar wind zone (PWZ) could be the main origin of the high energy radiation, and we can classify this set as intra-wind or PWZ models. The closer the binary, the more these two scenarios are expected to produce similar results. Almost an order of magnitude difference in opacities can be seen between both systems discussed, with those in LS 5039 being higher, corresponding to the much shorter orbital periodicity (e.g., see Sierpowska-Bartosik & Torres 2009 for a comparison plot). Put otherwise, it would imply that a) intra-wind processes can not be completely neglected for LS 5039, since the opacities for electrons in there is high and cascades can happen b) inter-wind models can not be completely neglected for LS I +61◦ 303 (for these kind of more elongated systems, the probability for cascading in the pulsar wind region are lower and most of the energy carried by e± in the PWZ can then be released in the shock region, where the local magnetic field traps the pairs to produce photons via synchrotron and IC processes). These models do not consider either possible contributions of a proton component (which can generate γ-rays through pp or pγ processes (see Chenyakova et al. 2006). These extra components can, as discussed by these authors, also generate additional variability in the electron injection. These models do not contain a relativistic MHD approach of the collision of winds, but are rather based on simplifying assumptions of the hydrodynamical balance (see Romero et al. 2007 and Zdziarski et al. 2008 for a discussion on this issue). Through the study of intra-winds models, γ-ray astronomy opens a window to study the electron distribution and magnetization properties of the pulsar winds in binaries, a virgin territory otherwise. Assuming intra-wind models, one can already prove that a mono-energetic distribution of leptons in the putative pulsar wind is ruled out by observations of LS I +61◦ 303 and LS 5039. Assuming power-law distributions in the winds of pulsars seems justified and possible, although there is a


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not an priori expectation of the normalization and slope for them, and they so become free parameters of the models, which may in addition be subject to orbital variability, perhaps especially in close binaries. Although more complete models can certainly reduce/erase the need for such a change in the slope of the injection of leptons, as discussed, this is a caveat in the current versions. In any of these flavors of models, orbital periodicity is naturally encompassed. Short and random timescale variability can additionally be expected on top of this periodic behavior, for instance, as a result of granularity or clumping in the stellar wind, or the appearance of random shocks in the inner wind of the pulsar, which may modify local conditions off the average analysis discussed. The anti-correlation between GeV and TeV results is naturally encompassed in both of these flavors too (this is resulting just from the opacities evolution along the orbit and the system’s geometry, this is a general output of binary models where the radiation is produced close to star even in the case of black holes). IC emission is enhanced (reduced) when the highly relativistic electrons seen by the observer encounter the seed photons head-on (rear-on) i.e. at superior (inferior) conjunction. Inversely, VHE absorption due to pair production will be maximum (minimum) at superior (inferior) conjunction. Gamma rays emitted in the vicinity of the compact object with energies above the ∼30 GeV threshold inevitably pair produce with stellar photons (see e.g. Protheroe & Stanev 1987). On the contrary, emission in the Fermi range is largely unaffected by absorption but can be affected by cascading of higher-energy photons. The phases of minimum and maximum flux in Fermi and H.E.S.S., as well as the anti-correlation, are then consistent with these generic expectations, suggesting Inverse Compton scattering is the dominant radiative process above 100 MeV with the additional effect of pair production (affecting photons above 30 GeV) further modulating the γ-ray phenomenology (Bednarek 2006, 2007; Sierpowska-Bartosik & Torres 2008ab; Dubus et al. 2008). All in all, these models seem to work reasonably well for the VHE results, but both flavors fail in predicting the cutoff found by Fermi at GeV energies. Browsing SEDs from nominal models published smoothly connect both energy regions and predict levels of GeV-fluxes in excess of what is observed by Fermi (in the range ∼10-100 GeV). The Fermi cutoff is an unexpected feature in published models and it constitutes an observational surprise.

5.1 A perspective on the GeV cutoffs of LS I +61◦ 303 and LS 5039 The passage of a compact object through a dense equatorial disk, such as the one commonly found in Be stars, would crush a putative pulsar wind nebula closer to the neutron star, increasing synchrotron losses and introducing a strong dependence with orbital phase of the electron energy distribution (e.g., Dubus 2006b). This may explain the appearance of the cutoff in the Fermi spectrum of LS I +61◦ 303. However, there is no such disk around the O6.5V star in LS 5039. Thus, the existence of the cutoff in both systems argues against explanations related with the properties

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Fig. 4 Interpreting the Fermi and TeV results of γ-ray binaries with the 2-components idea. See text for details.

of the companion, and it seems to require that the radiative process, or the primary injected population, are different in the low and high energy domains (Abdo et al. 2009b). The GeV variability is also intriguing. If the GeV energy cutoff is interpreted in the outer gap model of pulsars, it is determined by the balance between acceleration and losses to curvature radiation, with the γ-ray emission being pulsed. The absence of pulsations in Fermi data is not constraining, given the difficulty of detecting faint pulsars directly in gamma-rays, especially when in binary systems. But even when detected as DC radiation, GeV magnetospheric emission due to curvature radiation would be produced near the pulsar, and has no obvious reason to be modulated with the orbital motion. In addition, the GeV–TeV anti-correlation would also remain unexplained. Despite of this, the orbital-average spectral results for LS I +61◦303 and those found at the SUPC of LS 5039 do resemble the spectral properties of pulsars. The typical Fermi pulsar emission (of which dozens have been measured) has a hard power-law spectrum with a photon index in the range 1.0–2.0 and all of them present an exponential cutoff, the typical value of which is at about 2 GeV (see e.g. the Fermi pulsar catalog; Abdo et al. 2010). In what follows, we entertain the possibility that the GeV emission detected by Fermi is produced by two components. One would be the magnetospheric GeV emission coming from a (putative) pulsar in the system. As discussed, this emission is expected to be steady along the orbit (i.e., unaffected by the orbital motion, since its origin is within the pulsar’s light cylinder), and pulsed. The other component would come from regions located farther away from the pulsar, i.e., from either the inter-wind region or from the wind zone or from both: this radiation would then be unpulsed, and it is naturally expected to vary with the orbital phase. For clarity, we will refer to this un-pulsed component as the wind contribution. Fig. 4 graphically shows this idea for the richest GeV and TeV sets of data, corresponding to the observations of LS 5039 at INFC (TeV maximum, GeV minimum, phases 0.45–0.9; Fig. 4 left panel) and SUPC (TeV minimum, GeV maximum, phases < 0.45 and > 0.9; Fig. 4 right panel). Data comes from Fermi and H.E.S.S.


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in the GeV and TeV energy ranges, respectively (Abdo et al. 2009b, Aharonian et al. 2006). The green curve in Fig. 4 represents a typical Fermi pulsar spectrum (a power-law slope of Γ = −1.8 and an exponential cutoff at 2 GeV), and is here supposed to be steady along the orbit, hence reproduced in both INFC and SUPC panels of Fig. 4. There is nothing special in the shape of the assumed pulsar spectrum when compared with all pulsars found by Fermi. However, the flux level of the green curve is here constrained by observations: On one hand, it cannot be much larger, since otherwise (being unaffected by the orbital motion) the INFC LS 5039 spectrum would have been found at a larger flux level. On the other hand, one could have assumed a lower-flux pulsar contribution, but in that case the pulsar magnetosphere would become more and more irrelevant the less contributing it is at all phase ranges along the orbit, and a yet to be developed theoretical model would need to account for the whole range of observations, from GeV to TeV, with no magnetosphere contribution. Hence, the most interesting testing scenario is whether it is possible (and useful to understand the observed phenomenology) to have comparably contributing pulsar and wind components when the GeV emission is maximum (equivalently, a pulsar domination when the GeV emission is minimum). The light shaded area in Fig. 4, between 10–100 GeV, emphasizes the region where no data is available at the moment. The other shadowed regions in Fig. 4 represent the minimum and maximum of the wind component allowed by the GeV data, given the assumption of the pulsar contribution, at INFC and SUPC. At INFC (left panel, red shadow) the assumed pulsar spectrum is consistent with the data itself, hence the minimum allowed value of the wind component is compatible with zero. In both plots, the dashed lines represent the wind contribution spectra assumed to derive the red and blue solid lines. These solid lines are the sum up of the pulsar (green line) and the wind (dashed lines) components. One can see from Figure 4 that the appearance of spectral cutoff and the GeV variability can be accommodated in the framework of this idea. In particular, if these two components are emitting GeV photons such that, e.g., at the SUPC both contribute similarly to the GeV flux (see Figure 4 right panel), then: • The anti-correlation of GeV-TeV fluxes is naturally maintained, since it is a generic feature embedded in inverse Compton models describing the TeV fluxes and the pulsar only sums up to it an orbitally-steady contribution. Essentially: from inverse Compton models, the GeV emission is enhanced (reduced) when the highly relativistic electrons seen by the observer encounter the seed photons head-on (rear-on), e.g, see Boettcher & Dermer (2005), Bednarek (2007). • Fermi sees pulsar-like spectra which varies with the orbital phase as the resulting effect of a changing dominance of the two contributions along the orbit. For instance, at 10 GeV in INFC the wind-related contribution, responsible of the TeV flux, may naturally take over and be larger than that of the pulsar, leading to the disappearance of the cutoff. The left panel of Fig. 4 shows that if one sums up a pulsed and a wind contribution, the cutoff may naturally disappear (or get very large) in INFC. In the case of SUPC (blue lines), instead, one is summing up a

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pulsed contribution with something that also must increase (because of the predicted GeV-TeV anti-correlation found in all inverse Compton models, and the constrain of the last Fermi upper limit) towards low energies and thus the cutoff is maintained. A possible increase of the energy (or total disappearance) of the GeV measured exponential cutoff (i.e., why there is no cutoff in the INFC of LS 5039; and why we see such a high cutoff in the integrated-along-the-orbit spectrum of LS I +61◦ 303) can thus be accommodated within this idea. Fermi maybe summing up components that in its range of energies are changing dominance from the inner pulsar to the outer wind contributions. • It would be even harder to detect the pulsation in GeV data (since the pulsed emission is only a fraction of the γ-ray flux observed). However, this concept also implies that a pulsation search in Fermi data will be more successful in those phase ranges corresponding to the Fermi minimum (INFC), where the pulsed fraction is necessarily larger than at SUPC, due to the hardness of the spectrum measured at the neighboring energy band. • Pulsar models based on wind processes (intra or inter-wind) must underproduce the detected Fermi emission, since they lack the contribution made directly by the pulsar magnetosphere. We caveat though that we presented here only a conceptual exploration of this possibility, hence the relative level between the contributions can be altered while maintaining the same overall idea. We also emphasize that the shape of the curves plotted in Fig. 4 for the pulsar and wind contribution is very general. The wind contribution responsible for generating the TeV radiation should be below the upper limit put by Fermi at 10 GeV; and, particularly at SUPC, it should contribute more at lower than at higher energies (if based on inverse Compton, e.g., Bottcher & Dermer 2005, Dubus 2006, Sierpowska-Bartosik & Torres 2008). This 2-components idea can be tested by future observations. In particular, further observations by Fermi can confirm or rule out this concept by investigating the yellow energy range (as reported in Fig. 4) increasing the observing time. Another possibility to test the 2 component model is with a very deep INTEGRAL exposure of LS 5039. The current INTEGRAL fluxes, derived from 3 Ms of IBIS/ISGRI data are (3.54 ± 2.30) × 10−11 erg cm−2 s−1 for INFC, and a flux upper limit for the SUPC phase interval of 1.45 × 10−11 erg cm−2 s−1 (90% conf. level) in the 25–200 keV energy band (Hoffmann et al. 2009). The pulsar spectrum is not expected to be variable with the orbit, and the slope in the hard X-ray should be the extrapolation of that in the MeV band (before the cut-off, of course). We verified that the extrapolation of the assumed pulsar contribution (green line in Fig. 4) to low energies was in agreement with these results, and especially with the INTEGRAL upper limit at SUPC. More IBIS/ISGRI data needs to be collected to possibly constrain the spectral slope of the putative pulsar in LS 5039. In several recent conferences where results of the VERITAS array have been presented (e.g. Aliu et al. 2010, this volume), it was noted that LS I +61◦303 could now be in a low TeV-state at the usual phases where it was detected at such energies; whereas, it seems to be shining normally (or even at a higher level) in GeV. LS I +61◦ 303 is a more complex source than LS 5039, and Be-wind variations can


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introduce variability in the orbital profiles. The latter has been already found in Xrays (Torres et al. 2010). With data now at hand, and lacking orbitally-resolved GeV and TeV follow up, we cannot say more as to the impact of the 2-components idea in the case of LS I +61◦ 303. Finally, we remark that we are not ruling out that a comprehensive model of the wind shock or wind zone contribution that is producing the TeV radiation may –on its own– be enough to describe the GeV phenomenology in detail. We can only safely say that the current models did not appropriately predict it, despite the level of detail they already show. On the other hand, it can only be pertinent to consider that if these sources are pulsar-composed (see, e. g., Dubus 2006a), their magnetospheric contribution could be comparable to that found in all other pulsars detected by the Fermi LAT. If so, this idea presents a natural setup to understand the observed variability in the GeV spectra of these sources.

6 Epilogue At the moment of writing, new VHE facilities are in the process of design. The CTA/AGIS class would put together an array of dozens of IACTs in order to enhance the sensitivity (aimed to be improved by one order of magnitude at 1 TeV when compared with H.E.S.S./VERITAS) and energy acceptance (from a few tens of GeV to 100 TeV). One of the aspects that such facilities could study is the formation of relativistic outflows from highly magnetized, rotating objects. For instance, data on LS 5039, analyzed in the context of PWZ models already rule out that mono-energetic electrons are responsible for most of the emission. What else can future data tell us? How would that impact on current models for dissipation in pulsar winds (see, e.g., Jaroschek et al. 2008 and references therein)? It is not implausible that close systems may trigger different phenomenology within the PWZ, ultimately affecting particle acceleration there. Models of particle energization and dissipation in pulsar winds are currently made for isolated objects, and we lack knowledge on whether the inclusion of such objects in close binaries will affect the wind behavior or even the magnetosphere in appreciable ways. Could we gain knowledge on this using future short-timescales γ-ray observations? Also among the possibilities for future instruments, it is also worth noticing that of the determination of the duty cycles of high-energy phenomena by using continued observations of key objects (such as Cyg X-1) with current instrument’s sensitivity using sub-arrays of future ACTs. It is interesting to note that neutrino detection or non-detection with ICECUBE will also shed light on the nature of the γ-ray emission / limit the neutrino-to-photon ratio irrespective of the system composition (e.g., see Aharonian et al. 2006b, and Torres & Halzen 2007 for applications to LS 5039 and LS I +61◦303, respectively). For instance, Neronov & Ribordy (2009) presented a hadronic model for γ-ray binaries in which the multi-TeV neutrino flux from the source can be much higher and/or harder than the detected TeV flux, and where most neutrinos are produced in pp interactions close to the bright massive star, in a region optically thick for the TeV

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photons. The secondary pairs of these processes would participate in the emission at lower energies. The nature of LS 5039 and LS I +61◦ 303 γ-ray binary systems is still unknown. Whereas current data are consistent, and in some cases prefer, an interpretation based on non-accreting pulsars a final proof in either way (pulsations, accretion lines) is pending. This work has been supported by grants AYA2009-07391 and SGR2009-811. The author warmly acknowledges A. Caliandro, R. Dubois, G. Dubus, D. Hadasch, N. Rea, and A. Sierpowska-Bartosik for discussions.

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Relativistic motion and beamed radiation in gamma-ray binaries Benoˆıt Cerutti, Guillaume Dubus, and Gilles Henri

Abstract Gamma-ray binaries are composed of a massive star and possibly a young energetic pulsar. The stellar wind may confine the pulsar wind in a collimated relativistic outflow. Recent X-ray observations by Suzaku and INTEGRAL of LS 5039 show a steady and periodic X-ray emission correlated with the TeV modulation. The X-ray flux is maximum and minimum at both conjunctions, suggesting that the modulation is due to the peculiar orientation of the binary system with respect to the observer. The X-ray modulation could be explained by the relativistic motion of the flow in the pulsar wind. We investigate the Doppler-boosting effect in synchrotron radiation and inverse Compton scattering in gamma-ray binaries. This model can explain the X-ray modulation in LS 5039 and possibly explain the puzzling phasing of the TeV maximum emission in LS I +61◦ 303.

1 Introduction Gamma-ray binaries are composed of a massive O/Be type star and an unknown compact object in an eccentric orbit. These binary systems have the peculiarity to emit most of their non-thermal radiation in gamma rays (above 1 MeV), hence their name [8]. Today, three gamma-ray binaries are firmly identified as part of this class of object and are orbital modulated TeV sources: LS 5039 [3], LS I +61◦303 [1, 4] Benoˆıt Cerutti Laboratoire d’Astrophysique de Grenoble, UMR 5571 CNRS, Université Joseph Fourier, BP 53, 38041 Grenoble, France, e-mail: [email protected] Guillaume Dubus Laboratoire d’Astrophysique de Grenoble, UMR 5571 CNRS, Université Joseph Fourier, BP 53, 38041 Grenoble, France, e-mail: [email protected] Gilles Henri Laboratoire d’Astrophysique de Grenoble, UMR 5571 CNRS, Université Joseph Fourier, BP 53, 38041 Grenoble, France, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_44, © Springer-Verlag Berlin Heidelberg 2011

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and PSR B1259 − 63 [2]. Gamma-ray binaries may all harbor a young energetic pulsar ([8], see also the contribution by D. Torres in this volume) as in PSR B1259 − 63 where there is a young 48 ms radio pulsar. In the classical picture, pulsar winds are composed of an ultra-relativistic cold plasma of electron-positron pairs propagating at the speed of light up to the termination shock, where the wind momentum is balanced by the external ram pressure (see e.g. [13, 12] and the contribution by J. Arons in this volume). At the shock, the flow is decelerated at a mildly relativistic speed of ≈ c/3. Pairs are isotropized, reaccelerated and radiate via inverse Compton scattering with stellar photons and synchrotron radiation. In gamma-ray binaries, the stellar wind may confine and collimate the pulsar wind at sub-AU scales in a comet-like structure. The non-thermal emission from pairs in the shocked pulsar wind should be boosted by the mildly relativistic motion of the flow. We investigate below the effects of Doppler-boosted emission in gamma-ray binaries.

2 Observational backdrop This study was triggered by the new X-ray observations of LS 5039. The X-ray emission is stable, orbital modulated and correlated with the TeV emission [11, 14]. The X-ray flux is maximum at inferior conjunction and minimum at superior conjunction, suggesting that the X-ray modulation is related to the peculiar orientation of the binary system with respect to the observer. Any intrinsic variation of the physical parameters in LS 5039 appears then quite unlikely to explain this modulation, since conjunctions are special orbital phases only for the observer. Alternatively, the X-ray modulation could be due to the Doppler-boosted emission in the mildly relativitic shocked pulsar wind collimated by the massive star wind in LS 5039. The boosting effect depends on the relative position of the flow with repect to the observer and could therefore provide a simple and geometrical explanation for the Xray modulation. This scenario was previously proposed to produce an orbital modulation of the X-ray flux in the “black widow pulsar” PSR B1957 + 20 [7].

3 Doppler-boosted emission in LS 5039 and LS I +61 303 In a one-zone leptonic model (see e.g. [9]), the X-ray emission is (mostly) emitted by synchrotron radiation of energetic pairs in the shocked pulsar wind. If the magnetic field is comoving with the flow of pairs and if pairs are injected with a power-law energy distribution of index p, synchrotron radiation flux is boosted by the factor D3+α where α = (p − 1)/2 and Dobs = 1/Γ (1 − β cosψobs ) the Doppler factor, with obs −1/2 Γ = 1 − β2 the bulk Lorentz factor of the flow. ψobs is the angle between the observer line of sight and the direction of motion of the flow. Inverse Compton emission is also affected by the Doppler-boost but differently as the source of soft radiation is external to the flow (massive star). The inverse Compton flux emitted

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Fig. 1 Effect of the Doppler-boost on synchrotron (grey lines) and inverse Compton (at 1 TeV, black lines) emission in LS 5039 (left) and LS I +61◦ 303 (right) along the orbit (two orbits shown) with β = 0 (top) and β = 1/3 (middle). In the bottom left panel is shown synchrotron radiation only with Suzaku lightcurve [14] and β = 0.15. The bottom right panel is the same as the one above but where Klein-Nishina effects are considered in the Compton scattering. The orbital parameters are taken from [6] for an inclination of the orbit i = 60◦ . The origin for the orbital phase is set at periastron for both binaries.

by the same population of pairs (those emitting synchrotron radiation) is changed in the Thomson regime [10]. This pattern is similar, though not by a factor D4+2α obs identical, in the Klein-Nishina regime. In LS 5039, the shocked pulsar wind might be radial (i.e. flowing away from the companion star) as the stellar wind velocity is much greater than the orbital velocity of the pulsar, and confined in the orbital plane. In this case, the boost is maximum at inferior conjunction and minimum (deboost) at superior conjunction. Assuming a constant injection of isotropized pairs localized at the compact object position and a constant magnetic field in the comoving frame, the X-ray modulation (shape and amplitude) is well explained for a mildly relativistic motion β ≈ 0.15 (Fig. 1, left panel). The TeV emission is also affected by the boost but the modulation is qualitatively left unchanged since the escaping emission is maximum close to superior conjunction due to gamma-ray absorption with stellar photons. In LS I +61◦303, the stellar wind is composed of a fast tenuous polar wind and a slow dense equatorial wind. If the pulsar remains in the slow equatorial component, the flow is more likely trailing backward in the orbit. Assuming that the flow is always tangent to the orbit and taking the same injection of pairs as in LS 5039, synchrotron and inverse Compton emission are boosted at orbital phases φ ≈ 0.5 − 0.6 (with φ = 0.275 at periastron [6], see Fig. 1 right panel), i.e. close to apastron where both X-ray and TeV observations show a maximum [5], even for a mildly relativistic flow (β = 0.3). Applying the same model to PSR B1259 − 63 does not

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change much the emission [10], partly due to the lower inclination of the orbit (i = 30◦ ).

4 Conclusion The relativistic motion of the shocked pulsar wind can significantly change the non-thermal emission in gamma-ray binaries even for mildly relativistic flow. In LS 5039, the X-ray orbital modulation is reproduced by boosted synchrotron radiation for a bulk velocity of the flow β = 0.15. The TeV modulation remains almost unchanged. This simple geometrical model could also account for the puzzling phasing of the TeV maximum emission in LS I +61◦ 303 and the correlation with the X-ray emission. Acknowledgements The authors acknowledge the support of the European Community via contract ERC-StG-200911.

