Focusing Telescopes in Nuclear Astrophysics

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FOCUSING TELESCOPES IN NUCLEAR ASTROPHYSICS

Edited by: PETER VON BALLMOOS

Reprinted from Experimental Astronomy Vol. 20, Nos. 1–3, 2005

Library of Congress Cataloging-in-Publication Data is available

ISBN 1-4020-5303-7 (hardbook) ISBN 1-4020-5304-5 (eBook) ISBN 978-1-4020-5303-7 (hardbook) ISBN 978-1-4020-5304-5 (eBook)

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands.

Printed on acid-free paper All Rights Reserved c Springer 2006 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Printed in the Netherlands

TABLE OF CONTENTS

P. von Ballmoos / Preface

1–2

Section I: Scientific Requirements and Prospects J. Knödlseder / Prospects in space-based gamma-ray astronomy

3–13

S. Sazonov, E. Churazov, R. Sunyaev and M. Revnivtsev / Annihilation of positrons in the Galaxy

15–22

Richard E. Griffiths / Prospects and requirements for measurements of extragalactic γ -ray lines

23–30

P. Giommi and S. Colafrancesco / Non-thermal cosmic backgrounds and prospects for future high-energy observations of blazars

31–40

Andrea Comastri, Roberto Gilli and Günther Hasinger / Rolling down from the 30 keV peak: Modelling the hard X-ray and γ -ray backgrounds

41–47

M. D. Leising / Focusing supernova gamma rays: Questions for a high sensitivity gamma-ray telescope

49–55

M. Hernanz and J. José / Nucleosynthesis in nova explosions: Prospects for its observation with focusing telescopes

57–64

David M. Smith / Puzzles and potential for gamma-ray line observations of solar flare ion acceleration

65–73

Section II: Gamma-ray Optics P. Ubertini / The INTEGRAL – HESS/MAGIC connection: A new class of cosmic high energy accelerators from keV to TeV

75–83

Brian D. Ramsey / Replicated nickel optics for the hard-x-ray region

85–92

Carsten P. Jensen, Kristin K. Madsen and Finn E. Christensen / Small d-spacing WC/SiC multilayers for future hard X-ray telescope designs

93–103

Ernst-Jan Buis, Marco Beijersbergen, Giuseppe Vacanti, Marcos Bavdaz and David Lumb / Design aspects of grazing angle multilayer mirrors for soft γ -rays

105–113

M. P. Ulmer, M. E. Graham, S. Vaynman, J. Echt, M. Farber, S. Ehlert and S. Varlese / Progress toward light weight high angular resolution multilayer coated optics

115–120

J. Tueller, H. A. Krimm, T. Okajima, S. D. Barthelmy, S. M. Owens, P. J. Serlemitsos, Y. Soong, K.-W. Chan, Y. Ogasaka, R. Shibata, K. Tamura, A. Furuzawa, Y. Tawara, H. Kunieda and K.Yamashita / InFOCµS hard X-ray imaging telescope

121–129

Fiona A. Harrison, Finn E. Christensen, William Craig, Charles Hailey, Wayne Baumgartner, C. M. H. Chen, James Chonko, W. Rick Cook, Jason Koglin, Kristin-Kruse Madsen, Michael Pivavoroff, Steven Boggs and David Smith / Development of the HEFT and NuSTAR focusing telescopes

131–137

Giovanni Pareschi and Philippe Ferrando / The SIMBOL-X hard X-ray mission

139–149

Hubert Halloin and Pierre Bastie / Laue diffraction lenses for astrophysics: Theoretical concepts

151–170

Hubert Halloin / Laue diffraction lenses for astrophysics: From theory to experiments

171–184

N. V. Abrosimov / Mosaic and gradient SiGe single crystals for gamma ray Laue lenses

185–194

P. Courtois, K. H. Andersen and P. Bastie / Copper mosaic crystals for Laue lenses

195–200

Robert K. Smither, Khaliefeh Abu Saleem, Dante E. Roa, Mark A. Beno, Peter Von Ballmoos and Gerry K. Skinner / High diffraction efficiency, broadband, diffraction crystals for use in crystal diffraction lenses

201–210

Niels Lund / An “ESA-affordable” Laue-lens

211–217

Alessandro Pisa, Filippo Frontera, Gianluca Loffredo, Damiano Pellicciotta and Natalia Auricchio / Optical properties of Laue lenses for hard X-rays (>60 keV)

219–228

D. E. Roa, R. K. Smither, X. Zhang, K. Nie, Y. Y. Shieh, N. S. Ramsinghani, N. Milne, J. V. Kuo, J. L. Redpath, M. S. A. L. Al-Ghazi and P. Caligiuri / Development of a new photon diffraction imaging system for diagnostic nuclear medicine

229–239

F. Frontera, A. Pisa, G. Loffredo, D. Pellicciotta, V. Carassiti, F. Evangelisti, K. Andersen, P. Courtois, L. Amati, E. Caroli, T. Franceschini, G. Landini, S. Silvestri and J. Stephen / HAXTEL: A Laue lens telescope development project for a deep exploration of the hard X-ray sky (>60 keV)

241–251

Peter von Ballmoos, Hubert Halloin