References 1. Acciari, V. A., et al. (VERITAS Collaboration): VERITAS Observations of the γ-Ray Binary LS I +61 303. ApJ 679, 1427–1432 (2008) 2. Aharonian, F. A., et al. (HESS Collaboration): Discovery of the binary pulsar PSR B1259-63 in very-high-energy gamma rays around periastron with HESS. A&A 442, 1–10 (2005) 3. Aharonian, F. A., et al. (HESS Collaboration): 3.9 day orbital modulation in the TeV γ-ray flux and spectrum from the X-ray binary LS 5039. A&A 460, 743–749 (2006) 4. Albert, J., et al. (MAGIC Collaboration): Periodic Very High Energy γ-Ray Emission from LS I +61 303 Observed with the MAGIC Telescope. ApJ 693, 303–310 (2009) 5. Anderhub, H., et al. (MAGIC Collaboration): Correlated X-Ray and Very High Energy Emission in the Gamma-Ray Binary LS I +61 303. ApJL 706, L27–L32 (2009) 6. Aragona, C., et al.: The Orbits of the γ-Ray Binaries LS I +61 303 and LS 5039. ApJ 698, 514–518 (2009) 7. Arons, J., & Tavani, M.: High-energy emission from the eclipsing millisecond pulsar PSR 1957+20. ApJ 403, 249–255 (1993) 8. Dubus, G.: Gamma-ray binaries: pulsars in disguise? A&A 456, 801–817 (2006) 9. Dubus, G., Cerutti, B., & Henri, G.: The modulation of the gamma-ray emission from the binary LS 5039. A&A 477, 691–700 (2008) 10. Dubus, G., Cerutti, B., & Henri, G.: Relativistic Doppler-boosted emission in gamma-ray binaries. Submitted to A&A (2010) 11. Hoffmann, A. D., et al.: INTEGRAL observation of hard X-ray variability of the TeV binary LS 5039/RX J1826.2-1450. A&A 494, L37–L40 (2009) 12. Kennel, C. F., & Coroniti, F. V.: Confinement of the Crab pulsar’s wind by its supernova remnant. ApJ 283, 694–709 (1984) 13. Rees, M. J., & Gunn, J. E.: The origin of the magnetic field and relativistic particles in the Crab Nebula. MNRAS 167, 1–12 (1974) 14. Takahashi, T., et al.: Study of the Spectral and Temporal Characteristics of X-Ray Emission of the Gamma-Ray Binary LS 5039 with Suzaku. ApJ 697, 592–600 (2009)

A leptonic One-Zone model of the X-Ray/VHE correlated emission in LS I +61 303 V. Zabalza, J.M. Paredes and V. Bosch-Ramon

Abstract The MAGIC collaboration has recently reported correlated X-ray and VHE gamma-ray emission from the gamma-ray binary LS I +61◦ 303 during ∼60% of one orbit, thus suggesting that the emission in these two bands has its origin in a single particle population. Using a one zone population of relativistic leptonic particles with dominant adiabatic losses located at the position of the compact object we are able to reproduce the observed X-ray and VHE lightcurves. From the best fit result, we obtain the magnetic field, energy budget and acceleration efficiency of the accelerator, and discuss these in the context of the young non-acretting pulsar and acretting compact object scenarios. The results also confirm that the GeV emission detected by Fermi does not come from the same parent particle population as the X-ray and VHE emission.

1 Introduction LS I +61◦ 303 is one of the few X-ray binaries (along with PSR B1259-63, LS 5039 and Cygnus X-1) that have been detected in very high energy (VHE) gamma rays. It is a high-mass X-ray binary containing a compact object with a mass between 1 and 4 M⊙ orbiting the main star every ∼ 26.5 d in an eccentric orbit [see 6]. Observations of persistent jet-like features in the radio domain prompted a classification of the source as a microquasar [14], but later observations along a whole orbital period revealed a rotating elongated feature that was interpreted as the interaction V. Zabalza · J.M. Paredes Departament d’Astronomia i Meteorologia and Institut de Ciències del Cosmos (ICC), Universitat de Barcelona (UB/IEEC), Mart´ı i Franquès 1, 08028, Barcelona, Catalonia, Spain, e-mail: [email protected],[email protected] V. Bosch-Ramon Max Planck Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg (Germany) e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_45, © Springer-Verlag Berlin Heidelberg 2011

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between a pulsar wind and the stellar wind [8]. In the X-ray domain LS I +61◦ 303 shows an orbital periodicity [13] with quasi-periodic outbursts in the phase range 0.4–0.8 . The source shows short-term flux and spectral variability in timescales of kiloseconds [17, 15]. LS I +61◦ 303 has been detected in the VHE domain by MAGIC [4] and VERITAS [2]. It shows a periodic behaviour [3] with maxima occurring around phase 0.6–0.7 and non-detectable flux around periastron (φ = 0.275). Models of both accreting and non-accreting scenarios have attempted to explain the broadband spectrum and its orbital behaviour [9, 7]. The combined effect of short-term variability in the X-ray domain and night-tonight variability in the VHE domain has precluded a clear detection of X-ray/VHE emission correlation from archival observations. In 2007, a campaign of simultaneous observations with the MAGIC Cherenkov telescope and the XMM-Newton and Swift X-ray satellites revealed a correlation between the X-ray and VHE bands [5]. The suggestion that the emission in both energy bands comes from the same population of accelerated particles turns these observations in an ideal data set to test the properties of the accelerator in LS I +61◦ 303. Here we present a leptonic one zone model to explain the exceptional data from these observations.

2 Model description and results The discovery of correlation between the X-ray and VHE bands is important because it points towards the mechanism of emission modulation at both bands. The fast and simultaneous changes in flux in both bands indicate that the modulation mechanism has to directly affect the emission level of the IC and synchrotron processes. There are two mechanisms that may modulate IC emission independently of synchrotron emission: anisotropic IC scattering and photon-photon pair production [12, 10]. Synchrotron emission, on the other hand, would only be independently modulated through a modulation of the magnetic field. The only way to simultaneously modulate both the X-ray and VHE emission is to consider a modulation of the number of emitting particles through dominant adiabatic losses, which are a manifestation of the energy losses of electrons through (magneto)hydrodynamical processes in the accelerator region possibly related to the interaction of the pulsar wind or the black hole jet with the stellar wind of the massive companion. In the regime of dominant adiabatic losses the emitted X-ray flux is proportional to the number of emitting particles, so the orbital dependency of adiabatic losses can be inferred from the X-ray lightcurve. The hard X-ray spectrum with photon index Γ ≃ 1.5 also points towards dominant adiabatic losses, which imply an injection electron index of αe ≃ 2. [18] applied the same reasoning to understand the X-ray/VHE correlation found in LS 5039. In this work we adopt a leptonic model for X-ray and VHE gamma-ray emission from LS I +61◦ 303 in which emission comes from a single region with homogeneous physical properties located at the position of the compact object. We have calculated the broad band emission from this region along the orbit and obtained the

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Fig. 1 SED averaged over the observation periods during peak between phases 0.6 and 0.7, with synchrotron (dot-dashed) and IC (solid). The crosses show the XMMNewton EPIC-pn spectrum averaged over three observations and deabsorbed taking NH = 5 × 1021 cm−2 . The MAGIC simultaneous spectrum is shown as a red bow-tie.

fluxes and spectral indexes that would be observable in the X-ray (0.3–10 keV) and VHE gamma-rays (Eγ >400 GeV). The lack of detectable VHE emission during periastron [3] and the lack of pair production absorption due to angular effects indicates that the number of emitting particles is low even though significant X-ray emission (about half of the peak flux) is detected. This can be explained by considering that not all of the X-ray emission is correlated with the VHE band, but only an excess or flaring fraction over a pedestal flux. We have used the excess X-ray flux over a fixed pedestal to infer the phase dependency of adiabatic losses along a whole orbit. In Fig. 1 we show the SED averaged over the phase ranges of the three observations with phases between 0.6 and 0.7, along with the observed X-ray and VHE spectra. As can be seen in Fig. 2, we have been able to reproduce the X-ray and VHE lightcurves obtained during the 2007 multi-wavelength campaign. The adiabatic cooling times range from a few tens to a few hundred seconds and results in a quite efficient accelerator with η ≃ 7 −130 and accelerator sizes of R ≃ (1 −16) ×1012 cm. The X-ray/VHE flux ratio is best described by an ambient magnetic field of B = 0.25 G, and the fit is very sensitive to this parameter. The energy budget needed for these results is around ∼ 1035 erg/s, well within values attainable by both of the proposed scenarios for the source. A detailed account of this model and its results and implications will be shortly submitted for publication.

3 Discussion While this work is not able to discern between the two proposed scenarios, the quality of the data and simple model place strong constraints on the accelerator physical properties that will have to be fulfilled by any detailed model of the source. However, it is clear that, at least during the phases around the X-ray and VHE peaks, adiabatic losses dominate over radiative losses. Phase-averaged emission in the GeV band is much lower and peaks at apastron instead of periastron when compared with

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Fig. 2 Top: X-ray lightcurve observed during the multiwavelength campaign with XMM-Newton (filled circles) and Swift/XRT (open circles). The pedestal flux is indicated by a horizontal dashed line. Bottom: VHE daily lightcurve observed by MAGIC. Observations with significance above 2σ are shown in filled squares while 95% CL upper limits are shown otherwise. In both panels the predicted lightcurve from the model (with B = 0.25 G) in each band is shown as a solid red line.

the Fermi detection of the source [1]. Therefore, we conclude that GeV emission is not originated in the same particle population as X-ray and VHE.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Abdo, A. A., Ackermann, M., Ajello, M., et al. 2009, ApJ, 701, L123 Acciari, V. A., Beilicke, M., Blaylock, G., et al. 2008, ApJ, 679, 1427 Albert, J., Aliu, E., Anderhub, H., et al. 2009, ApJ, 693, 303 Albert, J., Aliu, E., Anderhub, H., et al. 2006, Science, 312, 1771 Anderhub, H., Antonelli, L. A., Antoranz, P., et al. 2009, ApJ, 706, L27 Aragona, C., McSwain, M. V., Grundstrom, E. D., et al. 2009, ApJ, 698, 514 Bosch-Ramon, V., Paredes, J. M., Romero, G. E., & Ribó, M. 2006, A&A, 459, L25 Dhawan, V., Mioduszewski, A., & Rupen, M. 2006, in VI Microquasar Workshop Dubus, G. 2006, A&A, 456, 801 Dubus, G., Cerutti, B., & Henri, G. 2008, A&A, 477, 691 Frail, D. A. & Hjellming, R. M. 1991, AJ, 101, 2126 Khangulyan, D., Aharonian, F., & Bosch-Ramon, V. 2008, MNRAS, 383, 467 Paredes, J. M., Marti, J., Peracaula, M., & Ribo, M. 1997, A&A, 320, L25 Massi, M., Ribó, M., Paredes, J. M., et al. 2004, A&A, 414, L1 Rea, N., Torres, D. F., van der Klis, M., et al. 2010, arXiv:1002.2223 Rolke, W. A., López, A. M., & Conrad, J. 2005, NIMPRA, 551, 493 Sidoli, L., Pellizzoni, A., Vercellone, S., et al. 2006, A&A, 459, 901 Takahashi, T., Kishishita, T., Uchiyama, Y., et al. 2009, ApJ, 697, 592

New Optical Results on γ-ray Binaries J. Casares, J.M. Corral-Santana, A. Herrero, J.C. Morales, T. Muñoz-Darias, I. Negueruela, J.M. Paredes, I. Ribas, M. Ribó, D. Steeghs, L. van Spaandonk and F. Vilardell

Abstract We present new optical spectroscopy of the γ-ray binary LS 5039. Our data show evidence for sub-orbital modulation in the radial velocities with amplitude ∼7 km/s and period ∼ Porb /4. This short-term oscillation is stable over at least 7 years and it is likely triggered by non-radial oscillations of the O6.5V optical star. We also present the results of a spectroscopic campaign on MWC 148, the optical counterpart of the new γ-ray binary candidate HESS J0632+067. Long-term variations in the Hα and Hβ emission line parameters are clearly detected which, if modulated with the binary orbit, would imply a period >200 days.

1 Introduction There are only three confirmed galactic High Mass X-ray Binaries (HMXBs) with persistent TeV emission (PSR B1259-63, LS 5039 and LSI +61 303, see [1]) and one recently proposed candidate (HESS J0632+067 [2]). The VHE emission in the 3 confirmed binaries is strongly modulated with the orbital period, suggesting that the emitter is rather compact and close to the massive star. However, the origin of the VHE emission remains unclear, with competing leptonic and hadronic scenarios which invoke either inverse Compton scattering of stellar photons or proton-proton collisions in a jet/pulsar wind scenario. Obviously, the nature of the compact star is an important ingredient in the different γ-ray production models. PSR B1259-63 contains a pulsar whereas a black hole is not ruled out in LS 5039 and LSI +61 303. In this context optical studies can bring new insights through constraining the compact object mass with dynamical studies. J. Casares Instituto de Astrof´ısica de Canarias (IAC), E-38200 La Laguna, Tenerife, Spain and Departamento de Astrof´ısica, Universidad de La Laguna (ULL), E-38205 La Laguna, Tenerife, Spain, e-mail: [email protected] ⋆ The affiliation of other co-authors is listed in the acknowledgements. N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_46, © Springer-Verlag Berlin Heidelberg 2011

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2 Revised Orbital Solution in LS 5039 LS 5039 was the first γ-ray binary detected by HESS, with a TeV luminosity of ∼1034 erg s−1 . It was previously classified as a HMXB with spatially resolved radio emission at milliarcsec scale, atributed to either a relativistic jet or a pulsar wind. The first determination of the 3.9d orbital period and system parameters was reported by [3]. The orbital parameters were found to depend on the spectral lines used in the cross-correlation analysis. In particular, the Balmer and HeI solutions are blueshifted with respect to the HeII solution and also show a larger scatter. This is expected if low excitation lines are contaminated by P-Cyg profiles and, hence, the HeII velocities provide a much better description of the orbit of the optical star [3]. A tentative low inclination angle in the range 23–27◦ was derived under the assumption that the companion star is pseudo-synchronized, i.e., synchronized at periastron. This results in a compact object of 3–5 M⊙ and, thus, the possibility that LS 5039 harbours a low-mass black hole (see [3] for details).

Fig. 1 Updated radial velocity curve in LS 5039. Left: velocities folded on the best ephemeris with a two Fourier term fit sumperimposed. Filled circles indicate INT data from 2002 & 2003 reported in [3], open triangles are SAAO data from 2005 and open circles INT data from 2007 and 2009. Right: Same as left but with an extra sine wave to account for the short-term modulation.

New spectrocopy was obtained in 2005, 2007 and 2009 using the 1.9m telescope at SAAO and the INT at La Palma. Fig. 1 displays the new radial velocity points, together with data from [3], folded on the best orbital solution. The orbital modulation is clearly distorted by a short-term oscillation with amplitude ∼ 7 km s−1 and a ∼1d period or Porb /4. In order to test the significance of this perturbation we fitted the eccentric orbital modulation with a 2-term Fourier series and obtain a reduced χ2 of 11.3 (left panel in Fig. 1). We subsequently added an extra sine wave to account for the short period oscillation and find that the reduced χ2 drops to 7.1 (right panel in Fig. 1), thus confirming that the short-term modulation is highly significant. We note

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that this modulation must be stable over our 7 years database, otherwise it would be blurred in the phase folded radial velocity curve. Table 1 Orbital solutions for LS 5039 Parameter

Eccentric Fit

Eccentric Fit + 1d oscillationa

Porb (days) T 0 (HJD−2 450 000) e w (◦ ) γ (km s−1 ) K1 (km s−1 ) a1 sin i (R⊙ ) f (M) (M⊙ ) rms of fit (km s−1 )

3.90597± 0.00009 2478.11± 0.08 0.30± 0.03 215± 6 17.3± 0.5 23.1± 0.9 1.70± 0.07 0.0043± 0.0005 8.3

3.90608± 0.00008 2478.08± 0.06 0.35± 0.03 212± 5 17.3± 0.5 24.2± 0.9 1.75± 0.07 0.0047± 0.0006 6.4

a

The period has been fixed to Porb /4

Ignoring this perturbation can certaintly bias the final orbital solution as illustrated in Table 1. The 2 columns compare the binary parameters obtained through a proper eccentric model fit to the HeII velocities with and without the 1d oscillation. Both, the eccentricity and radial velocity semi-amplitude K1 are underestimated if the 1d oscillation is neglected. Also the periastron angle and the absolute phasing differ. The key binary parameters are still consistent within 1-σ but the difference can be larger when the fit is performed over scarcely sampled radial velocity curves. We note that this short-term modullation is very reminiscent of the 5 km s−1 oscillation detected in Vela X-1 at 1/4 of the orbital period [4]. Following the work on Vela X-1 we propose that the 1d modulation in LS 5039 is caused by tidally excited non-radial oscillations of the O6.5V star in its eccentric orbit. The presence of this oscillation may also have an impact on the VHE radiation models because of the role played by the stellar photons and hence it should be investigated.

3 Probing Binarity in MWC 148 MWC 148 is the optical counterpart of the point-like TeV source HESS J0632+067 and it has been recently proposed as a candidate γ-ray binary based on the spectral properties and variability observed in both radio and X-rays [2]. In Oct 2008 we started a spectroscopic campaign to observe MWC 148 using several telescopes at the Teide and Roque de los Muchachos observatories. The averaged spectrum shows Hα and Hβ emission lines superimposed on a B0-type stellar spectrum dominated by HeI absorption lines (without any emission component). From the HeI profiles we estimate a rotational broadening v sin i = 370 km/s. Since Be stars are known to rotate at typically 0.7–0.8 times the critical rotation velocity (i.e. ∼565 km/s for a

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B0V star) the binary inclination must be moderately high, in the range ∼55–70◦. Cross-correlation of the absorption lines with a broadened template star gives velocity excursions of a few tens km s−1 but no clear periodicity is observed. Fig. 2 Time evolution of Hα emission line parameters in MWC 148 from October 2008 until April 2010. Top panel shows the EW, middle panel the FWHM and bottom panel the centroid velocity obtained through a Gaussian fit. The same trend is observed in Hβ but with lower amplitude.

However, a dramatic change in the emission line parameters is detected between November 2009 and January 2010 (see Fig. 2). The lines become narrower, the EW drops by a factor 2 and radial velocity variations are also seen. If these changes are modulated with the binary phase then the orbital period must be longer than 200 days. However, superorbital Hα variations due to precession of the circumstellar disc are also commonly seen in Be X-ray binaries [5]. Clearly many more observations are needed before the orbital period and binary parameters can be constrained. Acknowledgements Affiliation of co-authors is as follows: J.M. Corral-Santana and A. Herrero (IAC & ULL, Spain), J.C. Morales and I. Ribas (IEEC, Spain), T. Muñoz-Darias (Obs. Brera, Italy), I. Negueruela and F. Vilardell (Univ. Alicante, Spain), J.M. Paredes and M. Ribó (Univ. Barcelona, Spain), D. Steeghs and L.van Spaandonk (Univ. Warwick, UK). J.C. acknowledges support from the Spanish MCYT through the project AYA2007-66887 and I.N. through project AYA2008-06166-C03-03. J.M.P. and M.R. acknowledge support by DGI of the Spanish MEC under grant AYA2007-68034-C03-01 and FEDER funds. M.R. also acknowledges support from MEC and European Social Funds through a Ramón y Cajal fellowship. Partly funded by the Spanish MEC under the Consolider-Ingenio 2010 Program grant CSD2006-00070: first science with the GTC.

References 1. 2. 3. 4. 5.

Holder J. 2009 in Fermi Symposium, arXiv:0912.4781 Hinton J.A. et al. 2009, ApJ, 690, L101 Casares J., Ribó M., Ribas I., Paredes J. M., Mart´ı J., Herrero A. 2005, MNRAS, 364, 899 Quaintrell H. et al. 2003, A&A, 401, 313 Negueruela I., Reig P., Coe M.J., Fabregat J. 1998, A&A, 336, 251

The International X-ray Observatory and other X-ray missions, expectations for pulsar physics Yukikatsu Terada and Tadayasu Dotani

Abstract Pulsar systems are very good experimental laboratories for the fundamental physics in extreme environments which cannot be achieved on ground. For example, the systems are under conditions of high magnetic field strength, large gravitational potential, and fast rotation, representing highly-ionized hot plasmas with particle acceleration etc. We can test phenomena related to these extreme condition in the X-ray to sub-MeV bands. In future, we will get fantastic capabilities of higher sensitivities, larger effective area, higher energy resolutions, and X-ray imaging capabilities with wider energy band than current missions, in addition to opening new eyes of polarization measurements, and deep all sky monitoring capabilities, with future X-ray missions including ASTRO-H, eRossita, NuSTAR, GEMS, International X-ray Observatory (IXO) and so on. In this paper, we summarize current hot topics on pulsars and discuss expected developments by these future missions, especially by ASTRO-H and IXO, based on the current design parameters.

1 Introduction Currently, we have nice missions like Chandra, Newton, and Suzaku, as well as INTEGRAL, Swift, MAXI, and so on. In very near future in 2010s, we will have the ASTRO-H mission in addition to small satellites like NuSTAR, eROSITA, GEMS, etc. After the decade, we will have an ultimate X-ray mission, named international Xray observatory (IXO) in 2020s as shown in Fig.1. The performances of these future missions are summarized in section 2. Y. Terada Saitama University, 255 Simo-Ohkubo Sakura-ku Saitama city Saitama 338-8570, Japan, e-mail: [email protected] T. Dotani ISAS/JAXA, 3-1-1 Yoshinodai Chuuo-ku Sagamihara-city Kanagawa 252-5210, Japan, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_47, © Springer-Verlag Berlin Heidelberg 2011

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Fig. 1 Artists view of the current and next-generation X-ray missions

Then, what should we do on pulsars with future missions? Table 1 summarizes the key sciences of NuSTAR, ASTRO-H, and IXO, which are officially announced.

Table 1 Key Science on future missions. Objectsa

IXO (2021–)

BH,NS,AGN

• Matter under Extreme • Physics under extreme • Survey of Massive BH Condition environment • Relativistic space-time • Galactic Center Region near BH

SNR,SN,Star, BH,AGN

• Life cycles of matter • Evolution of Cluster of • Nucleaosynthesis in SN and energy galaxies • Co-evolution of BH and galaxy

SNR,NS, WD,CG CG a

ASTRO-H (2014–)

NuSTAR (2011–)

• Variety of the non- • Cosmic-ray accelerathermal universe tor • Formation of Structure • Evolution of Cosmic structure with DM

BH: black hole, NS: neutron star, WD: white dwarfs, SNR: supernova remnant, SN: supernova, AGN: active galactic nuclei, CG: cluster of galaxies

Title Suppressed Due to Excessive Length

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These key topics cover many sciences widely, but they can be roughly categorized into four classes; (1) the fundamental physics on extreme environment, (2) the life cycle of materials, (3) non thermal emissions from accelerated particles, and (4) the formation of cosmic structure. Among these items, topics related to neutron stars are shown in bold style in the table. Therefore, one of our goals on pulsars with future missions is in the fundamental physics on extreme environments. In this paper, we pick up the following items and describe in detail in section 3, as examples of pulsar sciences with future missions. • • • • •

General relativity under strong gravity, Equation of State in neutron stars, Plasma physics under a strong magnetic field, Emission mechanism from Magnetars, Diversity of Pulsar systems, white dwarf pulsars.

2 Future X-ray Missions 2.1 Overview of X-ray Missions Many kinds of X-ray missions are listed in section 1, such as Suzaku, Chandra, XMM-Newton, NuSTAR, GEMS, eROSITA, ASTRO-H, and IXO. Specific features and characteristics of these missions can be summarized in diagrams of Fig. 2. Imaging capabilities, like effective areas, angular resolutions, wide-energy band-pass, and the field of view, are indicated in the left 1/3 hemisphere of the diagram. Spectroscopic features, like energy resolutions and wide-band sensitivities, are shown in the right 1/3 part. Other additional characteristics, like fast timing capabilities and polarization measurement, are plotted in the bottom part of the diagram. As shown in the Fig. 2 top left, the current missions have complementary performances; Chandra has super high angular resolution, XMM-Newton has large effective area, and Suzaku has wide-band and high-sensitive spectroscopic performances. Thus, these three current missions covers upper hemisphere of the diagram, complimentary. In very near future, we will have small satellite missions, named NuSTAR, GEMS, and eROSITA. As shown in the Fig. 2 top right, these three missions will explore new capabilities in the left bottom part of the diagram; i.e., hard X-ray imaging, polarization, and deep all sky survey. The details are summarized in section 2.2. Following these small missions, we will have general-purpose X-ray observatories, ASTRO-H and IXO, covering high performances in the diagram, as shown in Fig. 2 bottom. Most prominent feature of ASTRO-H is the high energy-resolution spectroscopic feature with the micro-calorimeter array. IXO will have an excellent X-ray mirror with huge effective area of 30,000 cm2 . The detail descriptions of ASTRO-H and IXO are given in sections 2.3 and 2.4, respectively.

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Yukikatsu Terada and Tadayasu Dotani Effective Area Angular Resolution

Chandra

Effective Area Wide-band Spectroscopy

XMM

Angular Resolution

Wide-band Spectroscopy

Suzaku Wide-band Imaging

Wide-band Energy Resolution Imaging NuSTAR

Energy Resolution

eROSITA Fast Timing

Wide Field of view

Wide Field of view

Polarization Effective Area Angular Resolution

Angular Resolution

Wide-band Spectroscopy

IXO

ASTRO-H

Wide-band Energy Resolution Imaging

Fast Timing

Wide Field of view

Fast Timing

Polarization Effective Area Wide-band Spectroscopy

Wide-band Imaging

GEMS

Energy Resolution

Fast Timing

Wide Field of view

Polarization

Polarization

Fig. 2 Comparison of features between X-ray missions. (Top left) diagram of the current missions, Suzaku, XMM-Newton, and Chandra. (Top right) the next small missions, NuSTAR, eROSITA, and GEMS. (Bottom left and right) ASTRO-H mission and the IXO.

In summary, future missions will have capabilities of the followings. • • • • • •

High energy-resolution spectroscopy(ASTRO-H, IXO) Hard X-ray imaging (NuSTAR, ASTRO-H) Huge collection area of X-rays (IXO) High sensitivities in soft gamma-ray band (ASTRO-H) All sky monitoring function (eROSITA) Polarization measurement (GEMS, ASTRO-H)

2.2 The Small Satellite Missions in 2010s The nuclear spectroscopic telescope array (NuSTAR) is a NASA SMEX (small explorer) mission, which is planned to be launched in 2011 to archive the hard X-ray imaging in 5 to 80 keV band for the first time, carrying the focusing hard X-ray telescope. The previous X-ray mirrors utilize total-reflection to focus soft X-ray photons. It requires very small incidence angles, and therefore, in principle, the re-


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flection energies with the practical design of mirrors are limited in the soft X-ray band below 10 keV. The new hard X-ray mirrors use the Bragg reflection process to focus hard X-ray photons. The mirrors are coated by multi-layers to reflect hard X-rays via Bragg reflection to cover up to 80 keV band with the effective area of 70 – 1000 cm2 . The focal length of the optics is as long as 10 meters as illustrated in Fig. 3. The current design of NuSTAR represents the angular resolution of 7.5 arcsec (FWHM) and energy resolution of 1.2 keV at 68 keV with CdTe focal-plane detectors.

http://www.nustar.caltech.edu/

eROSITA

GEMS

http://www.mpe.mpg.de/heg/ http://heasarc.gsfc.nasa.gov/docs/gems/ www/Projects/EROSITA/main.html

Fig. 3 Artists view of the next-generation small missions, NuSTAR, eROSITA, and GEMS.

The extended ROentgen Survey with an Imaging Telescope Array (eROSITA) will perform the first imaging all-sky survey in the medium energy X-ray range up to 10 keV with an unprecedented spectral and angular resolution. The instruments will be carried by Spectrum-Roentgen-Gamma (SRG) satellite, which will be launched in 2012. The telescope will consist of seven X-ray optics, which consist of mirrors and pn-CCD cameras developed for XMM-Newton. The on-axis effective area will reach 2000 cm2 with seven telescopes in total. The satellite will be operated at three types of all-sky scanning observation modes, covering 20,000 deg2 in 3 years with

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the sensitivity at the 10−14 erg cm−2 s−1 level below 2 keV band, or 200 – 300 deg2 at 10−15 erg cm−2 s−1 sensitivity below 2 keV band. The Gravity and Extreme Magnetism SMEX (GEMS) is also a NASA SMEX mission, which will be launched in 2014. The mission performs X-ray polarization measurements in the 2 – 10 keV band with the photo-electron tracking gas-pixel detector. The energy range is mainly determined by the X-ray telescope, which covers below 10 keV band having a focal length of 4.5 meters as illustrated in Fig. 3. The goal of the current design of the polarization measurement is the minimum detectable polarization (MDP) at 0.2% (99% confidence) at 1 Crab flux or MDP of 2% at 10m Crab level [1].

2.3 The ASTRO-H Mission The ASTRO-H mission is the sixth series of the Japanese X-ray satellites [2], which will be launched in 2014. This is the Japan and US collaboration mission with a part of ESA members. In addition to engineering interests on many challenging instruments and the spacecraft bus system using SpaceWire networks as a future standard satellite, ASTRO-H will be a multi-purpose observatory of many scientific topics as already listed in Table 1. Table 2 Design parameters of ASTRO-H. Optics

Instruments

Parametersa

SXS + SXT (0.3 – 10 keV)

Micro Calorimeter + Soft X-ray Mirror

∆ E = 7 eV (4 eV goal) EA = 260 cm2 at 6 keV

SXI + SXT (0.4 – 10 keV)

P-ch CCD camera + Soft X-ray Mirror

∆ E = 150 eV FOV = 38 arcmin PSF = 1.7 arcmin(FWHM) EA ∼ 368 cm2 at 6 keV

HXI + HXT (5 – 70 keV)

DSSD+CdTe stack surrounded by BGO + Hard X-ray Mirror

∆ E ∼ 2 keV FOV = 9 arcmin PSF = 1.7 arcmin(FWHM) EA ∼ 300 cm2 at 30 keV 1 – 10 µ Crab sensitivityb

SGD (10 – 600 keV)

DSSD+CdTe stack surrounded by BGO (no focusing mirror)

∆ E ∼ 2 keV FOV = 33.3 arcmin EA ∼ 100 cm2 0.1 – 1 m Crab sensitivityb

a

∆ E means the energy resolution, EA means the effective area, PSF means the point spread function (or angular resolution), and FOV means the field of view. b Sensitivity at 1 M sec exposure.


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ASTRO-H carries four types of X-ray optics, SXS+SXT (Soft X-ray Spectrometer plus Soft X-ray Telescope), SXI+SXT (Soft X-ray Imager plus Soft X-ray Telescope), HXI+HXT (Hard X-ray Imager plus Hard X-ray Telescope), and SGD (Soft Gamma-ray Detector), as listed in Table 2. The design parameters of these instruments are also summarized in the table. The most important feature of ASTRO-H is the high resolution spectroscopy with the micro calorimeter array, named SXS, with the energy resolution of about 7 eV (or 4 eV as a goal) with a rather large effective area of 200 cm2 [3]. In ground developments, they have already achieved the energy resolution of 3.8 eV. The second importance is the hard X-ray imaging capability up to 80 keV band by the HXI+HXT system with the larger effective area of 300 cm2 at 30 keV than that of NuSTAR. The HXT employs the “multi-layer super mirror” technique using the Brag reflection as described in section 2.2, which already verified by balloon experiments of InFOCµS series. The focal plane detector of the HXT is the hard X-ray instrument named HXI, which is the stack of 4 DSSDs (double sided Si strip detectors) and 1 CdTe strip detector surrounded by the BGO crystals as anti-coincidence shield counters [4]. The mission also carries the CCD camera, named SXI, on the focal plane of the other SXT, with the wide field of view of about 38 arc minutes in the 0.4 – 10 keV band. The third importance of this mission is the super high sensitivity in the soft gamma-ray energy band. This feature is achieved by the SGD (soft gamma-ray detector), which is Si-and-CdTe Compton-cameras with a narrow field of view. Although the SGD employs the Compton camera technique, the detector has little imaging capability, achieving quite high sensitivities at 1 mCrab level at the subMeV energy range by using the Compton kinematics as a powerful method to reject backgrounds [5, 6]. In other words, the ASTRO-H will improve their sensitivities in the hard X-ray band above 10 keV band by one or two order of magnitude by the HXI and the SGD, respectively, than the current mission.

2.4 The International X-ray Observatory The international X-ray observatory (IXO) is an international mission in collaboration with NASA, ESA, and JAXA to be realized in 2020s [7]. The satellite is now planned to be launched as early as 2021, combining a super large X-ray mirror with many instruments as listed in Table 3. The most prominent feature of IXO is a huge single X-ray mirror with a 3.0 m2 collecting area and 5 arc-second angular-resolutions in the softer energy band. The energy coverage of the X-ray mirror will be extended to the hard X-ray range with an effective area of 150 cm2 at 30 keV, with a focal length of about 20 meters. IXO will carry a micro calorimeter detector, named XMS (X-ray Micro calorimeter Spectrometer), which is the next generation of the micro-calorimeter array from ASTRO-H, adopting the transition-edge-sensor technique. The XMS will achieve the energy resolution of about 2.5 eV in the 0.3 – 7 keV band. IXO also carries a grating

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Table 3 Design requirements for IXO instruments. Instruments

Detector

Parameters

Mirror

soft X-ray Mirror soft X-ray Mirror hard X-ray Mirror

EA = 3 m2 at 1.25 keV EA = 0.65 m2 at 6 keV EA = 0.015 m2 at 30 keV

XMS (0.3 – 7 keV)

Micro Calorimeter

∆ E = 2.5 eV (FWHM) and FOV = 2 arcmin ∆ E = 10 eV (FWHM) and FOV = 10 arcmin PSF = 5 arcsec (HPD)

WFI/SXI (0.1 – 15 keV)

CCD camera

∆ E = 150 eV (FWHM) and FOV = 18 arcmin PSF = 5 arcsec (HPD)

WFI/HXI (7 – 40 keV)

Si+CdTe+BGO

PSF = 30 arcsec (HPD)

XGS (0.3 – 1 keV)

Grating Optics

E/∆ E = 3000

HTRS

Si Drift

106 cps with < 10% deadtime

XPOL

Polarimetry

1% MDP, 100 ksec, 5 × 10−12 cgs (2-6 keV)

optics, named XGS (X-ray Grating Spectrometer), achieving a resolving power of E/∆E ∼ 3000. IXO also have a wide band imager, a kind of a hybrid detector consisting of WFI (Wide Field Imager) and HXI (Hard X-ray Imager), which have almost the same design as the SXI and HXI on-board ASTRO-H. The mission also has new types of instruments, such as HTRS (High Time Resolution Spectrometer) and XPOL (X-ray Polarimeter), as listed in Table 3. The HTRS is a silicon drift sensor having a high count-rate acceptance up to 106 counts-per-second with less than 10 % dead time. The XPOL is a a fine-grid Gas-Pixel-Detector having high polarization sensitivity reaching 1 % level for a 1mCrab full-polarized light with 10 ksec exposure.

3 Pulsar Sciences with Future X-ray Missions 3.1 General relativity under strong gravity X-rays from compact accreting objects come from in-flowing materials onto the objects. Therefore, we can probe the extreme environment near the compact object via X-ray spectroscopy, such as strong gravity and relativistic motion of the accreting matter.


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3.1.1 Recent Studies The discovery of the gravitationally red-shifted line emission from a massive black hole, active galactic nuclei MCG-6-30-15, is one of the most important results with ASCA [8]. They found a red-shifted double-wing line structure of Fe K line in the Xray spectrum taken with ASCA. Such a profile was theoretically predicted by Fabian et al (1984) six years before the observational report [9]. The profile is caused by a Doppler effect of the rotating motion on the accretion disk as well as the gravitational red shift by the strong gravity of the black hole following the Einstein’s general theory of relativity. Recently, gravitationally red-shifted line emissions are reported from several neutron star systems, such as Serpens X-1 [10], 4U1820-30, and GX349+2 [11] with XMM-Newton and Suzaku. However, the line profile has a very extended lowenergy wing, and it is difficult to distinguish from continuum emissions when the observation is in a narrow energy range. Thus, some other groups pose a question on the discovery of the gravitational red-shifted emissions [12]. They argue that if they take into account the pile-up effects of the detector correctly, then the wide wings around the Fe line band are disappeared; i.e., the spectra do not require the gravitationally red-shifted profile. This situation is mainly caused by the difference of the definition of the continuum model. So, the wide-band spectroscopy is the key of this observation. 3.1.2 Future prospects The recent argumentation on the discovery of gravitationally red-shifted emissions from neutron stars is mainly caused by the difference of the continuum models. In future works, we first have to verify of the line profiles with wide band spectroscopy in the X-ray band. ASTRO-H will detect X-ray emissions of objects up to 400 keV with very high sensitivities in the hard X-rays to the soft gamma-ray band. Then, we can test a complex continuum model by separating several components, such as reflection radiation, Compton-scattered component, disk black body emission, etc, to recognize the line structure. Then, we can enjoy the general relativity around neutron stars. With the huge effective area of the IXO mission, it can catch line profiles in a very fast time resolution with very good statistics. According to the calculation of the time evolution of X-ray spectra from an accretion disk [13], we can catch the trajectory of accreting blobs one by one [14]. Then, as well as the Doppler effect of the rotation of the accretion disk, the gravitational red-shifts as a function of in-falling time will be observed directly with the IXO [15]. Therefore, this study will directly link to the challenges of the verification of the general relativity.

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3.2 Equation of State in neutron stars Inner structure of a neutron star is highly dependent on the physics in high energies [16]. Currently, it is considered to have a shell structure, from center to surface: inner core, outer core, inner crust, outer crust, and atmosphere. This structure strongly depends on the equation of state of cold materials of neutron stars in high-density and high-pressure environments under a strong gravity. 3.2.1 Recent Studies The equation of states of matters in a neutron star, described by the pressure and the density, can be observed by global parameters like mass and radius of the object. The mass-radius relationships for neutron stars, reflecting the equation of states of cold super-dense matter, are calculated in several conditions by many authors [16]. Thus, measurements of the mass and the radius are important for the tests of these theoretical expectations. Observationally, we can measure the mass of a neutron star from the binary motion if the object has a companion star [16], but it is limited to very few objects. Radius of a neutron star can be derived by the flux of the black body emission with the Stefan-Boltzmann’s low when the distance to the object is known, but there are many difficulties in the infrared and optical observations of black body component, because of many contamination lights [17]. Measurement of gravitationally red-shifted emission or absorption lines will give us the information of gravity; i.e., the ratio between the mass and the radius. This method is already successful in the white dwarf cases [18]. In 1980s, absorption feature was found with Tenma and EXOSAT from neutron stars, X1636-536, X160852 etc, during its X-ray bursts [19, 20, 21], and studies of estimation of the mass and radius were performed [22]. Recently, a red-shifted absorption lines are found from a neutron star, EXO0748-676, during the X-ray flare, in the grating spectra of XMM-Newton satellite [23]. They found many significant absorption features with a red-shift of z=0.35, which is consistent with models of neutron stars if they assume the mass of the neutron star is in a range of typical value of 1.3 to 2.0 solar masses. 3.2.2 Future prospects With the current instruments, from absorption lines on X-ray spectra of an atmosphere on a neutron star, we measure only the gravitational red-shift value, as an observational parameter related to the mass and radius of the neutron star. In other words, we cannot obtain the mass and radius ’independently’ with the current instruments. In future, the IXO provides the sensitive X-ray spectroscopy and fast photometry with high energy resolutions, and thus IXO can achieve phase-resolved high-


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resolution spectroscopy. The spectroscopic observation of X-ray bursts with IXO, showing the atomic absorption lines, will give us information of the acceleration of gravity at the stellar surface and the gravitational red-shift separately [24], through the X-ray spectroscopic features by the pressure broadening and general relativistic effects [25]. Therefore, we can determine the radius and mass separately with the IXO [26]. In this way, it is feasible to test the equation of states of neutron stars by measuring the mass and the radius of the objects with the future missions.

3.3 Plasma physics under a strong magnetic field Accreting binary pulsars are good targets to study radiation transfer of X-ray photons under strong magnetic field in a range of 1012 Gauss. Several objects show the cyclotron resonance scattering features (CRSFs) in their X-ray spectra, because the cyclotron resonance energy E a comes in the X-ray energy band as Ea = 11.6B12(1 + zg )−1 keV, where B12 is the magnetic field strength in unit of 1012 Gauss and zg is the gravitational red-shift at the resonance points. Since the first discovery of CRSF from neutron stars from Her X-1 [27], the cyclotron resonance features are well studied with many X-ray missions on about 15 X-ray pulsars [28]. However, there still remain many mysteries on the radiation transfer process under the strong magnetic field. 3.3.1 Recent Studies Observation of CRSF in the X-ray band is one of the direct measurements of the magnetic field strength of neutron stars. In this measurement, the resonance energy Ea is considered to represent the surface magnetic field strength of the object. Interestingly, recently, several X-ray pulsars such as 4U 0115+63 and X0331+53 show the changes of Ea as a function of their X-ray luminosities [29]; the cyclotron energies are increased when X-ray luminosity became low. This phenomenon should be due to the variation of the height of the X-ray emitting accretion column by their luminosity or accretion rate. This means that, if we observe the object in a lower luminosity phase, we will measure the magnetic field at lower part of the column near the surface of the neutron star. Nakajima et al. (2006) interprets the luminosity dependence of the resonance energy in terms of the correlation between the X-ray luminosity and the column height assuming the dipole shape of the magnetic field[29]. The studies are closely related to the basic questions on the accretion manner along the magnetic field line and/or the magnetic-field structures of neutron stars. Among 15 X-ray pulsars showing CRSFs, several objects show harmonic feature of the resonance absorption lines. One of the most impressive demonstrations is the detection of four harmonics from X0115+634 with BeppoSAX [30]. The resonance energy of higher harmonics is strongly related to the quantum electromagnetism;

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whether the ratio of resonance energies between the fundamental and second harmonics is exactly 2.0 or not. Currently, it is consistent with 2.0 within large statistical errors with the recent measurements, and thus more sensitive instruments in the harder X-ray band are needed. Furthermore, recently, RXTE found a hint of luminosity dependence of the ratio of resonance energies, posing several interesting questions on the radiation transfer in the accretion column under the strong magnetic field [31]. The CRSFs from many X-ray pulsars have been detected only in absorption. Recently, a Japanese group reported a hint of a cyclotron resonance ’emission’ feature instead of absorption from a neutron star 4U1626–67 in the dim phase with Suzaku [32]. Considering that the atmospheres on magnetized white dwarfs are known to show cyclotron emission features in the ultraviolet band [33], whether the feature is in absorption or emission may depends on the optical depth of the plasma; i.e., optically thin plasma produces emission lines, whereas thick case produces absorptions. In the case of 4U1626–67, the emission feature was found only in a dim phase and other phases show absorption spectra, thus, the variation of the optical depth by its directions is suggested. 3.3.2 Future prospects With future missions, we will get wide-band spectroscopic capabilities and polarization instruments. From the recent observations, we can set the following fundamental questions to solve with future missions. • Geometry of plasma and magnetic field on neutron stars, whether it is dipole field or not • Cyclotron resonance physics related to quantum magnetism • Radiation transfer in the accretion plasmas under strong magnetic field

To solve the first item, we need to search for CRSFs from X-ray pulsars in lower X-ray luminosity phase. Several X-ray pulsars show the luminosity dependence of the resonance energies, but some other objects do not, even when their luminosities are two orders of magnitude lower than those in the brighter phase [34], where the fluxes are comparable to the sensitivity limit of the current instruments like HXD on-board Suzaku. The HXI and SGD instruments on-board ASTRO-H, having one or two orders of magnitude higher sensitivities in the hard X-ray band, will be indispensable for the study. The second item can be recognized into two sub topics; resonance energies of harmonics, as described in section 3.3.1, and the shape of resonance feature (whether it is Gaussian or Lorentz shape), which will help our understandings on the electron energy-distributions and cyclotron resonance process [35]. These two topics will request us the wide-band spectroscopy, which will be achieved soon by the future mission, ASTRO-H. To have new information on the third topic, as well as numerical approaches on the radiation transfer in accretion columns, we have to try first, observationally, to

575

0.1

0.1


Wien hump

BOTTOM phase

10−4

keV/cm2 s keV

Emission

ASTRO-H

1

10 Energy (keV)

100

10−7

10−6

10−5

10−3 10−4 10−5

keV/cm2 s keV

Emission

Suzaku

10−6 10−7

Absorption Wien hump

10−3

BOTTOM phase

PEAK phase

Absorption

0.01

0.01

PEAK phase

1

10 Energy (keV)

100

Fig. 4 (left) X-ray spectra of 4U1626-67 at bright and dim phases of the spin modulation taken with Suzaku. The best fit models are shown in line. (right) The same X-ray spectra but expected for the ASTRO-H observation with 100 ksec exposures.

verify the cyclotron resonance emission feature, which was statistically insignificant with the current mission. As demonstrated in Fig.4, ASTRO-H will give us fine phase-resolved X-ray spectra with higher qualities to distinguish it is absorption or emission. As already described in section 3.3.1, the emission may be caused by an anisotropy of the optical depth of cyclotron resonance photons in plasmas of neutron stars. This should be an application of higher optical-depth cases of accretion plasmas of cataclysmic variables, where we can observe anisotropic transfer of atomicresonance photons in plasmas on the magnetic pole of white dwarfs [36, 37]. In addition, polarization measurements around the resonance energy with future missions, like ASTRO-H and IXO (GEMS does not cover the hard X-ray band), will give us more information on the transfer of X-mode and O-mode photons under strong magnetic field [38].

3.4 Emission mechanism from Magnetars Anomalous X-ray Pulsars (AXPs) and Soft Gamma-ray Repeaters (SGRs) are recognized as neutron stars with super strong magnetic fields reaching 1015 Gauss, named magnetars [39]. Mysterious features of magnetars still pose us many fundamental questions. Why they have so strong magnetic field? What is the energy source of the X-ray emissions? How they are formed?

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3.4.1 Recent Studies Pulsars are rotating magnets, and their electromagnetic radiations are normally originated from the rotational energy of the neutron star. Actually, X-ray emission from normal pulsars are only 0.1 – 1 % of the spin-down energy loss [40]. One of most mysterious feature of magnetars is their X-ray luminosities, which always exceed the rotational energy loss. Thus, the energy source of the radiation of magnetars is a mysterious question. One possible answer is a decay of magnetic field. Pons et al (2007) found a clear relation between the magnetic field strength and the effective temperature of the neutron star surface of normal pulsars and magnetars, and they argue that the decay of magnetic field heats the surface of neutron stars especially for magnetars [41]. Recently, theoretical groups proposed a conversion mechanism from magnetic energy into radiation [42]. However, the energy source of magnetars emissions and its conversion mechanism are still open question. Another important discovery of magnetars is the hard X-ray component above 10 keV, from 1E 1841–045 and other three AXPs with INTEGRAL and RXTE [43, 44]. Recently, in addition to the flare phases, such a hard tail was fond even in the quiescent phase from a magnetar 1E 1547.0–5408 with Suzaku [45]. Since the components have a very hard photon index of about 1.0 and have a large pulsed fraction, the radiation energies will exceed the spin-down energies even largely if the hard X-ray emission is included. The nature of this component is also an open question. In addition to the above two questions related to the fundamental physics on magnetic field of magnetars, another importance in the astrophysics is the evolution of magnetars. ’How they are formed? ’ Hints on this question can be found in a recent discovery of a pulsar wind nebula near the magnetars, 1E1547.0-5408 [46], and an important report of the association of two magnetars candidates with a TeV supernova remnant, CTB37B [47]. 3.4.2 Future prospects We have many fundamental questions on magnetars. As presented in the previous section 3.4.1, we can pick up the following three topics; • What is the energy source of radiation? • What is the origin of the hard X-ray component? • How the magnetars are formed?

The first step for future missions to study the first question is to perform the direct measurement of the magnetic field strength of magnetars. Do they really have a magnetic field reaching 1014−15 Gauss? This value is indirectly estimated from the spin frequency and its derivative assuming that the energy loss is completely due to a dipole magnetic radiation. However, there is no observational justifications for this assumption, because no electromagnetic emission originated from the dipole


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magnetic radiation is detected. Thus, it is important to measure the magnetic field strength directly as a first step. In future missions, we have two ways to measure magnetic field strength directly. One method is to search for a possible proton cyclotron resonance feature in the X-ray spectra of magnetars like electron CRSFs shown in section 3.3, since the proton resonance energy will come into the soft energy range when the magnetic field strength is in the range of 1014−15 Gauss. Observationally, verification of the absorption feature as the proton cyclotron line is critical for this study, which can be achieved by detecting higher harmonics features in addition to the fundamental line. Therefore, high-energy resolution spectroscopy with ASTRO-H and IXO will help us. The other method is to perform polarization measurements in the soft energy range. The polarization fraction between the linear and circular polarizations, which will be available with GEMS and IXO, will give us information to constrain the magnetic field strength of magnetars [48]. To study the second topic, the wide-band spectroscopy in the sub MeV band is a discovery space of the hard X-ray component of magnetars, in order to distinguish many kinds of emission models, like Synchrotron emission, non-thermal bremsstlahlung, super thermal bremsstrahlung, or a broad emission via photon splitting effect under a quantum critical magnetic field. In addition, to promote the third topic, continuous efforts of hard X-ray surveys of magnetars and X-ray follow-up observations of TeV sky are important. Hard X-ray imaging capability with NuSTAR and ASTRO-H will be very helpful.

3.5 Diversity of Pulsar systems: white dwarf pulsars The final topic is the diversity of pulsar systems. Basic parameters in pulsar systems should be only three; magnetic field strength, characteristic age, and the inclination of the magnetic dipole axis to the spin axis. However, we have so many kinds of systems like radio pulsars, millisecond pulsars, magnetars, CCOs, XDINS, GeV pulsars, TeV nebulae, etc, as plotted in Fig.5. Why so highly diverse? What is the unified picture of pulsars? These questions are one of the final goals of pulsar physics. 3.5.1 Recent Studies To find out hints on the question of the large diversity of pulsar systems, one interesting approach is to search for white dwarf pulsars. Why we do not have WD pulsars? Magnetosphere of neutron stars and white dwarfs should be the same; basically, they are the rotating magnets. Generally speaking, white dwarfs have weaker magnetic field and longer spin periods as shown in Fig.6 left. Normally, it is hard to observe neutron stars with long spin period below the death line. Are emission mecha-


10 39 erg / 10 38 s erg / 10 37 s erg / 10 36 s erg / 10 35 s erg / 10 34 s erg /s

578

−10

Magnetars GeV Pulsars

−12

3

y

Log[dP/dt]

10

−14

4

y

5

y

6

y

7

y

8

y

10

10

−16

10

10

−18

10

Radio Pulsars

−20

ms Pulsars −3

−2.5

−2

−1.5

−1

−0.5

Abedo et.al 2010 + magnetars

0

0.5

1

1.5

Log [P(s)]

Fig. 5 Scatter plot between period and period derivative of neutron stars [49]. 1036

1016

0.01 0.1

1

10 100 103 104 105 10 P(sec)

6

1

V

V

0

10 1

10 1

2

V

4

g/s 10 2

0

er

/s

g/s er

er g

8

4

er

/s

0.01 0.1

10 2

1026

10 2

1027

104

g/s

1029 1028

106

10 1

1030

6

108

White Dwarfs

1031

er g

White Dwarfs

Neutron Stars

1032

10 3

Neutron Star

1033

2

1010

1034

10 3

Magnetic Momentum

B(G)

1012

10 1

6

V

1035

1014

10

100 103 104 105 106

P(sec)

Fig. 6 Scatter plot between period and magnetic field strength (left) or magnetic moment (right) of neutron stars and white dwarfs [50, 28, 51, 37, 52].

nisms in rotating compact objects, like rotation-powered pulsars, turned off in white dwarf systems? To compare the systems between neutron stars and white dwarfs, we can make a scatter plot of the magnetic momentums, instead of surface magnetic fields, as shown in Fig.6 right. So the several magnetized white dwarfs are the kind of magnetars. Observationally, non-thermal incoherent radio emission has in fact been detected from seven WDs via systematic radio surveys [53, 54, 55, 56, 57], and several objects were reported to show TeV emission [58, 59, 60]. If we find out white dwarf pulsars, we can survey wide parameter ranges of the magnetic fields, the spin periods, and the system scales, by two or three orders of magnitude from the neutron star cases. In addition, if they generate high energy


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particles, they should be very important on galactic cosmic-ray origins, because white dwarfs exist everywhere in the universe.

Suzaku

10−4

Non-thermal

10−7

60

10−6

80

Thermal

10−5

Suzaku HXD 10-30 keV P = 33.6 msec

Crab (Neutron Star)

keV/cm2 s keV

100 0.05

0.1

10−3

0.15

0.01

Suzaku XIS 4-10 keV P = 33.1 sec

0

1

0.5

Spin Phase

1.5

2

10−8

40

Counts/sec

Counts/sec

0.2

AE Aquarii (White Dwarf)

1

10 Energy (keV)

100

Fig. 7 Left panel show the spin profile in X-ray band of AE Aqr and Crab pulsar taken with Suzaku [63, 64]. Right panel shows the X-ray spectrum of AE Aqr with Suzaku [64].

Among the magnetized white dwarfs, AE Aqr is one promising object of white dwarf pulsar [61, 62], and recently the object is observed in the X-ray band with a purpose of searching for possible non-thermal emission with Suzaku [64]. They find some marginal pulsation like neutron stars as shown in Fig.7 left. With the current mission, the X-ray spectrum can be interpreted either by thermal component with very high temperature or a non-thermal power-law model, as shown in Fig.7 right. The X-ray luminosity of the hard X-ray component comes to about 0.5% of the spin down luminosity of the object; this number is quite similar to the neutron star cases [40]. Therefore, the AE Aqr is most promising candidate of the white dwarf pulsar. 3.5.2 Future prospects In the future, first of all, we have to try to confirm the first white dwarf pulsar candidate, AE Aqr. Normally, the X-ray emissions from cataclysmic variables show thermal radiations in the soft X-ray band below 20 keV, and thus the contamination of thermal emissions will easily disturb the survey of possible non-thermal emission behind the bright thermal radiation. However, ASTRO-H will detect non-thermal component in the hard X-ray band clearly, as demonstrated in Fig.8 left. In addition, we have more samples in isolated magnetized white dwarfs, from which thermal emissions from accretion plasmas are expected to be smaller than those in cataclysmic variables. With super high sensitivities of IXO, we can survey about three orders of magnitude dimmer objects than AE Aqr as shown in Fig.8; quantitatively, about 30 samples are there in the current catalog. The discovery space of white dwarf samples is now expanding with the deep optical survey, SDSS [65]. Finally, we will have more objects to compare characteristics between white dwarf pulsars and neutron star pulsars.

0.01

Yukikatsu Terada and Tadayasu Dotani 0.01

580

10−5

10−4

10−3

ASTRO-H (AE Aqr)

ASTRO-H ( 1/10 AEAqr) 10−6

Non-thermal

keV/cm2 s keV

10−4 10−5

Thermal

10−6

keV/cm2 s keV

10−3

ASTRO-H

10−7

10−7

IXO ( 1/100 AEAqr)

10 Energy (keV)

100

10−8

10−8

IXO ( 1/1000 AEAqr) 1

1

10 Energy (keV)

100

Fig. 8 Left panel show the X-ray spectrum of AE Aqr expected for the ASTRO-H mission with 100 ksec exposure. Right panel show X-ray spectra of possible non-thermal emission from objects with the X-ray flux of 1/10, 1/100, 1/1000 of AE Aqr with ASTRO-H or IXO with 100 ksec exposures.

4 Synergy with other wavelength observatories Many future missions like ASTRO-H and IXO are pointing satellite with a narrow field of view but superb sensitivities. How can we get new interesting transient objects, like magnetars, accretion powered pulsars, and new astrophysical objects? Tight collaboration with instruments having all-sky monitoring function, shown in Fig.9, is important for current and future missions.

Fig. 9 The all sky maps in TeV, GeV, X-ray, and infrared energy bands, from top to bottom, respectively.


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For the successful X-ray observations in future, collaboration with other wavelength is very important. We live in so lucky era to have very nice missions, like Cherenkov Telescope Array in TeV band, IXO, SPICA in the infra-red band, and ALMA in the radio band, as illustrated in Fig.10.

Fig. 10 Near future missions in various energy bands.

References 1. Swank J. et al in ’X-ray Polarimetry: A New Window in Astrophysics’, Rome 2009, edited by R. Bellazzini, E. Costa, G. Matt and G. Tagliaferri (2009) 2. Takahashi T. et al, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (2008) 3. Mitsuda K. et al, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (2008) 4. Kokubun M. et al, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series (2008) 5. Tajima H. et al, IEEE Transactions on Nuclear Science, 52 , pp2749 - 2757 (2005) 6. Tanaka T. et al, IEEE Conference Record (NSS/NIC), pp 2140 - 2144 (2009) 7. Bookbinder J. and the IXO collaboration, 8. Tanaka Y. et al, and massive black hole in the active galaxy MCG-6-30-15”, Nature 375, pp659-661, (1995) 9. Fabian A. C., Rees, M. J.,Stella L. and White, N. E., MNRAS, 238, pp729-736, (1984) 10. Bhattacharyya S. and Strohmayer T. E., ApJ 664, L103-L106 (2007)

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Title Suppressed Due to Excessive Length 63. Terada Y. et al, PASJ 60 ppS25-S35 (2008) 64. Terada Y. et al, PASJ 60 pp387-397 (2008) 65. Adelman-McCarthy J.K. et al ApJS 172, pp. 634-644 (2007)

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X-ray Polarimeters Marco Feroci and Paolo Soffitta

Abstract X-ray polarimetry is entering a new era, thanks to the significant technological developments allowing the design of new and very sensitive experiments. In this chapter we briefly remark the importance of the polarimetric diagnostic tools in the investigation of the physics of neutron stars, and provide an overview of both classical and new techniques for X-ray polarimetry in astronomy. Finally, we report about the characteristics and scientific potential of the focal plane X-ray polarimeters that have the highest chances to be flown over the next decade.

1 Neutron Stars Science with X-ray Polarimetry In this section we briefly itemize the most prominent areas of interest where the measurement of X-ray polarization can provide an insight to the physics of the neutron stars and of their close environment. In most models information on phase and energy dependent X-ray polarization would provide, in some case definitive, constraints to the underlying physics. Pulsar Wind Nebulae (PWN). PWN are bubbles of relativistic particles and magnetic field produced by the interaction of the relativistic pulsar wind with the ambient medium. Detailed hydrodynamical simulations (e.g., Bucciantini et al. 2005) show how spatially resolved polarimetry can constrain the flow speed and the amount of disordered or poloidal magnetic field. The degree of linear polarization can reach up the highest levels allowed by the synchrotron emission mechanisms, ∼70%, especially along the polar axis and the central regions of the torus. Marco Feroci Istituto Nazionale di Astrofisica (INAF), Istituto di Astrofisica Spaziale e Fisica Cosmica (IASF) Rome, Via Fosso del Cavaliere 100, Rome, e-mail: [email protected] Paolo Soffitta Istituto Nazionale di Astrofisica (INAF), Istituto di Astrofisica Spaziale e Fisica Cosmica (IASF) Rome, Via Fosso del Cavaliere 100, Rome, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_48, © Springer-Verlag Berlin Heidelberg 2011

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Rotation-powered Pulsars. The phase and energy resolved polarimetry of the Xray emission from rotation-powered pulsars can probe the emission sites and mechanisms of high energy radiation, constraining the different geometric models for pulsar emission (e.g., polar cap, outer gap, slot gap). Detailed phase-resolved polarimetry is indeed available at optical wavelengths for the Crab Pulsar (Slowikowska et al. 2009), challenging the relevant predictions from models based on different emission mechanisms (e.g., Dyks et al. 2004). Isolated neutron stars and Magnetars. The opacity of a highly magnetized plasma depends on the polarization properties of the radiation, therefore the emergent radiation from an isolated pulsar or a magnetar can be linearly polarized up to ∼20-30%, with characteristic dependency on energy, temperature and magnetic field (Pavlov & Zavlin 2000). The degree of polarization may indeed reach much higher levels if QED effects are taken into account. Heyl & Shaviv (2002) and Lai & Ho (2003) showed that the birefringence effects foreseen by QED in a magnetized vacuum imply different opacities for the two polarization modes (parallel and orthogonal to the magnetic field), leading to a high degree of polarization in the observed radiation. Vacuum polarizations effects have been studied by Niemiec & Bulik (2006), in magnetar bursts, where they show that the emerging radiation in 2-20 keV is highly (up to ∼100%) linearly polarized, except for narrow features at the proton cyclotron and vacuum resonance. X-ray Pulsators. It is still matter of debate whether the emission from a pulsar accreting onto the polar caps is in the form of a ’fan’ or ’pencil’ beam. In both these accretion geometries, high (up to ∼80% at the cyclotron frequency) linear polarization is expected, strongly dependent on the rotational phase. Correlating the measurement of the intensity as a function of the phase with similarly resolved polarimetry it is possible to distinguish between the two geometries (Meszaros et al. 1988). The observed degree of polarization depends on the orientation between the line of sight and the magnetic field. In addition, the amplitude of the swing of the polarization angle across the rotational phase would provide a measurement of the angle between the rotation axis and the dipole axis of the magnetic field, usually a free parameter in the models. Millisecond X-ray pulsars. The millisecond pulsars are faster rotators than ”standard” pulsators, and have a less intense magnetic field. In these sources the disk can arrive close to the neutron star surface. Compton scattering is expected to polarize radiation emitted by hot spots on the neutron star surface. Whether the polarization may derive from reflection from the disk (Sazonov & Sunyaev 2001) or from Compton scattering in the accretion flow (Viironen & Poutanen 2004) is a matter of debate. Phase resolved polarimetry compared with the pulse shape can discriminate between these two options.

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2 Fundamental Parameters of X-ray Polarimetry X-ray polarimetry is a relatively unusual technique in the field of X-ray Astronomy, for this reason its fundamental parameters and formulas are not widely known across the scientific community, although they are rather standard among specialists. To the benefit of the understanding of the next sections, we summarize here the main quantities, referring the interested reader to a more extensive and deep discussions, e.g., in Novick (1975). In general, a linear polarization analyzer is a device responding differently to radiation with different polarization properties. Since the linear polarization direction is invariant for rotations of 180◦ in the plane orthogonal to the travel direction of photons, usually the response is a modulation curve of the type described by the following formula: M(φ) = A + Bcos2(φ − φ0 ),

(1)

Mmax − Mmin B = . Mmax + Mmin B + 2A

(2)

where A is a constant term, B is the amplitude of the modulation, related to the degree of linear polarization, and φ is related to the angle of linear polarization. Under this simplified scenario, the response to unpolarized radiation is a flat curve, that is B=0. This general description allows us to introduce some important quantities. We define as modulation the following ratio:

In the ideal case of 100% linearly polarized radiation, the maximum observed modulation is a measurement of the efficiency of the device as a polarization analyzer, and it is defined as Modulation Factor µ. In the general case of any polarization degree, the knowledge of the response of the polarimeter allows the user to normalize the observed modulation and derive the polarization degree of the impinging beam: P=

1 B . µ B + 2A

(3)

The linear polarization is defined as a positive quantity. As such, any measurement will provide a response greater or equal to 0. It is therefore possible to compute which level of polarization will result as a consequence of the counting statistics. This leads to the definition of the ”polarization sensitivity” in terms of the Minimum Detectable Polarization (MDP), to a pre-defined confidence level (here assumed to be 99%), as r 4.29 B + ǫFA MDP (99%) = , (4) ǫµFA T where B is the background rate, ǫ is the detection efficiency of the polarimeter, F is the source flux, A is the collecting area, T is the total integration time.

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For the case of focal plane polarimeters, that we will concentrate on in this paper, the background is negligible in most of the practical cases. In these conditions, the formula (4) can be approximated as MDP(99%) =

µ×

4.29 √ NCounts

(5)

where NCounts (equal to ǫ × F × A × T ) is the total number of source counts. This approximation is useful to understand the number of photons required for a sensitive polarimetric measurement in realistic conditions. If we assume the reasonable value of µ=0.5 to reach a minimum detectable polarization of, say, 5% approximately 3×104 counts are needed, few orders of magnitude higher than what typically requested for imaging detection or (moderate-resolution) spectroscopy.√The same formula (4) also allows to identify a merit factor of polarimeters, as µ × ǫ.

3 Classical Techniques and Observational Status The linear polarization of X-rays in laboratory and in astronomical contexts can be measured by exploiting the well known dependence of the Bragg diffraction and Thompson/Compton scattering on the photon polarization status. The techniques based on these effects present important limitations when implemented in experiments, nonetheless they were the ones used to achieve the only X-ray polarization measurements available in X-ray astronomy to date. In this section we will briefly illustrate the techniques and experimental set-up and summarize the observational results they made possible.

3.1 Bragg Polarimeters The Bragg diffraction is, under proper conditions, very sensitive to the linear polarization state of the incoming photon. Let us consider the geometry of Bragg diffraction from a crystal, as shown in Figure 1. If a photon impinges with an angle of 45◦ with respect to the surface of the crystal and it is diffracted at the same angle, the Bragg diffraction ensures that the emerging photon has an electric vector oscillating in the direction orthogonal to the plane of incidence, identified by the directions of the incoming and diffracted photons and the normal to the plane of the crystal. In this respect, a Bragg crystal is a perfect polarizer. As such, it can be used as a polarization analyzer: in ideal conditions, if a Bragg crystal is oriented at 45◦ with respect to the direction of the radiation source to be analyzed, only those photons linearly polarized with electric field oscillating in the direction orthogonal to the plane of incidence will be diffracted at 45◦ . If the crystal is rotated around the pointing direction, the amplitude and phase of the modulation of the diffracted photons provides

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a direct measurement of the degree and angle of linear polarization of the source. In fact, unpolarized radiation gets diffracted uniformly as the system rotates. What above would make polarimetric life easy. However, the ideal conditions are met only in a very narrow (i.e., few electronvolts) energy range around the Bragg energy E B (θ) defined as: nhc E B (θ) = , (6) 2d sin θ where h and c are respectively the Planck’s constant and the speed of light, d the crystal lattice spacing and n an integer which specifies the diffraction order. To overcome this problem, Bragg crystals are manufactured in such a way to slightly ”misorient” the crystal lattice in order to have the Bragg law satisfied at an angle of 45◦ for a wider energy range. This kind of crystals are dubbed ”mosaic crystals”. The efficiency of diffraction, i.e. the total intensity of diffracted radiation, is a characteristic of the crystal. It is commonly expressed with the integrated reflectivity R E : Z π 2 RE = P E (ϑ)dϑ, (7) 0

where ϑ is the angle of diffraction and PE (ϑ) is the normalized intensity reflected at an angle ϑ. A higher integrated reflectivity means that the intensity of diffracted radiation is higher. When the polarization properties are considered, it is useful to define an integrated reflectivity for each of the two polarization planes, as RπE and RσE . They are useful to define their ratio k=RπE /RσE as a merit factor of the crystal polarimetric efficiency. Figure 2 shows how k depends on energy and angle, thus illustrating the overall efficiency of the crystal as a polarization analyzer and its effective bandwidth (in the range of ∼2-300 eV using mosaic crystals). The very narrow energy response of such polarimeter on one side brings to small effective areas, on the other allows high energy resolution even with low resolution detectors.

Plane of the crystal

σ−component π−component

θ =45°

Unpolarized Incident Radiation

Plane of incidence

Normal to the plane of the crystal

Diffracted Polarized Radiation

Fig. 1 The geometry definitions in Bragg diffraction, as used in the text (from Muleri 2009).

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Since a Bragg crystal is able to analyze the linear polarization status of the photon beam only in the direction orthogonal to the plane of incidence, an X-ray polarimetry experiment based on this effect must be rotated about the pointing axis, in order to sample all the possible angles of polarization. In practice, the geometry of such an experiment is outlined in Figure 3: a Bragg crystal is placed at the focus of an Xray optics with a 45◦ inclination with respect to the optical axis. An X-ray detector surrounding the crystal (or co-rotating with it) collects the diffracted photons. The azimuthal modulation of the detected count rate is a measurement of eq.1 and allows to determine the degree and angle of linear polarization of the observed source. The use of a position-sensitive detector permits to image the source, according to the point spread function of the optics and the position resolution in a secondary focus 90◦ apart. Of course, by rotating the detector and the crystal the brightness of the secondary image is modulated by the polarized X-rays. This configuration allows for minimizing the background due to the fact that (not considering possible misalignment) the secondary source is always located in the same detector area during the rotation. In non focal plane experiment it is possible to devise a configuration in which the Bragg cristals are disposed in a paraboloid surface covering 360◦ (e.g., ROXANE Proposal) with the detector in the central area of this parabolic surface. It should be noted that this configuration implies a dispersive measurement (i.e., photons with different polarization angles hits separate detector areas), thus disfavoring the background rejection issue.

Fig. 2 The ratio of integrated reflectivity for radiation polarized parallel and perpendicular to the plane of incidence, as a function of the diffraction angle (from Muleri 2009), for a graphite crystal.

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3.2 Thompson/Compton Polarimeters The other physical effect that has been often used to generate linearly polarized X-rays is the Compton (and Thompson) scattering. The dependence on linear polarization of the photon is already in the Klein-Nishina formula: ! dσKN 1 = r02 ω2 ω − sin2 θ cos2 φ , (8) dΩ ω where r0 is the classical electron radius, ω is the ratio between scattered and incident photon energies, θ is photon scattering angle and φ the angle between the direction of scattering and that of polarization (see Fig. 4). If the energy E is much smaller than the rest mass of electrons, ω ≈1 (Thompson limit) and then: dσT = r02 1 − sin2 θ cos2 φ dΩ

r0 =

1 e2 , E ≪ me c2 4πω0 mc2

(9)

When the scattering is limited in the plane orthogonal to incident direction, i.e. θ = π/2, Eq. 9 becomes: dσT = r02 sin2 φ . (10) dΩ In its ideal case, also Thompson scattering at 90◦ allows for building a perfect analyzer. However, such an approximation does not really hold in practical experiments. In a Thompson polarimeter, the scattered photon does not produce a detectable energy release in the scatterer, so the latter is a passive element. The thinner

Fig. 3 A general sketch of the geometrical configuration for a bragg polarimeter

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the scatterer and the detector are, the higher is the experimenter ability to select photons scattered at 90◦ and the higher the modulation factor µ is. However, a very thin scatterer and detector lead to a very small probability for the detection of Thompson scattered photons, that is a low efficiency ǫ. A trade-off between these two effects implies to have a reasonable thickness of the scattering element, bringing to a wider acceptance in scattering angle θ, in turn causing a decrease in the modulation factor, according to eq. 9 (see, e.g., Matt et al. 1996 for an extensive treatment). Another competing effect is the multiple scattering. This applies mostly to the case of an experiment that does not use X-ray optics, where the cross-section area of the scatterer is effectively the geometric area of the polarimeter. Here a wider scatterer allows to intercept more source photons, thus reaching a larger efficiency, but when the photon is scattered near 90◦ it must cross a thicker layer, with a higher chance to be scattered a second time, losing information on the polarization of the original photon. In addition to that, even in the absence of a multiple scattering, a large section of the scatterer loosen the ability to reconstruct the kinematics of the event (that is, the real point of interaction). Then, in general, in Thompson polarimeters the scatterer is a long (that is, thick in the direction parallel to the source photons) and thin (to favor the escape of the scattered photon) pin of low Z material (to optimize the ratio between the cross section for Thompson scattering and photoelectric absorption). A general sketch of such geometry is given in Fig. 5. This makes the selection of the scattering angle looser, and the modulation factor smaller, but the efficiency higher. In contrast to a Bragg polarimeter, in principle a Thompson polarimeter can operate without any rotation. However, in practice rotation is often required to avoid or average out systematic effects. The scattering cross section is dominant over other photon-matter interactions in a wide range of energies, between the decrease of the photoelectric effect (say, above a few tens of keV, depending on materials) up to the rise of pair-creation probability, above a few MeV. For this reason, scattering polarimeters can effectively operate in

Polarization vector Scattering point Initial direction

φ

θ Final direction

Fig. 4 The definitions of the geometry of the Compton scattering, as used in the text (from Muleri 2009).

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the hard X-rays. In this case, the Thompson limit does not longer hold and the full treatment of Compton scattering is required. A practical consequence is that the energy transfer to the Compton electron is not negligible and can be used to have the scatterer as an active device (that is, producing a detectable signal). In many cases (e.g., when the active scatterer is segmented) this allows to have a large geometrical section for the scatterer, without losing information on the kinematics of the event. Since it is much more difficult to focus hard X-rays, scattering polarimeters usually require large collecting areas and the possibility to use an active scatterer is crucial. It should be noted, however, that eq. 8 shows that at increasing energies (say, above ∼100 keV) the modulation of the process with the photon polarization status gradually decreases (see, e.g., Matt et al. 1996). A typical implementation of such geometry is, for example, the one studied by Costa et al. (1995). The active scatterer is made of a low Z detector (a plastic scintillator) and it is segmented in order to be able to reconstruct the point of the first scattering. The scattered photon is then expected to be absorbed by a segmented ”wall”, the ”absorber”, symmetrically surrounding the scatterer, providing the calorimetric elements for the kinematics. The absorber is a high Z detector (e.g., a fast inorganic scintillator), in order to achieve a high quantum efficiency at high energies. The same approach can be used in pixellated detectors, even when not specifically designed as polarimeters. In this case, double events can be associated to photons that are Compton scattered in one pixel and photoelectrically absorbed in another pixel. The relative positions of the two pixels with respect to the source direction allows to estimate the scattering direction and to build a modulation curve. When a Compton polarimeter is used for hard X-rays, its sensitivity is generally determined by the lowest discrimination threshold it can be set at the scattering

Fig. 5 A general sketch of the geometrical configuration for a scattering polarimeter

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stage, where the least energy release is left over. This directly determines the bandpass of the experiment. The other major issue, especially in non-rotating experiments doing polarimetry as a ”by-product”, is the control of the systematic effects.

3.3 Observational results Despite the great importance of polarimetry as an investigation tool in X-ray Astronomy, very few experiments have successfully operated in this field in the past. In fact, the available results concerns mostly, if not only, the Crab Nebula. The most important is certainly the measurements carried out in the 70’s by Bragg polarimeters onboard rocket flights and the satellite mission OSO-8. Novick et al. (1972) made the first successful measurement of the linear polarization of the Crab Nebula in 1971 using two experiments onboard an Aerobee-350 sounding rocket. The experiments were a Thompson scattering polarimeter, using Lithium scatterers and proportional counters, operating in 5-20 keV, and a Bragg polarimeter, using ∼45◦ diffraction at 2.6 and 5.2 keV in a graphite crystal towards proportional counters. Although the experiments were exposed to the source for only 247s net, they both resulted independently in a positive detection of the linear polarization of the Crab Nebula. The combined measurement provided a degree and angle of polarization of (18.2±6.1)% and 155◦ ±10◦, respectively. When combined further to a marginal result from a previous experiment by the same group (Wolf et al. 1970), the final (assumed energy-independent) degree and angle of polarization were (15.4±5.2)% and 156◦±10◦ , respectively. A few years later, in 1976, a similar Bragg experiment was flown onboard the OSO-8 satellite. A ∼70 hours pointing at the Crab Nebula brought to an accurate measurement of the X-ray polarization of the nebular emission (the contribution from the pulsar was removed) in 2.4-2.8 keV as (19.2±1.0)% and 156.4◦±1.4◦ , and in 4.8-5.6 keV as (19.5±2.8)% and 152.6◦±4.0◦ (Weisskopf et al. 1978). The general agreement between this measurement and the optical polarization data supported the interpretation of the Crab Nebula emission as synchrotron emission. The most significant plots of this historical measurement are shown in Figure 6. This result is still today the most accurate measurement of linear X-ray polarization from a celestial source. In fact, it took more than 30 years to get the next satellite measurement of the same source, in a harder energy band. By analyzing 3 years of data from the SPI experiment onboard the INTEGRAL satellite, by studying the angular distribution of the Compton pairs in different Ge detector elements, Dean et al. (2008) derived a measurement of the linear polarization of the Crab Nebula as (46±10)% and 123◦±11◦ at energies between 0.1 and 1 MeV.

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4 A jump in sensitivity: the focal plane photoelectric polarimeters for soft X-rays The capability to measure the angular distribution of photoelectrons allows for building X-ray polarimeters exploiting the photoelectric effect, therefore with a large energy bandwidth, good energy resolution, accurate timing and very good position capabilities. Actually the photoelectron emission direction follows an angular distribution which brings memory of the linear polarization of the incoming photon. In the following equation we show the angular distribution of photoelectrons ejected after the interaction of X-rays with atomic K-shells (Heitler, 1954): dσKph dΩ

=

me c2 7 r02 α4 Z 5 ( )2 E

√ 4 2 sin2 θ cos2 ϕ (1 + β cosθ)4

(11)

where θ is the emission angle and φ is the angle between the projection of the emission direction in the plane perpendicular to the incoming direction and the electric vector of the incoming photon (the azimuthal angle). Given the cos2 (ϕ) dependence of the photoelectron cross-section with the azimuthal angle, we expect the modulation factor of a polarimeter based on the photoelectric effect to be 100 %. Experimentally, however, it is difficult to devise a photoelectric X-ray polarimeter sensitive to photoelectrons only. This would involve the use of a very thin absorption solid layer (photocathode) at very grazing incidence,

Fig. 6 The historical measurement of the linear polarization of the Crab nebula performed by Weisskopf et al. (1978). The left panel shows the modulation of the Crab nebula photons, compared to the non-modulation of the background during Earth occultation. The panel on the right, shows the determination of the polarization angle, at 2.6 and 5.2 keV.

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the use of a Micro Channel Plate (MCP) as collector and the rotation of the apparatus (e.g., Nichols et al. 2000). The photoelectron deposits in the photo-catode an energy that cannot be measured and that depends on its trajectory. Moreover the MCP has a very low energy sensitivity, therefore the spectroscopic capability of such an apparatus would be poor. A different approach consists in devising an X-ray polarimeter with the analyzer and the absorber made of the same material, a gas cell, and measuring the secondary charge created by the photoelectron. Actually, the photoelectron ejected by the gas atoms leaves a collection of secondary charges (a track) along its path which is the result of its continuous slowing down due to anelastic scattering with the electron clouds of the atoms and elastic scattering with atomic nuclei. The latter are responsible for abrupt changes of direction of the photo-electron and therefore for the decreasing sensitivity of the X-ray polarimeter. The direction changes much less during inelastic scattering. The determination of the initial direction of the photo-electron is essential, and it is possible if the detector is capable to resolve the track in the energy range (soft X) typical of conventional grazing incidence X-ray optics. Attempts to exploit the polarization sensitivity of photoelectric effect date back to the beginning of X-ray Astronomy. However the techniques were not effective because the instruments could not visualize the track. One technique was to detect either the coincidence between two wires in a proportional counter (Riegler et al., 1970) or the small difference in rise time (Sanford et al., 1970; Hayashida et al., 1999) of a pulse. More recently, coincidence in adjacent pixels (Tsunemi et al., 1992) in a CCD or multipixel events (Buschhorn et al., 1994) at high energy were used to detect X-ray polarization. However, the range of a photoelectron in silicon is so small - (E/(10 keV))1.72 µm (Holland et al., 1995) - that the use of a CCD as

Fig. 7 The geometry of the photoelectric effect. θ is the emission angle; ϕ is the azimuthal angle that is the angle between the projection of the emission direction in the plane perpendicular to the incoming direction and the electric vector of the incoming photon (from Muleri 2009).

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a polarimeter at the focus of a conventional X-ray optics is quite hard. At higher energy, in the domain of the multilayer optics, the electron range increases but the CCD becomes transparent to X-rays. The photoelectron track, in principle, could be visualized by means of its scintillation light in a suitable gas mixture and actually this was performed at high energy (54 keV, Austin et al., 1994) or at lower energy more recently by Sakurai et al. (2004). Imaging of the photoelectron track by a subdivided pixel detector, however, represents the most effective way to arrive at a low energy X-ray polarimeter (Costa et al. 2001, Black et al. 2007). To this purpose, it is essential to derive the emission angle of the photoelectron and the point of absorption of the photon. Usually, in gas detectors, one derives the position of an event by evaluating the barycenter. In gas detectors capable of photoelectron tracking, the impact point and the barycenter have different locations. The track actually consists of a small ionization straight initial path and a high ionization final skein. The barycenter is close to the skein, the impact point is close to one end of the low ionization path. This end can, possibly, include the small track of the Auger electron. Simple algorithms based on the evaluation of the second and third momentum are computed to determine either the impact point and the emission angle. The histogram of the emission angles is called modulation curve from which the polarization of the source is derived.

4.1 The Gas Pixel Detector (GPD) solution The progress of the techniques in the micro-electronics was recently exploited for building pixel detectors with very fine position capabilities (Costa et al. 2001, Bellazzini et al. 2007). The Gas Pixel Detector is essentially a gas cell containing an X-ray window and an element which multiplies the secondary charge produced by a photoelectron (the Gas Electron Multiplier, GEM, parallel to the entrance window) and a pixellated charge collector (a CMOS ASIC chip). The GEM is a thin metalized kapton foil perforated by microscopic holes with a pitch of 50-80 µm, whose electric field (few hundreds volt) amplifies the charge signal by a factor of 500-1000. The top layer of the ASIC chip is patterned with 105 hexagonal metal pixels. Each pixel, a hexagonal electrode, is connected to a charge-sensitive amplifier followed by a shaping circuit. The chip is auto-triggered and provides the coordinates and the charge of each pixel in a fiducial rectangular portion, the region of interest, that contains the photoelectron track. Figure 8 shows the basic elements and working principle of a photoelectric polarimeter (Costa et al. 2001), while Figure 9 shows a real photoelectron track as imaged by a real GPD and the direction reconstructed by the algorithms. The collection of the impact points from a point source allows for deriving its position. The location accuracy typical of the GPD is 150 µm FWHM. The GPD at the focus of an X-ray optics has a location accuracy, generally, limited only by the Point Spread Function of the latter. Such photoelectric polarimeter also allows for moderate-resolution spectroscopy: an energy resolution (FWHM) of about 16% in

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a GPD filled with a mixture of 2-atm Ar-DME 60-40 has been measured at 5.9 keV, comparable to conventional proportional counters. In the current GPD models the depth of gas in the cell is typically in the range of few cm, because the thermal diffusion during the drift blurs out the track and limits the reconstruction. The compromise between the efficiency (i.e., absorption depth) and modulation factor depends on the gas mixture and density. Typical values are µ ∼0.40 and ǫ ∼ 7% at 3.7 keV (e.g., Muleri et al. 2010).

4.2 The Time Projection Chamber (TPC) polarimeter solution. If the entrance window is normal to the GEM it is possible to disentangle the modulation factor (which decreases in the GPD, with the drift thickness) from the efficiency (which, instead, increases with it) at the expense of the imaging capability. This method (Figure 10, Black et al., 2007) allows for the formation of a twodimensional images of photoelectron track from a one-dimensional strip readout. The track drifts from the interaction point to the amplifier plane, which is similar to the GEM, and then is collected by the readout strips. Those readout strips are located parallel to the direction of the incoming photon. As illustrated in Fig. 10, it is possible to derive the 2-D image of the track in the plane orthogonal to the incoming photon by digitizing the charge pulse arriving at each strip with a dedicated free running ADC and binning it accordingly to the drift velocity set on the base of the one-dimensional pixel size.

Fig. 8 The concept of the GPD. A gas electron multiplier amplifies the initial stream of charges after the drift. A readout plane (the top layer of a pixellated ASIC CMOS chip) collects and processes the charges (from Costa et al. 2001).

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Fig. 9 A track imaged by the Gas Pixel Detector. The anelastic scattering with the electron cloud is responsible for leaving the stream of charges along the photoelectron charge. The elastic scattering with the nuclei is responsible for changing the direction of the photoelectron. By means of a simple algorithm, the conversion point and the initial emission direction can be derived. The energy of the photon is obtained by summing-up the charge contained in each pixel.

The number of pixels are minimized by grouping the strips according to their position and to the maximum track length to be collected, which is set by the highest photon energy. Since it is not possible to derive the time of the interaction with the gas but only the differential time from the arrival to the amplification plane, one dimension is lost and the TPC polarimeter does not provide 2-D imaging of the source. The 1-d imaging capability is also reduced by the grouping of the readout strips. Due to the two different methods (timing and spacing) to derive the image

Fig. 10 The concept of the Time Projection Chamber solution with the image of a real track. The 1-D pixels are 120 µm and the sampling time is 40 ns (from Black et al. 2007).

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of the track (that results binned in squared pixels) and due to important effects of diffusion that depend on the absorption point, systematic effects are present, that need to be compensated and minimized by rotating the entire apparatus with respect to the incoming photon direction. However, the loss of imaging capability causes a higher background with respect to the GPD solution (spatial selection is no longer possible) and also the amount of resources is expected to be larger.

5 Observational Prospects In the last few years the development and refinement of the techniques has originated a few mission/experiment proposals, based on focal plane photoelectric polarimeters. In 2007 a small mission - POLARIX (Costa et al. 2010) - was approved for a phase A study by the Italian Space Agency (ASI). The study is now completed and the final decision by ASI is still pending. The same agency approved in 2008 an Italian participation to the HXMT mission (Costa et al. 2007) for the inclusion of a photoelectric polarimeter on a scientific payload otherwise aimed at a deep survey in the hard X-rays. Also this polarimeter is currently on-hold. Meanwhile, other focal-plane X-ray polarimeters have been proposed. In the following sections we review in some details those mission options that appear today as the most viable, starting with GEMS, the only definitely approved mission including an X-ray polarimeter after OSO-8. For the sake of conciseness we discuss here only the mission/experiment proposals dealing with focal plane polarimeters mostly operating in the ”conventional” X-ray band (2-10 keV). Many other proposals are put forward for both softer (below 2 keV) and harder (above 15-20 keV) X-rays. We refer the interested reader to the recent volume X-ray Polarimetry: a New Window in Astrophysics edited by R. Bellazzini, E. Costa, G. Matt and G. Tagliaferri (2010) for an extensive presentation of the worldwide experimental polarimetric efforts.

5.1 Gravity and Extreme Magnetism SMEX (GEMS) GEMS (Swank et al. 2010, Jahoda 2010) is a NASA Small Explorer (SMEX) mission finally approved for a launch in 2014. The scientific payload is entirely focussed on X-ray polarimetry, in the energy range 2-10 keV. The polarimeters are based on the time projection chamber (TPC) concept described in Sect.4.2 at the focus of 3 grazing incidence telescopes replicated from the design of the Suzaku mirrors (4.5 meter focal length) but smaller in size. Following the design of the TPC, the instrument will not perform images within its ∼12 arcmin total field of view. An additional student-class experiment based on a Bragg deflector with artificial multi-layer crystals will provide a narrow response at 0.5 keV. The working principle of the TPC and Bragg polarimeters requires that the satellite spins around the boresight axis, that GEMS will do at a rate of 0.1 rpm. The

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effective area of the 3 TPC polarimeter units altogether peaks between 2 and 3 keV at about 300 cm2 . The mission is expected to operate in a low-Earth orbit for a nominal lifetime of 2 years. The observing strategy generally foresees long pointings (up to 106 s). The first 9 months will be devoted to the Core Program observations, composed of 35 most interesting sources. These span from the most famous blackhole candidates (Cyg X-1, GRS 1915+105, ..) to accretion-powered X-ray pulsars (e.g., Her X-1, Vela X-1, ...), for which an MDP of ∼1% is anticipated, to SNRs, rotation-powered isolated pulsars and magnetars, for which the MDP will be around 5% (see Swank et al. 2010 for the full list). GEMS will also allow for phase or energy resolved polarimetry, enabled by a sub-ms time tagging and a moderate energy resolution, although with sensitivities somewhat worse (factor of a few to ten). Instead, due to the lack of imaging capabilities, angular-resolved polarimetry can only be carried out on sources with extension much wider than 12’ (e.g., SN 1006). The main characteristics of the GEMS mission are summarized in Table 1. A plot of the expected GEMS sensitivity and measurement capability of the target sources for the 9-month core program is shown in Figure 11. Table 1 Characteristics of the GEMS mission Classes

Subclass

Energy band: Field of view On-axis effective area Detectors background Angular resolution Polarization sensitivity

2 - 10 keV 12’ (diameter) ∼ 300 cm2 at 2-3 keV < 0.05 cts s−1 telescope−1 12’ (extension of the field of view) ∼6% MDP at 1 mCrab in 2-10 keV (105 s)

5.2 New Hard X-ray Mission (NHXM) The New Hard X-ray imaging and polarimetry Mission (NHXM, Tagliaferri et al. 2010, Fig.12) is a mission capable to detect photons of energy between 0.5 and 80 keV. X-rays in this wide energy band are focussed by means of 4 multilayer mirror modules and a 10-m focal length, mounted on a deployable structure. An engineering model with two integrated shells was tested at MPE Panter facility, showing an Half Power Diameter of about 18 arcsec and 25 arcsecs at 0.93 keV and 30 keV, respectively, consistent with the requirements. The expected effective area of one mirror module is shown in Fig. 13. The satellite will be placed into a low inclination orbit at 600-km altitude following its predecessors BeppoSAX and Swift, characterized by a low and stable background. A Vega rocket, the smallest European launcher, is sufficient to host NHXM. The service module hosting the

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mirrors, is derived from the BeppoSAX satellite and uses a PRIMA-S bus. The ground station will be at Malindi. A Silicon Advanced Pixel Sensor (Low Energy Detector) based on DEPFET readout and stacked with a pixellated (250 µm) CdTe detector (High Energy Detector) will be installed at the focus of three out of four telescopes. An active anticoincidence well will surround both detectors. Imaging and spectroscopy will, therefore, be possible with high quantum efficiency and low background. An X-ray polarimeter based on the Gas Pixel Detector technology will be placed in the focal plane of the fourth mirror module. Due to the very wide energy coverage of the X-ray optics two independent GPD polarimeters will cover the full energy range: a Low Energy Polarimeter (LEP) operative between 2 and 10 keV filled with a 1-atm mixture of He-DME with a thickness of 1 cm and a Medium Energy Polarimeter (MEP) operative in 6-35 keV, filled with a mixture of 3-atm Ar-DME and with 3 cm of active thickness. The Beryllium window will have a thickness of 50 µm for the LEP and 150 µm for the MEP. The ASIC chip and √ the GEM will be equivalent for both X-ray polarimeters. The quality factor (µ × ǫ) for the HEP is larger than for the LEP, in order to compensate in sensitivity for the smaller effective area of the optics at higher energies. LEP and MEP are mutually exclusive during a single observation and they will be set on a mechanical rotary stage. The possibility to add a further polarimeter with extended sensitivity up to 80 keV (High Energy Polarimeter, HEP) is being considered. It would be based on Compton scattering on a cylindrical plastic scintillator (similar to the geometry shown in Fig. 5). A set of fast inorganic crystals will surround the scatterer forming a cylindrical

Fig. 11 The expected polarization sensitivity (MDP, lines for 105 and 106 s) of GEMS compared to a model-predicted polarization level of a set of target sources: neutron stars, black holes and supernova remnants (Jahoda 2010).

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Fig. 12 NHXM (New Hard X-ray Mission) is designed to use 4 multilayer mirrors modules in a deployable structure to image X-ray photons from 0.5 to 80 keV. The mirror modules are hosted into the service module while the detector plane is placed at the opposite side, at the end of the deployable structure.

Fig. 13 On-axis Effective area of one mirror module for NHXM

well and it will collect coincidence photons. The symmetry of the system (together with extended testing and simulations, and the knowledge of the actual pointing) would make it possible to avoid the rotation of the HEP. The Compton polarimeter

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Fig. 14 Minimum Detectable Polarization for the LEP and MEP of NHXM.

would be located underneath the LEP/MEP slit, and would observe simultaneously with them. NHXM is conceived as an observatory. With its unprecedented angular resolution and sensitivity at hard X-rays and the wide-band spectro-imaging-polarimetric capability, it will address not only the long-standing issue of the cosmic X-ray background at hard X-rays, but many other astrophysical issues, such as radiative transfer in highly magnetized plasma, black hole census and the physics of accretion. In Figure 14 we show the expected polarimetric sensitivities (MDP) for a number of potential target sources as a function of their typical flux, for 105 and 106 s exposure times. In both energy ranges, day-long integrations on ∼ 1 mCrab sources - like for example the quiescent state of the soft gamma repeater SGR 1900+14 - allow to reach ∼10% linear polarization sensitivities. It is worth stressing the imaging capability of the polarimeter onboard NHXM. The 15 arcsec angular resolution will allow to image individually the different components in extended sources as well as observing point-like sources in crowded regions like the Galactic Center. In Figure 15 we illustrate the importance of this property during an observation of the Crab Nebula, for which the X-ray observations by Chandra (Weisskopf et al. 2000) and optical flux and polarization measurements (e.g., Hester et al. 1995, Slowikowska et al. 2009) have shown the complex variability of the different regions of the nebula (jet, torus, knots, ...).

5.3 International X-ray Observatory (IXO) The International X-ray observatory (IXO, e.g., Bookbinder 2010) is a joint venture between ESA, NASA and JAXA, currently planned for launch in 2021. At the time of writing IXO is waiting for the down-selection of US ’Decadal Survey’ and ESA ’Cosmic Vision’. It is a major observatory, the resources necessary for IXO being a total mass of 6500 kg and a total power of 4.5 kW. The satellite is expected to operate in the second Lagrangian point (L2).

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Fig. 15 A Chandra X-ray image of the Crab Nebula. The two circle quantify the size of the point spread function of the polarimeter onboard NHXM (larger, 15”) and IXO (smaller, 5”) (adapted from Weisskopf et al. 2000).

The mission most challenging effort is the production of the very large X-ray optics: 3 m2 of effective area at 1 keV with an angular resolution of 5”. Two options are being investigated, the ’Silicon Pore Optics’, the baseline, and the ’Slumped Glass Optics’. At present time, prototypes of the baseline provided a Half Energy Width (HEW) of 9” at 3 keV. Prototype of the second option showed an HEW of 6.5”. The payload consists of six instruments: an X-ray grating spectrometer (XGS), an X-ray microcalorimeter (XMS), a wide field imager (WFI), a hard X-ray imager (HXI), a high time resolution spectrometer (HTRS) and the X-ray polarimeter (XPOL). The XGS will have a resolution better than 3000 and will be operative with an effective area larger than 1000 cm2 in the 0.3 - 1 keV energy range. The XMS will operate between 0.2 and 10 keV with an energy resolution of 2.5 eV (inner array, 2x2 arcmin2 ) and 10 eV (outer array, 5x5 arcmin2 ). The WFI (exploiting the active pixel sensor technology) will have a field of view of 18 arcmin. The HXI is made of pixellated CdTe and it is surrounded by an anticoincidence system of BGO crystals. The HXI will be mounted back to back with the WFI and will be sensitive in the 10-40 keV energy range. It is required to have a field of view of 8x8 arcmin2 , a position resolution better than the quality of the optics and an energy resolution better than 1 keV. The HTRS will be capable to sustain a rate of up to 2×106 counts/s (12 Crabs) in the 0.3-15 keV energy range with a energy resolution of 150 eV and a dead time lower than 2% at 1 Crab. The X-ray polarimeter on board IXO, XPOL, will be filled with a He-DME gas mixture and will mount an improved version of the ASIC CMOS chip capable of sustaining with acceptable dead time the high source rate provided by the large

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Fig. 16 The polarization sensitivity of the XPOL experiment onboard IXO for several potential target sources of different classes and fluxes. Two typical observing times are assumed: short (20 ks) and long (200 ks) exposures.

collecting area of the optics. The events generated by dim sources (< 150 mCrab) will be sent to telemetry in the form of raw data, including the complete and detailed information about the track (energy content of the pixels in a frame surrounding the track, coordinates and trigger time). In case of bright sources a suitable Digital Signal Processor will calculate on-board the emission angle and the impact point thus reducing the telemetry load. On-board calibration of XPOL will be possible thanks to a ’filter wheel’ which will carry a polarized X-ray source based on Bragg diffraction at nearly 45◦ and an unpolarized X-ray source provided by fluorescence lines at suitable energy. Thanks to the exceedingly large collecting area coupled to the excellent angular resolution of IXO (∼3-4 times better than NHXM), the discovery potential of the XPOL experiment is huge. Figure 16 shows the anticipated polarization sensitivity for a number of (classes of) sources. Taking as a reference the soft gamma repeater SGR 1900+14 in quiescence, a comparison between Figure 16 and 14 evidences how a 5 times improvement in sensitivity is reached in 1/5 of the integration time. This not only implies the capability to investigate weaker sources, but to study in much higher detail the time and phase variability of the polarization properties of the radiation emitted from these sources, with uncertainties on the measurements of the degree and angle of polarization in the range of ∼1-2% and ∼1◦ , respectively. The time sharing with the other focal plane experiments will restrict such fine studies to only a selected number of targets, so IXO would highly benefit of previous pathfinder missions.

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6 Conclusions X-ray polarimetry is acknowledged since the early stages of X-ray astronomy as a powerful tool of investigation of the emission processes at work in the cosmic sources of high energy radiation. However, the technical difficulties in designing and building sensitive X-ray polarimeters limited their application onboard space missions and stratospheric balloons and the observational results available to date are limited to the Crab nebula only. The recent technological developments enabled the design of sensitive instrumentation based on the tracking of the photo-electron. This led to the successful submission of experiment proposals onboard forthcoming space missions. Among these, the NASA SMEX mission GEMS is finally approved for a launch in 2014 and it will be dedicated to soft X-ray (2-10 keV) polarimetry of the Galactic sources and the brightest extragalactic objects. This experiment will be, by construction, nonimaging. Two other experiments were proposed for focal plane polarimeters. The XPOL experiment onboard IXO will have an enormous potential, offering imaging capabilities and an unprecedentedly large collecting area. IXO passed already a first level of selection in ESA, entering a definition study, while the final approval by NASA and JAXA is yet to come. The same technology proposed for IXO is now proposed for a new mission, NHXM, originated as a national mission in Italy and likely evolving towards a European proposal. Such a mission proposal would have the great advantage of allowing high resolution imaging, spectroscopy and polarimetry in a wide soft/hard X-ray energy range simultaneously on the same targets. The collecting area will not be as large as IXO, but the capability to obtain the most complete simultaneous view ever of the X-ray emission properties of the observed sources is an asset that makes such a mission unique. Whatever the future will bring in terms of specific missions, it is rather clear that X-ray polarimetry has now reached a level of maturity that will soon lead to routinely obtain X-ray polarimetry data as a standard tool of investigation in astrophysics. In this context, the inclusion of the linear polarization properties of the detectable emission, often a powerful discriminant element, is still rarely considered both in the theoretical modelling, as well as in the technical tools for the data analysis. The high energy astrophysics community should work in filling this gap over the next years to get prepared for this new observational window. Acknowledgements The authors warmly thank the support by the High Energy Group at INAFIASF Rome, especially Enrico Costa and Fabio Muleri for useful comments and for kindly providing materials for this review.

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New results on high energy cosmic ray electrons observed with Fermi LAT Alexander Moiseev, on behalf of the Fermi LAT Collaboration

Abstract The Large Area Telescope on-board the Fermi Gamma-Ray Space Telescope has collected more than 8 million cosmic ray electrons with energy above 7 GeV since the inception of its science operation on orbit. The observed spectrum has a harder spectral index than previously reported instances, which suggests the presence of nearby sources of high energy electrons. One viable candidate is nearby pulsars, possibly some of those recently discovered by Fermi. At the same time the dark matter origin of such sources cannot be ruled out. In this paper I present the Fermi LAT high statistics measurement of the cosmic-ray electron spectrum and its interpretation in terms of astrophysical sources for high energy electrons and a standard cosmic-ray propagation model.

1 Introduction The problem of cosmic ray (CR) origin has puzzled scientists for decades. Galactic magnetic field diverts charged cosmic rays and therefore does not allow tracing their origination point by measuring arrival direction (the Larmor radius for a 1 TeV particle is ∼ 2 × 10−4 pc assuming galactic magnetic field strength B = 4µG). It is believed that the majority of CR are produced in pulsar systems such as supernova remnant (SNR) and pulsar wind nebulae (PWN), but this hypothesis has never been directly confirmed. As a result of their low mass, high energy cosmic ray electrons (CRE) rapidly lose their energy during propagation through local magnetic fields via inverse Compton and synchrotron radiation with strong energy dependence (dE/dt ∼ E 2 ) and thus cannot travel far from their sources. The characteristic energy loss time for few-TeV electrons is ∼ 105 years, and corresponding travel distance is ∼ 1 kpc (for Kolmogorov diffusion with diffusion coefficient D(E) ∼ 1028 × (1 + E/E 0 )0.33 cm2 /s and E 0 ∼ 1 − 10GeV ), consequently they can Alexander Moiseev CRESST/NASA and University of Maryland, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_49, © Springer-Verlag Berlin Heidelberg 2011

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Alexander Moiseev, on behalf of the Fermi LAT Collaboration

serve as a probe of nearby Galactic sources and propagation. On the other hand, the measured spectrum and charge composition of CRE can contribute to modelling of their possible sources (such as SNR), especially if the source can be identified by its estimated age and distance. Recently published results by ATIC [1], H.E.S.S. [2, 3], Fermi-LAT [4, 5] on the electron spectrum, and PAMELA [6] on the positron fraction in CRE provided new and critical information on the origin of CRE. The ATIC and PPB-BETS [7] teams reported evident spectral feature in the energy range of 300 - 700 GeV which may indicate the presence of an exotic component. However, this result was not confirmed by the Fermi-LAT, which provided an accurate CRE spectrum from 7 GeV to 1 TeV without prominent spectral features. The H.E.S.S. team reported a spectrum that sharply steepens above ∼ 900 GeV, possibly indicating an absence of sources of electrons above 1-2 TeV within 300-400 pc. The PAMELA collaboration published findings on the positron fraction increase with energy above a few GeV which is in conflict with the previously believed pure secondary origin of cosmic ray positrons. The most accurate and almost statistically error-free measurement of the CRE spectrum was provided by the Fermi-LAT [4, 5]. The Fermi Gamma-ray Space Telescope with the Large Area Telescope (LAT) onboard was launched on June 11, 2008 on 565 km Earth circular orbit. The LAT is a pair-conversion gamma-ray telescope with field-of-view 2.4 sr, effective area (for photons) of ∼ 8, 000cm2 at 1 GeV, and energy range from 20 MeV to more than 300 GeV [8]. It consists of 16 identical towers that provide conversion of a gamma-ray into e+ e− pair and determine its arrival direction (18 double-plane Si-strip Tracker) and energy (segmented hodoscopic CsI Calorimeter). The instrument is covered by a segmented Anticoincidence Detector (ACD) which rejects the charged particle background. The electronic system includes flexible and robust hardware trigger along with software filters. Although the LAT is a gamma-ray telescope, in early stage of its design it was recognized that intrinsically the LAT is also a capable electron spectrometer [9]. The facts that a) the most of the time the LAT operates in scanning mode and b) its wide aperture make it particularly suitable for measurement of the isotropic cosmic radiation (as CRE flux is assumed to be). Large sensitive area and high efficiency secure high statistics. Note that the LAT cannot distinguish electrons from positrons and, in fact, detects both, so hereafter for simplicity we will refer to the sum as electrons, unless otherwise specified. In this paper I will present the main aspects of the electron data analysis, discuss the result and its possible interpretation.

2 Detection of electrons by LAT In this section the main aspects of the analysis, which include event selection, energy determination, spectral reconstruction, systematic uncertainties assessment and analysis validation, are presented. The full details are given in [5].

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The main challenge of the electron analysis is to identify and separate electrons from all other species, mainly CR protons. It is based on the LAT gamma-ray analysis [8], but differs by the fact that in gamma-ray analysis the major role in removing proton background belongs to the ACD. In the case of the electron analysis both electrons and background protons are charged particles, so the ACD is less useful. Another challenge is to extend the energy range up to 1 TeV (the standard LAT analysis is optimized up to 300 GeV). Based on extensive Monte Carlo simulations [10], which were validated in a CERN beam test with a specially designed and built beam test unit [11], we established efficient selection criteria to distinguish electron events from the much more numerous hadron events. In order to keep the hadron contamination in the electron candidate sample under ∼ 20%, the hadron-electron separation power above ∼ 10 GeV must be 103 − 104 , increasing along with the energy. This was successfully achieved by utilizing the full power of all LAT subsystems: tracker, calorimeter and ACD act together. At the end of the analysis we determined the rate of background events that squeezed through the electron selections, and subtracted it from the total rate of the electron candidates. As a result, the rate of electrons was obtained. Electron event selection is a complicated process that utilizes numerous physical variables from all 3 LAT subsystems, as well as combined variables calculated with a Classification Tree technique. Most of the selections are either energy dependent or scaled with energy. The most efficient separators between electromagnetic and hadronic events are the lateral distributions of the shower image. Histograms in figure 1 show the difference between distributions for selected variables for electron and protons events. More than 20 variables characterizing the event are used in the selection process.

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Residual hadron contamination in the electron event sample is determined by applying selection cuts to the on-orbit simulation. This rate is subtracted from that of the flight electron candidates. The contamination, defined as a ratio between the rate of residual hadrons to the total electron candidate rate, ranges from ∼ 4 % at 20 GeV to ∼ 20 % at 1 TeV and shown in fig.2. Energy reconstruction and resolution is another key item of our analysis. It is based on simulation and calibration of the calorimeter in several beam tests at SLAC (electrons), CERN (electrons, pions, gammas and protons) and GSI (Carbon and Xe nuclei) [11]. We achieved good agreement between simulations and beam test data in energy reconstruction up to the highest available electron energy at SPS CERN, 280 GeV. Consequently, we can be confident in our Monte Carlo model and, relying on its simulations, we have reasonable grounds to extend the energy range to 1 TeV. Practically unbiased energy reconstruction is demonstrated in fig. 3 where the example of the ratio of reconstructed energy to Monte Carlo energy is plotted for one energy interval. Energy resolution for isotropic flux is shown in fig. 4: it is ∼ 6 % at 20 GeV and gradually increases to ∼ 13% at 1 TeV for the standard analysis (half width for 68 % event containment). For the subset of events with long paths in the calorimeter (longer than 12 X0 ) energy resolution better than 5% up to 1 TeV is achieved (shown in figures 4 and 5).

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Final validation of our Monte Carlo simulations was performed using the flight data. As a result, we estimated the systematic errors in our resulting spectrum to range from ±5% at the low energy end to ±(12 − 15) % at the high energy end. It originates primarily from uncertainties in the EGF and the primary proton flux. We performed extensive cross-checks of the LAT capability to reconstruct the spectrum. Fig. 6 shows good agreement between the spectrum reconstructed by the standard analysis and that obtained with the long path selection, which falls within the systematic errors. We also simulated the LAT response to spectral feature similar to that reported by ATIC [1]. Fig. 7 illustrates how such a feature would be detected when assuming different energy resolution.

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3 Result and Discussion The resulting spectrum obtained during the first year of the Fermi LAT science observation (August 2008 - August 2009) is shown in fig. 8 [5]. It contains ∼ 8 million electron events in the energy range of 7 GeV to 1 TeV. Energy bins were chosen to be the full width of 68% containment of the energy dispersion. Within the systematic errors, shown by the grey band, the entire spectrum can be fitted by a power law with spectral index within the interval 3.08 ± 0.05. The spectrum is significantly harder than that reported by previous experiments. At the same time, the spectrum suggests some spectral flattening at 70 - 200 GeV with a noticeable excess above 200 GeV as compared to power-law spectral fit. We made an attempt to fit it assuming a twicebroken power law injection spectrum: Γ = 1.6 below 4 GeV, Γ = 2.5 above 4 GeV, and Γ = 5 above 2 TeV (see fig. 8). The fit does not exactly follow gentle spectral features. Hereafter, all the calculations were made using the GALPROP code [12]. This model includes spatial Kolmogorov diffusion with energy dependence index δ = 0.33, diffusive re-acceleration characterized by an Alfven speed vA = 30km/s, with halo height of 4 kpc. Energy losses by inverse Compton scattering and synchrotron radiation were computed as a function of energy and position. Secondary electrons and positrons from CR proton and helium interactions with interstellar gas make a significant contribution to the total lepton flux, especially at low energy. The solar modulation was treated using the force-field approximation with Φ = 550MV [13].

Fig. 8 The e+ + e− spectrum as measured by the Fermi LAT (red circles) along with other experimental data. The fit by a conventional GALPROP model (see the text for the model details) is shown by solid blue line after the solar modulation with Φ = 550MV has been applied. The dashed blue line shows the spectrum before the modulation, the dotted blue line - only e− . Secondary e+ (red lines) and e− (orange lines), dashed lines - before modulation, and solid lines - after modulation, are calculated according to [14].

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Better fit to the Fermi LAT electron spectrum can be achieved by adjusting the injection spectra and propagation parameters. However, the recent PAMELA result on the positron fraction adds critical constraints. So far, cosmic ray positrons have all been considered secondary, generated in CR interactions with interstellar gas (see e.g. [14]). That, however, should result in an e+ /(e+ + e− ) ratio to fall along with energy which conflicts with the PAMELA result. A viable interpretation (see e.g. [15] and references therein) is to include an additional component of e+ e− pairs with a hard spectrum. Fig. 9 illustrates such a scenario where a good fit to both - the Fermi electron spectrum and the PAMELA positron fraction is achieved by including an additional component of e+ e− with an injection spectral index Γ = 1.5 and an exponential cutoff.

Fig. 9 The Fermi LAT e+ + e− spectrum (left panel) and PAMELA positron fraction (right panel) are fitted with an additional component (shown by the dashed line). Dotted lines correspond to the spectra without the additional component.

The nature of such additional component has been discussed in numerous recent papers. Suggested scenarios can be divided into three basic groups: e+ e− component is produced a) in astrophysical objects such as pulsar systems, b) in dark matter, c) by other astrophysical effects. However, all of them assume that the e+ e− component has a harder spectrum than the pure e− flux. This is illustrated in fig. 10 where the resulting electron spectrum (similar to that measured by Fermi LAT) is shown as composed of a larger flux (with softer index) of “primary” negative electrons (e.g. directly accelerated in SNR shocks), and a smaller flux of e+ e− with harder spectral index which starts showing up at higher energy. It appears that the analysis of data collected by the Fermi LAT and PAMELA strongly suggests the presence of a previously unrecognised additional component of e+ e− with a spectrum harder than that of “primary” negative electrons. The origin of this component is still unclear. Recent discovery by Fermi LAT of numerous new gamma-pulsars, some of them potential sources of e+ e− , may shed some light on the origin of this component. Gendelev et al. [16] estimated the contribution from these pulsars to the e+ e− flux. Fig. 11 shows contributions to the e+ e− flux from seven most prominent mature pulsars and compares it with that measured by the Fermi LAT. The main point is that the contribution from separate pulsars should be seen as a structure in the spectrum

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as shown by a black line in fig. 11, right panel. If such a structure in the e+ + e− spectrum is found, it would be a solid argument for the astrophysical origin of pairs. Yet, since in this scenario both - the negative electron and the pair components are believed to be produced in pulsar systems, we need to understand why they have different spectra. Negative electrons can be produced and accelerated in SNR, and more energetic pairs - in mature pulsars and millisecond pulsars (MSP) [17]. Eight MSP recently discovered by Fermi make this hypothesis viable. For more discussion see e.g. [10, 19, 20] in these Proceedings.

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4 Conclusion Today we may be approaching the first direct detection of cosmic ray sources. Furthermore, we can now discuss not only the origin of CRE, but also refer the results to the pulsar modeling. It is possible that we are dealing with at least two distinct mechanisms of “primary” electron production. One produces a softer spectrum of negative electrons, the other - a harder spectrum of e+ e− pairs. Exotic (e.g. dark matter) origin is not ruled out. More accurate results are expected from Fermi LAT and PAMELA. Combined Pamela and Fermi results are very powerful diagnostic tools [10]. Critical new results on the positron fraction are expected from the AMS. Results from Fermi LAT on high energy CRE anisotropy are coming soon, which can help in identifying the source of CRE.

5 Acknowledgements The Fermi LAT Collaboration acknowledges support from a number of agencies and institutes for both development and the operation of the LAT as well as scientific data analysis. These include NASA and DOE in the United States, CEA/Irfu and IN2P3/CNRS in France, ASI and INFN in Italy, MEXT, KEK, and JAXA in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council and the National Space Board in Sweden. Additional support from INAF in Italy and CNES in France for science analysis during the operations phase is also gratefully acknowledged. The author is grateful to Olga Schmidt, Robert Hartman, David Thompson and Markus Ackermann for reading the paper and providing comments.

References J. Chang et al., Nature 456, 362 (2008) F.A. Aharonian et al., Physical Review Letters 101, 261104 (2008), 0811.3894 F.A. Aharonian et al., A&A 508, 561 (2009) A. Abdo et al., Physical Review Letters 102, 181101 (2009), arXiv:astro-ph/0905.0025 M. Ackerman et al., Physical Review D, submitted (2010) O. Adriani et al., Nature 458, 607 (2009), 0810.4995 S. Torii et al., arXiv:astro-ph/0809.0760 W.B. Atwood et al., ApJ 697, 1071 (2009) A.A. Moiseev, J.F. Ormes, and I.V. Moskalenko, in Proceedings of the 30-th International Cosmic Ray Conference, Merida, Mexico, 2, 449, arXiv:astro-ph/0706.0882 10. C. Sgro‘, J. Bregeon, and L. Baldini, in Proceedings of the 31-st International Cosmic Ray Conference, Lodz, Poland (2009), arXiv:astro-ph/0907.0385 11. L. Baldini et al., in The First GLAST Symposium, edited by S. Ritz, P. Michelson and C.A. Meegan, vol. 921 of American Institute of Physics Conference Series, p. 190 (2007) 12. V.S. Ptuskin, I.V. Moskalenko, F.C. Jones, A.W. Strong, and V.N. Zirakashvili, ApJ 642, 902 (2006) 1. 2. 3. 4. 5. 6. 7. 8. 9.

New results on high energy cosmic ray electrons observed with Fermi LAT 13. 14. 15. 16. 17. 10. 19. 20.

L.G. Gleeson and W.I. Axford, ApJ 154, 1011 (1968) I.V. Moskalenko and A.W. Strong, ApJ 493, 694 (1998) D. Grasso et al., Astroparticle Physics 32, 140 (2009), 0905.0636 L. Gendelev, S. Profumo, and M. Dormody, JCAP02 016 (2010) A.K. Harding, HEAD meeting, Waikoloa, Hawaii, 2010 P. Blasi, These Proceedings W. Bednarek, These Proceedings O. de Jager, These Proceedings

621

Positrons from pulsar winds Pasquale Blasi and Elena Amato

Abstract Pulsars, or more generally rotation powered neutron stars, are excellent factories of antimatter in the Galaxy, in the form of pairs of electrons and positrons. Electrons are initially extracted from the surface of the star by the intense rotation induced electric fields and later transformed into electron-positron pairs through electromagnetic cascading. Observations of Pulsar Wind Nebulae (PWNe) show that cascades in the pulsar magnetosphere must ensure pair multiplicities of order 104 − 105 . These pairs finally end up as part of the relativistic magnetized wind emanating from the pulsar. The wind is slowed down, from its highly relativistic bulk motion, at a termination shock, which represents the reverse shock due to its interaction with the surrounding ejecta of the progenitor supernova. At the (relativistic) termination shock, acceleration of the pairs occurs, as part of the dissipation process, so that the cold wind is transformed into a plasma of relativistic non-thermal particles, plus a potential thermal component, which however has never been observed. As long as the pulsar wind is embedded in the supernova remnant these pairs are forced to escavate a bubble and lose energy adiabatically (because of the expansion) and radiatively (because of magnetic and radiation fields). We discuss here the observational constraints on the energy and number content of such pairs and discuss the scenarios that may allow for the pairs to escape in the interstellar medium and possibly contribute to the positron excess that has recently been detected by the PAMELA satellite. Special attention is dedicated to the case of nebulae surrounding high speed pulsars, observationally classified as Pulsar Bow Shock Nebulae. The pairs produced in these objects may be effectively carried out of the Supernova Remnant and released in the Interstellar Medium. As a result, Bow Shock Pulsar Wind Nebulae might be the main contributors to the positron excess in the Galaxy.

Pasquale Blasi INAF/Arcetri Astrophysical Observatory, e-mail: [email protected] Elena Amato INAF/Arcetri Astrophysical Observatory, e-mail: [email protected] N. Rea and D.F. Torres (eds.), High-Energy Emission from Pulsars and their Systems, Astrophysics and Space Science Proceedings, DOI 10.1007/978-3-642-17251-9_50, © Springer-Verlag Berlin Heidelberg 2011

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1 Introduction Pulsars have long been known to be powerful factories of electron-positron pairs: the rotation of the pulsar leads to an induced electric field that extracts electrons from the star’s surface. These electrons lose energy via curvature radiation while propagating far from the star along the magnetic field lines, and the emitted photons are so energetic that an electron-positron pair can be formed in the intense neutron star magnetic field. The process can in principle repeat itself numerous times, increasing the number of pairs up to a large value of the so-called multiplicity, defined as the number of pairs derived on average from a single primary particle that leaves the star surface. How many pairs in the end leave the pulsar magnetosphere is a question that still does not have a definite answer in terms of theory of pulsar magnetospheres, depending on the location and structure of the magnetospheric gaps, the regions where there is an unscreened electric field parallel to the local magnetic field and particles can be accelerated. Progress on this topic has recently come from gamma-ray observations, by MAGIC first [2] and Fermi [3] later, which have allowed to locate the source of pulsed high energy emission in the outer magnetosphere, ruling out the possibility that gamma-rays are produced close to the stellar surface (polar cap scenario) together with the low energy radio emission. As we will discuss below, in spite of the theoretical uncertainties, rather stringent constraints on the pair multiplicity of pulsars can be obtained from observations of their nebulae. The pairs produced in the magnetosphere become part of the relativistic magnetized wind emanating from the pulsar and find themselves in a complex environment. The neutron star was born in a supernova explosion, from the collapse of a massive star, and therefore initially lies in a region bounded by the ejecta of its progenitor and further out by the Supernova blast wave propagating in the Interstellar Medium (ISM). When the cold magnetized wind launched by the star and propagating at almost the speed of light hits the sub-relativistically expanding ejecta, the impact results in a system of shock waves: the outer one propagates in the ejecta, while a reverse shock propagates back towards the star. This is the so-called termination shock, where the wind is slowed down, its bulk energy dissipated and turned into that of a relativistically hot, magnetized fluid, which then shines as a Pulsar Wind Nebula. Indeed, the termination shock is also where particle acceleration occurs. When the electron-positron pairs produced in the pulsar magnetosphere reach the termination shock, due to the severe energy losses they have suffered, their energy is not larger than few tens of GeV, in spite of the enormous potential drop available, which might be as large as 1016 V. At the termination shock, a relatively large fraction (up to few tens of percent) of the wind bulk energy is converted into accelerated pairs, which then radiate a very broad band photon spectrum, extending from radio frequencies to multiTeV gamma-rays, through synchrotron and Inverse Compton processes. The accelerated pairs propagate far from the termination shock, advected together with the toroidal magnetic field lines, as an expanding MHD fluid. They are confined within the cavity escavated by the wind and progressively lose energy,

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as also demonstrated by the fact that the radio emitting region is typically broader than the X-ray emitting region, in agreement with a scenario in which propagation is energy independent and the difference in size is due to the larger energy losses suffered by the higher energy particles responsible for X-ray emission. The question of whether some of these pairs can leave the system has acquired a special interest in recent times, after the discovery of a positron excess in the energy region 10-100 GeV by the PAMELA satellite [5]. The only guaranteed source of diffuse positrons in the Galaxy is represented by inelastic nuclear collisions of cosmic rays, which give rise to charged pions and in turn to positrons (and electrons) of secondary origin. The spectrum of such positrons is steeper than the cosmic ray spectrum, because of propagation and loss related effects. The PAMELA data show an increase of the e+ /(e+ + e− ) fraction with energy, that cannot be explained in the traditional scenario, and has been interpreted as the result of the intervention of an additional source of positrons. Several possibilities have been discussed in the literature: reacceleration of positrons originating as secondary products of CR interactions inside supernova remnants [10, 12], inhomogeneous distribution of sources in the solar neighborhood [40], dark matter annihilation in the Galaxy [19, 20, 27] and finally pulsars [29, 28]. Severe constraints on the origin of the PAMELA excess are imposed by the PAMELA observations of the antiproton [6] flux and by the recent measurement of the electron spectrum by the Fermi satellite, up to ∼ 1 TeV[4]. The former suggest that whatever the source of the positrons is, it has to be less effective in producing antiprotons, at least up to ∼ 1 TeV energy. The combination of Fermi and PAMELA results provide constraints on the spectrum of the positrons produced by the additional putative sources and on their spatial distribution. The case in which dark matter (DM) annihilation is assumed to be the main source of positrons offers an interesting demonstration of how powerful these constraints are: standard WIMPS would in fact result in a too low flux of positrons. In order to make DM annihilation a viable scenario, one is forced to assume either a boosting factor due to substructures and/or an enhancement of the annihilation cross section, as might be caused by the Sommerfeld effect [20]. While the former is unlikely to provide an effect of more than a few, an enhancement of the annihilation rate also leads to a corresponding increase of the antiproton flux, in conflict with observations. If, again, one wants to force a DM interpretation, the DM candidate has to be assumed as leptophilic. Following reasonable scientific standards, this scenario can be considered highly disfavored if not ruled out. As stressed above, pulsars naturally produce electron-positron pairs. Therefore they have been immediately proposed as possible sources of the positrons observed by PAMELA [29]. The main issue with pulsars as sources of cosmic ray positrons is in the possibility for the positrons to escape the supernova remnant environment. For this reason the authors of [29] explicitly referred to mature pulsars as sources. The qualitative nature of the justification for considering mature pulsars opens however the way to criticisms for this scenario, strengthened by the fact that the attention was there centered on pulsars rather than pulsar winds, while the latter are the real place where the genesis of the final positron spectrum should be sought.

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Here we discuss the problem of the positron excess and of its possible connection with pulsars in the context of the much more complex phenomenology of pulsar winds and pulsar wind nebulae, on which we now have a wealth of data in different radiation bands. The paper is organized as follows: in § 2 we briefly discuss the different parts of the relativistic wind launched by a pulsar inside a supernova remnant. In § 3 we discuss the importance of bow shock nebulae as possible vehicles to carry positrons (and in general pairs) outside the remnant to make them available in the cosmic radiation. In § 4 we describe the calculations of the positron flux at Earth as a result of injection from individual pulsars. We dedicate special attention to discussing the effect of discreteness in the Galactic pulsar distribution on the positron excess and on the spectrum of electrons (meaning here the sum of electrons and positrons) at Earth. Finally, § 5 is then devoted to a critical discussion of the achievements and challenges of the pulsar wind scenario for the positron excess.

2 A pulsar wind inside a supernova remnant In this section we discuss some selected topics which are of relevance for the problem of pair production in the pulsar environment and therefore for the problem of the positron excess in cosmic rays. For obvious reasons we will not provide here a full review of all the Physics involved in the production of pulsar winds and their interactions with the surrounding medium. Excellent recent reviews of these issues can be found in [8, 25]. A rotating magnetized neutron star loses rotational energy. The decrease of the rotation frequency Ω = 2π/P (where P is the rotation period) can be written in general form as Ω˙ = −αΩn , (1) where n is the so-called braking index (n = 3 for magnetic dipole). The spin down luminosity of the pulsar can easily be written in terms of the moment of inertia I: ˙ = αIΩn+1 . E˙ = IΩ|Ω|

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(4)


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The special case of magnetic dipole corresponds to n = 3 and α = (5/8)B2s R4s /M s c3 , where B s is the surface magnetic field, R s is the radius and M s the mass of the neutron star. The total energy lost by the star is (1/2)IΩ20 ≈ 1050 erg, most of which is converted into a magnetized, relativistic wind in a time comparable with τ0 . The relativistic wind launched by the pulsar impacts on the much slower ejecta of the supernova that generated the pulsar in the first place. This creates a reverse shock that moves inward and a contact discontinuity is formed between the PWN material and the ejecta. This reverse shock is what is usually named termination shock. The nebulae that we observe are produced by non-thermal particles downstream of the termination shock where the incoming pairs are partly thermalized and, even more important, accelerated to very high energies (in the case of the Crab, radiation from particles with energies up to a few ×1015 eV is observed). The physical picture that describes the launching and the propagation of the pulsar wind from the star magnetosphere to the termination shock still presents a number of lose-ends. We will not touch these issues here, while extensive discussion can be found in [8, 31]. What is relevant for our present goals is that: 1) the wind is mostly made of electron-positron pairs, while the presence of a numerically negligible, but energetically important fraction of ions cannot be excluded (see also below); 2) the wind must originate as a Poynting flux dominated outflow, but from observations of Pulsar Wind Nebulae we infer that at the termination shock most of its energy is in the form of particle kinetic energy; 3) at the termination shock the wind is highly relativistic, with a Lorentz factor Γ in the range 104 − 107 , as derived again from observations and modeling of PWNe. The terminal Lorentz factor of the wind is crucially important in a number of respects for the constraints it puts on the physics of the pulsar magnetosphere. In the last few years, much has been learnt on the wind properties close to the termination shock thanks to extensive comparison between the results of 2-D relativistic MHD simulations of the pulsar outflow and observations of PWNe ([32, 22, 23, 45]). Nonetheless, among all unknown parameters, the wind Lorentz factor is the most elusive to this kind of diagnostics, since the dynamics of the post-shock flow is independent of Γ as long as Γ ≫ 1. At present, the only viable means to put constraints on it resides in the modeling of the global emission spectrum of Pulsar Wind Nebulae: investigations have only just started [16]. The evolution of the Pulsar Wind Nebula depends on the properties of the surrounding supernova ejecta. In the simplest picture one can assume that the supernova ejecta form a spherical shell around the pulsar. In this case, during the ejecta dominated stage the wind expands in a quasi-spherical way and drives a shock in the ejecta. When the supernova enters its Sedov phase, the reverse shock driven by the blast wave reaches the inner part of the remnant and in principle excites a few reverberations in the nebular structure [44, 14]. On the other hand, by the beginnig of the Sedov phase the kick birth velocity of the pulsar, whose distribution shows a peak at ∼ 400 − 500 km/s [9], is expected to have forced the pulsar off center, so that the structure of the nebulae in this phase is likely rather asymmetrical. The issue of the effect of the reverse shock on the population of electron-positron pairs in

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terms of adiabatic compression and/or spatial displacement, would be worth being investigated in more detail. In order to establish, if possible, a connection between Pulsar Winds and the positron flux in Cosmic Rays, what is really important for us is the pair spectrum that is released in the ISM and the only way to obtain some insights on this issue is through observations of PWNe. As stressed above, all radiation observed in PWNe comes from particles radiating downstream of the termination shock, where the pairs initially produced in the pulsar magnetosphere are accelerated to non-thermal energies. On purely observational grounds, the spectrum of radiation observed from several PWNe requires a spectrum of radiating electrons and positrons which has the shape of a broken power law with a break at Lorentz factor of ∼ 105 , namely E b ∼ 50 GeV for electrons [16]. The slope below this point is typically α1 ≈ 1 − 1.5, while the slope at high energies is α2 ≈ 2 − 2.4. This seems to be a rather general trend, and as we discuss in the next section, appears to be common also to fast pulsars outside their SNRs (bow shock nebulae). The acceleration process responsible for the production of this spectrum is all but clear, for many good reasons. First the broken power law is not typical of stochastic acceleration processes, in which usually a single power law spectrum is produced (or in some cases a curved spectrum, rather than two power laws). Second, any stochastic acceleration process that we are aware of leads to the production of a nonthermal tail on top of a thermal distribution of particles which take into account the unavoidable heating process. This is certainly true in the case of shock acceleration: at the relativistic termination shock one would expect to have a thermal distribution corresponding to particles with mean energy ∼ (Γ − 1)me c2 , where Γ is the Lorentz factor of the wind, and a non-thermal tail in the high energy part. No evidence has ever been found of this thermal component in PWNe, which makes the situation really puzzling. One could speculate that the thermal “bump” is at lower energies, where either it is not observed or cannot be observed (for instance if its energy corresponds to frequencies of the synchrotron photons below the ionospheric cutoff of the atmosphere). This possibility however opens more theoretical problems than it solves: for an electron spectrum N(E) ∝ E −α1 , with α1 < 2 as observed, most particles are in the lowest energy end of the distribution, while most energy is at the high energy end. Moving the thermal peak at very low energies implies that the number of pairs reaching the termination shock is much larger than can be accounted for by current theoretical models of pair cascading in the pulsar magnetosphere. While the slope of the spectrum at E > Eb , α2 ∼ 2 − 2.4, appears to be similar to that expected from diffusive shock acceleration at a relativistic shock, a closer look reveals more problems: the termination shock is a highly relativistic quasiperpendicular shock, and in these circumstances simple physical arguments lead to think that shock acceleration cannot take place efficiently, as also confirmed by PIC simulations [41], which have never shown evidence of acceleration in perpendicular shocks occurring in pure pair plasmas if the magnetization is at the level implied for most of the pulsar outflows [45]. Moreover, diffusive shock acceleration could not explain, even in principle, very flat low energy spectra α1 < 2, with the possible exception of the so-called large angle scattering regime [13, 42], but there are serious


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doubts that the conditions for large angle scattering may be actually realized in Nature. In principle, acceleration by cyclotron absorption [30, 7] could produce the desired spectra if a substantial fraction of the pulsar wind energy is carried by protons. However, this condition can only be realized if the wind Lorentz factor is sufficiently high: it is indeed difficult to imagine that the pulsar wind can carry a proton density in excess of the Goldreich-Julian value, so in order for them to be energetically dominant the wind Lorentz factor needs to be sufficiently high and the pair multiplicity relatively low (Γ ∼ 106 and κ ∼ 103 in the case of Crab). The requested values of Γ and κ agree with current theoretical modeling of pair production but are at odds with the inferences of the most recent studies on the subject [16]. In any case this scenario would leave the issue of the thermal peak untouched. Another scenario that can be considered to explain the observed spectra is that arising from a picture in which the striped magnetic structure [21, 35] implied for the wind at low latitude around the pulsar rotational equator leads to reconnection at the termination shock, with associated particle acceleration [36]. The shape of the spectrum is poorly constrained in this case, due to its strong dependence on the geometry of the reconnection region. A priori it is however difficult to envision a reason to have a broken power law. On the other hand, the arguments to deduce that there should be a thermal component downstream of the shock might be weaker in this case, since energy could be transferred to bulk motion of the plasma rather than disordered (thermal) energy (Jon Arons, private communication).

3 A pulsar wind escaping the parent supernova remnant: bow shock nebulae The typical birth velocity of a pulsar born in a core collapse supernova event is ∼ 400 − 500 km/s [9], while about 50% of the pulsars have velocities larger than this. This fact might be of the highest relevance for the problem of the escape of electron-positron pairs from the pulsar environment, since a fast pulsar can release a large part of its energy through a relativistic pair wind that propagates directly in the ISM, where the confining effect of the ejecta is absent. After the pulsar is born, its proper motion takes it far from its birth place, across the central part of the remnant and later across the shocked hot ejecta. If we assume that the SNR is in its Sedov phase, the radius of the blast wave is traced by the relation: R sh (t) = RS

t ts

!2/5

,

(5)

while the pulsar covers a distance R pulsar = vkick t. It is straightforward to see that, for the typical values of vkick quoted above, the pulsar leaves the parent supernova remnant after a time of order ∼ 40, 000 − 50, 000 years (the assumption of Sedov expansion is justified for reasonable values of the supernova and ISM parameters).

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The motion of the pulsar in the ISM is at this point supersonic, therefore the impact of the relativistic wind on the ISM leads to the formation of a bow shock structure. The forward (bow) shock also drives a reverse shock (termination shock), as illustrated in a schematic way in Fig. 6a of Ref. [25]. At the termination shock particle acceleration leads to the formation of a non-thermal spectrum of pairs which produce a nebula, now referred to as bow shock nebula. The pairs which are accelerated at the termination shock (though, as discussed above, the acceleration mechanism is not known) propagate in the tail [15] and eventually end up in the ISM in the form of cosmic rays. The spectral distributions of accelerated pairs required to explain the spectra of observed radiation, in the few cases in which observations allow such a study, are very similar to those observed in PWNe inside SNRs. For instance in G319.9-0.7, the bow shock nebula powered by PSR J1509-5850, the radio spectrum [39] has a slope −0.26 (corresponding to an electron spectrum with slope α1 = 1.52); in the Mouse [46] the radio spectrum has slope −0.3, corresponding to α1 = 1.6. The high energy part of the spectrum is also similar to that observed in PWNe inside SNRs [26]. The fact that pulsars can exit their birth site after 40-50 kyr is clearly of paramount importance in terms of establishing a possible connection with the cosmic ray positron flux detected by PAMELA. We investigate this possibility by first estimating the rotational energy left in the pulsar at the time of escape from the remnant. We carry out this estimate keeping the braking index arbitrary to start with. The rotational energy left after a time T e , which we take as the escape time from the remnant, can be written as 1 Te E rot (t > T e ) = IΩ20 1 + 2 τ0

2 ! 1−n

.

(6)

It is easy to see that the critical parameters to estimate how much energy the pulsar can still convert into electron-positron pairs after its escape from the remnant are the initial rotation frequency Ω0 and the characteristic time τ0 (which in turn depends on Ω0 and on the braking index n as in Eq. 3). These parameters are directly measured only in the very rare cases in which one has observations spanning a long enough ¨ Using the period of time so as to allow derivation of all three quantities Ω, Ω˙ and Ω. expressions reported in the previous section one can then easily obtain the braking index as ¨ ΩΩ n= . (7) 2 ˙ Ω Moreover the characteristic time τ0 is such that τ0 + T age =

1 Ω , 1 − n Ω˙

(8)

˙ where T age is the age of the pulsar at the time of measuring the values of Ω, Ω ¨ and Ω. The difficulty in measuring all these rotational parameters justifies the fact that the full set of spin down parameters is known so far for only four pulsars, the


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Crab pulsar [37], Vela [38], B1509-58 [33] and B0540-69 [34]. In all these cases the measured braking index n is lower than in the dipole case (n = 3), ranging from the very low value of Vela (n = 1.4) to about 2.8 for B1509-58. For the sake of simplicity we consider two benchmark cases, a hypothetical dipole case (n = 3) with initial rotational period P0 = 10 ms (corresponding to Ω0 = 628.3 s−1 ) and a Crab-like case, with n = 2.5 and P0 = 19 ms, as deduced from observations. For the dipole case, one easily obtains that τ0 ≈ 5000 years. In this case, if the escape time is estimated as T e ≃ 4 × 104 years, from Eq. 6 one gets the energy available for conversion into pairs after the pulsar escapes the remnant: Erot (t > T e ) ≈ 2 × 1049 erg. If one calculates the time τ0 from observations, the result is quite different. The observed values of the spin down parameters are as follows: ˙ = −3.86 × 10−10 s−2 and Ω ¨ = 1.24 × 10−20 s−3 . Using Eq. 7 one finds Ω ≈ 190s−1 , Ω n = 2.51 and τ0 ≈ 730 years (a factor ∼ 7 shorter than for the dipole case) taking into account the age of the Crab pulsar (or using the measured value of the third time derivative of Ω, as in [37]). This approach also returns Ω0 ≈ 330s−1 . In this case, the energy available after escape is Erot (t > T e ) ≈ 3 × 1047 erg. The different conclusions in the two cases show how the results depend in a crucial way on the spin down history of the pulsar: the efficiency in conversion to pairs needed to explain the PAMELA data are also very different as we discuss in the section below. The dipole case would be even more at odds with the observed data if one assumed the same value of Ω0 ≈ 330s−1 in the two cases. The positrons produced by a pulsar after the escape from the SNR can hardly be confined by the bow shock. The nebulae that we observe have a morphology that suggests that relativistic particles are being advected far downstream of the pulsar, while the bow shock opens up. It is therefore only reasonable to envision that these positrons can escape the nebula and be part of the cosmic radiation propagating in the Galaxy and eventually reach the Earth. This addresses one of the main concerns that have been raised about a pulsar related origin of the PAMELA positrons, namely that of the leakage of such positrons outside the parent remnant. On the other hand, the issue of the fate of the positrons produced while the pulsar is inside the parent remnant remains there. A dedicated investigation of this problem, even independently of the positron signal, would be worthwhile.

4 The positron flux from pulsars The flux of positrons (and electrons) from pulsars has been calculated and discussed in previous papers [17] and compared with the flux of positrons observed by PAMELA [29, 28]. These calculations have however two limitations: 1) they all start with a ad hoc assumption on the spectrum of positrons at the sources, without a proper discussion of observational bounds and physical interpretation of the acceleration and escape of these particles. 2) The pulsars are assumed to represent a population of sources distributed continuously (in space and time) in the Galaxy,

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namely the discrete nature of the sources is ignored (though in [28] the authors discuss the role of known nearby pulsars). In this section we carry out the calculation of the positron and electron fluxes at the Earth assuming that they are accelerated in individual pulsar winds and propagate from each source to the Earth through the Galactic magnetic field. At the same time, we assume that ordinary cosmic rays (protons and electrons) are accelerated in supernova remnants associated with the formation of pulsars. This approach neglects the contribution of supernovae of type Ia, which are subdominant in our Galaxy. Their contribution will be discussed elsewhere. The calculation takes into account the temporal evolution of the distribution function of electrons and positrons. This allows us to offset the production time of positrons from a pulsar by the time required for the pulsar to escape the remnant after the time of explosion of the parent supernova. Moreover, the energetics available in the pulsar wind at that time is calculated as discussed in the previous section, taking into account the spin down of the pulsar before the escape from the remnant. The time and location of each supernova event in the Galaxy are drawn at random from the distribution of type II supernovae as given in [24]. Once time and location are known with respect to the location of the Sun, the diffusion equation is solved by using the appropriate Green function. In the range of energies we are interested in, the spectrum of the produced electrons and positrons is affected by propagation mainly through radiative losses, therefore for simplicity we neglect here the role of escape of electrons from the Galaxy, which play a role only below 10 GeV. In this case, the solution of the diffusion equation for an individual supernova remnant is [43]: h i Z ∞ exp −(r − rexp )2 /4λ(E, E ′) ′ n(E, t) = dE N(E ′ )δ(t − texp − τ(E, E ′ )), (9) |b(E)|(4πλ(E, E ′))3/2 E where λ(E, E ′ ) =

Z

E E′

dy

D(y) b(y)

τ(E, E ′ ) =

Z

E E′

dy

1 . b(y)

(10)

Here D(E) is the diffusion coefficient experienced by electrons and positrons while propagating throughout the Galaxy and b(E) = −AE 2 is the rate of energy losses due to synchrotron and inverse Compton scattering (ICS). The time texp is the time of explosion of the supernova in the case of electrons, while it is the time of escape of the pulsar in the case of production of electrons and positrons in the relativistic wind of the pulsar. The distribution function N(E) is the injection spectrum of either the SNR or the pulsar wind. In both cases the injection is assumed to be instantaneous. In the case of pulsars, the assumption is well justified because the spin down of the pulsar concentrates most injection at early times, close to the time of escape of the pulsar from the remnant. For SNRs, which in our picture only produce electrons, the injection of accelerated particles is not well understood (see for instance [18] for a detailed discussion of the issues involved in the CR escape from a SNR). However the effects of the assumption of instantaneous injection on the results have been tested and found to be minimal at all energies of interest for the positron production.


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The contribution of all pulsars is calculated by exploding Supernovae and taking into account the associated SNRs and pulsars for a period exceeding all relevant time scales in the problem (for instance escape time from the Galaxy and time of energy losses), so as to ensure that the galaxy is globally in a stationary situation. This does not mean that the flux of electrons and positrons at the Earth is stationary. In fact, proximity effects lead to a time-dependence of the fluxes and, even more important, to a dependence of the resulting fluxes upon the particular realization of the distribution of supernovae in the Solar neighborhood. The diffusion coefficient is assumed to be D(E) ∝ E 1/3 to avoid problems with CR anisotropy in the energy region 104 − 106 GeV. The normalization of D(E) is taken so as to satisfy the condition that the escape time of CRs at energy of 10 GeV/nucleon is ∼ 1.5 × 107 years, as deduced from the measurement of the B/C ratio [1]. This normalization depends of course upon the size of the halo H from which particles have to escape diffusively (all our calculations are carried out for H = 2 kpc). From the point of view of escape of a pulsar from the SNR, we consider two benchmark cases: one in which the pulsar spins down as a magnetic dipole, and the other one in which the spin down occurs with a braking index n = 2.5. The latter case is closer to observations, if we assume that the four pulsars for which the rotation parameters could be measured are ’typical’. The implications of these two models for the pulsar wind scenario of origin of the positron excess are, as we show below, rather impressive. It is important to realize that the approach presented here returns automatically the spectra of both primary electrons accelerated in SNRs and electrons and positrons produced in pulsar winds after the escape of the pulsar from the SNR. Actually the same approach (completed with the escape of cosmic rays from the Galaxy) also returns the spectrum of CR nuclei at the Earth, as discussed in [11]. The authors also reach there the conclusion that the anisotropy of CRs at the Earth exceeds the observations if the diffusion coefficient has an energy dependence around ∼ E 0.6 . Before illustrating the results of detailed calculations, it is worth discussing briefly some general points concerning the contribution of individual SNRs and pulsar winds to the spectrum of electrons and positrons at the Earth. For the sole purpose of this simple estimate, we assume for simplicity that the sources are distributed uniformly in the disc of the Galaxy, with a half-thickness Hd = 150 pc and a radius Rg = 15 kpc. The sources that can contribute to the flux at Earth at a given energy E are those lying within a distance from the Earth such that the propagation time is shorter than the loss time at that energy. If R is the rate of supernovae in the Galaxy (assumed to be one every 30 years), the number of supernovae within a given distance R from the Earth, exploding in a loss time, is Rτloss (R/Rg)2 . For our purposes: R ≈ (4D(E)τloss)1/2 . It follows that the number of sources which can contribute to the flux at energy E is N ≈R

4D(E) 2 τ ∝ E 1/3 /E 2 . R2g loss

(11)

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This simple estimate shows that the number of relevant sources is a rapidly decreasing function of energy. For typical values of the parameters ∼ 1000 sources contribute at 10 GeV, and ∼ 20 at 100 GeV. At 1 TeV only about 1 source can contribute. This conclusion has several implications: 1) the flux of electrons and positrons at high energy is a sensitive function of the local distribution of recent SNRs; 2) the slope of the electron spectrum as inferred from the standard stationary solution of the transport equation is typically not reproduced in a time dependent approach with discrete point sources exploding at random times. The distribution of type II supernovae [24] is not uniform across the disc of the Galaxy and shows a gradient along the radial direction. Using this distribution, it is possible to determine the number of SNRs/pulsars contributing at given energy in a more realistic way. The results are shown in Fig. 1 for energies of 10 GeV (first row), 100 GeV (second row) and 1 TeV (third row). The plots on the left show the time of explosion (on the y-axis) as a function of the distance from the Sun location, while the plots on the right show the location of the sources in a given realization (the distance scale is centered on the Sun location). One can clearly see how increasing the energy the number of relevant sources (in space and time) decreases rapidly. In the 10 GeV case one may notice the asymmetric distribution of local supernovae as follows from the off-center location of the Sun in the Galaxy. It is worth stressing that the sources in these plots do not contribute all in the same way: there are nearby sources which turned on a long time ago, while there are more distant sources which are recent and may contribute more. In other words, the flux at Earth is in general a complex combination of the contributions from these sources. Only for a truly continuous (in space and time) distribution of the sources one recovers the standard solution of the stationary transport equation. We discuss now the results of the calculations of the flux of electrons (from acceleration in SNRs) and electrons and positrons coming from pulsar winds after the pulsar escapes the parent remnant. As mentioned above, we consider two models for the spin down of the pulsar, one in which the pulsar rotation slows down as a magnetic dipole (braking index n = 3) and one in which the spin down corresponds to a braking index n = 2.5, similar to the one observed for the Crab pulsar. In both cases the average escape time from the remnant has been taken to equal 4 × 104 years. When the spin down is dipole-like, the predicted spectrum of electrons and positrons and the positron ratio are illustrated in Fig. 2. The data points in the left panel are from the Fermi satellite [4], while the data points on the right panel are from the PAMELA satellite [5]. The acceleration efficiency of protons is ∼ 10%, and the ratio of the accelerated spectra of electrons and protons is Kep = 9 × 10−3 . The injection spectrum of electrons, which are still assumed to be mainly accelerated via diffusive shock acceleration, together with protons, in Supernova blast waves is ∝ E −2.4 with a cutoff at 10 TeV. The pairs from pulsar winds have an injection spectrum ∝ E −1.2 with a cutoff at 700 GeV, as implied by observations of synchrotron radiation from PWNe in the relevant energy range. It is worth recalling that, as found in the previous section, the energy available in the pulsar rotation in the dipole case, after escaping the remnant, is of order ∼ 2 × 1049 erg. In this case the efficiency of


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Fig. 1 Temporal and spatial distribution of sources in one realization as a function of energy. Left Panels): Time of explosion of a supernova as a function of the distance from the Sun. Right Panels): Cartesian spatial coordinates (in kpc) of the supernova events on a grid centered on the location of the Sun. The first row refers to electron energy 10 GeV, the second to 100 GeV and the third to 1 TeV.

escape of pairs from the nebula required to explain the positron excess and at the same time provide a good fit to the observed electron (plus positron) spectrum is ξ± = 9 × 10−3 , corresponding to ∼ 1.8 × 1047 erg per pulsar wind. This estimate is similar to previous estimates appeared in the literature. It is worth stressing a few interesting things: 1) These predictions, though qualitatively similar, are quantitatively different if one changes the realization of sources, for the reasons explained above. We will discuss below the dependence upon realization. 2) If the discrete nature of the source is ignored, one would expect that electrons injected with a power law spectrum E −γ in a thin disc and allowed to propagate with diffusion coefficient D(E) ∝ E δ have an equilibrium spectrum n(E) ∝ E −γ τloss (E)/(4D(E)τloss(E))1/2 ∼ E −3.06 for γ = 2.4 and δ = 1/3. One can

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Fig. 2 Case of dipole spin down with escape of the pulsar from the remnant 40,000 years after the supernova event. Left): Spectrum of electrons from SNRs (solid line) and electrons and positrons from pulsar winds (dashed line). The thick solid line through the Fermi data points is the sum of the two. Right): Positron ratio compared with the PAMELA data points.

clearly see from the left panel of Fig. 2 that this is not the case, as a consequence of the local distribution of sources around the Sun. A good fit to the electron spectrum measured by Fermi is possible only because of the superposition of the contributions of SNRs and pulsar winds. This superposition naturally explains the presence of wiggles in the electron spectrum and is the very reason for the PAMELA positron excess. An excellent fit to the data can also be obtained if one assumes a pulsar spin down with braking index n = 2.5, as shown in Fig. 3. In this case the parameters have the same values as in the dipole case, but the required efficiency for pairs in pulsar winds is ∼ 28% (to be compared with the previous value of ∼ 9 × 10−3). It is worth stressing that this efficiency does not refer to the total rotational energy of the pulsar, but only to the energy available after the escape of the pulsar from the remnant. In this sense it does not sound as problematic that the required efficiency is of order tens of percent, since after the pulsar escapes the remnant high energy electrons can be hardly confined inside the nebula and they can only become part of the cosmic radiation, thereby contributing to the positron flux at Earth. As anticipated above, the fact that sources are discrete in space and time leads to an intrinsic dependence of the predictions on the realization. In order to illustrate this dependence, in Fig. 4 we show the results obtained for n = 2.5 in a different realization of sources. One can see that in both contributions, of SNRs and pulsars, there is an excess at high energies, suggesting that in this realization a supernova happened to explode close to us in recent times. One can also see that the total


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Fig. 3 Case of spin down with braking index n = 2.5, with escape of the pulsar 40,000 years after the supernova event. Left): Spectrum of electrons from SNRs (solid line) and electrons and positrons from pulsar winds (dashed line). The thick solid line through the Fermi data points is the sum of the two. Right): Positron ratio compared with the PAMELA data points.

flux is affected in the same way, but the positron ratio, which is measured at lower energies, remains basically unchanged, though future measurements with AMS2 might detect this type of proximity effects even in the positron fraction. As we discussed in § 2 and § 3, observations show that in the few cases in which we can measure the spectrum of the radiation and convert it to an electron spectrum, the low energy part has slope between −1 and −1.8. In order to illustrate the dependence of the predictions on the assumed injection spectrum of pairs in pulsar winds, we repeat our calculations for an injection spectrum ∼ E −1.5 . The results are illustrated in Fig. 5, where the spectrum of pairs is cut off at 1.8 TeV. The fit to Fermi and PAMELA data requires Kep = 8.5 × 10−3 and an efficiency of conversion of rotational energy into accelerated pairs of ξ± = 39%. Again, though quantitatively slightly different, qualitatively the conclusions are not excessively affected by the slope of the spectrum of electrons in the range of relevance for us.

5 Discussion The discovery by the PAMELA satellite of a positron flux in excess of the secondary positron flux produced by inelastic CR interactions in the Galaxy has attracted much attention for many reasons. First, it represents one of the few macroscopic anomalies in our understanding of the origin of galactic cosmic rays; second, it has been viewed

638


Fig. 4 Same as in Fig. 3 but for a different realization of source distribution in space and time.

Fig. 5 Same as in Fig. 3 but with slope of the injection spectrum of pairs −1.5.

by some as one possible evidence of annihilation of dark matter; third, it inspired some to search for astrophysical sources of positrons; fourth, it happened at roughly the same time at which the Fermi satellite provided an accurate measurement of the electron spectrum (meaning the spectrum of electrons plus positrons), that showed interesting wiggles and a shape not immediately reconcilable with the predictions


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of the standard model of CR propagation in the Galaxy (though one should admit that such standard model is not that standard after all). It has also revived the interest of the scientific community for pulsars and pulsar winds as galactic antimatter factories. The connection between pulsars and the PAMELA positron excess has been almost immediate [29], but not much attention was devoted to the actual physics of the electron-positron pairs acceleration and escape from the environment where the pulsar is produced. In this paper we discussed the strong and weak points of the theory of pair generation in pulsar winds and their mixing with the cosmic radiation eventually observed at Earth after propagation in the Galaxy. We argued that the PAMELA positron excess is well explained if the pairs are liberated after the pulsar, originated in a core collapse supernova, escapes the parent supernova remnant. This event typically occurs (4 − 5) × 104 years after the initial blast, as could be estimated by assuming an average birth kick velocity of the pulsar. The production of pairs occurs through a fascinating process: the induced electric field due to rapid rotation extracts electrons from the star’s surface, and these electrons find themselves in intense magnetic fields which lead to curvature radiation. In turn the photons produced in this way produce pairs and the process continues so as to form an electro-magnetic cascade which generates all the pairs we are interested in, though the maximum energy at this point is of order few GeV. In a young pulsar, the relativistic wind carrying these pairs away from the star eventually encounters the ejecta of the supernova so that a reverse shock is generated. This shock, referred to as the termination shock is the very site where the pairs are accelerated to very high energies. The PWNe that we observe are due to the radiation emitted by these accelerated pairs downstream of the termination shock. The luminosity of the PWNe is typically of the same order of the spin down luminosity of the central pulsar. As long as the pairs are in this complex environment, it is difficult to envision an obvious contribution to the cosmic ray positrons, as recognized by previous publications on this topic [29], both because of radiative and adiabatic energy losses. On the other hand, we have now clear evidence that pulsars remain inside the parent remnant only for 104 − 105 years. After this time, the pulsar actually escapes the region limited by the blast wave of the supernova and moves with its initial kick velocity in the ISM. The typical velocity of ∼ 500 km/s leads to supersonic motion, so that the relativistic wind that still emanates from the pulsar generates a bow shock and a nebula inside it. In a way similar to what happens when the pulsar is inside a remnant, a termination shock is also formed as a reverse shock and particle acceleration takes place around it. Although the acceleration process is all but known, on purely observational grounds we know that the spectrum of the accelerated pairs is a broken power law, with a low energy part (up to ∼ 100 − 1000 GeV) as flat as E −1 − E −1.8 . The open structure of bow shock nebulae appears to be an excellent avenue for particle escape from the nebula. The energy still available in the form of pulsar rotation after the escape from the remnant is of order ∼ 1049 erg if the pulsar spins down as a magnetic dipole (braking index n = 3) or of order ∼ 1047 in the case of braking index n = 2.5, similar to the one measured in the Crab pulsar.

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The flux of electrons and positrons produced in the parent SNR (through acceleration at the shock) and at the pulsar wind termination shock after the pulsar escapes the remnant has been calculated by taking into account the random nature of supernova events (in space and time). The results are extremely interesting and can be summarized as follows: • For the case of dipole spin down one needs ∼ 1% of the energy available in the pulsar rotation after escape from the remnant in order to explain at the same time the electrons (plus positrons) spectrum measured by Fermi and the positron ratio measured by PAMELA. The efficiency becomes ∼ 30 − 50% for the case with braking index n = 2.5. We want to point out that an efficiency of order unity is in a way more natural for the bow shock phase, since the pairs with energy below ∼ 1 TeV or so can only end up in the ISM as cosmic ray particles. It would therefore be rather problematic to explain the fate of pairs in the dipole case, where the required efficiency is only ∼ 1%. On the other hand one should keep in mind that a dipole-like spin down is not observed in any of the pulsars for which the braking index is known. • As a consequence of the previous point, the contribution of pulsars to the positron flux at the Earth is basically unavoidable since the production rate is guaranteed (within the uncertainties associated with the spin down rate) and the efficiencies required to fit both the electron spectrum and the positron ratio are less than unity. In the dipole case, when the ξ± ≪ 1 one would even have the problem of explaining where the rest of the positrons are. • The fit to the total electron spectrum is made possible by the combination of the contribution of electrons from acceleration at the forward shock of supernovae (with a spectrum E −2.4 ) and the contribution of electrons and positrons from pulsars, with flat injection spectrum. Both contributions are heavily affected by the local distribution of supernovae, especially at high energies, where energy losses limit the distance to the sources that contribute to the flux at the Earth. • The positron fraction observed by PAMELA is easily fit in all the configurations that we investigated, with the same efficiencies required to fit the total electron spectrum. The pulsar wind scenario also explains in a natural way the absence of antiprotons in excess of those produced in inelastic cosmic ray interactions in the Galaxy. Acknowledgements This work was partially supported by ASI through contract ASI-INAF I/088/06/0.

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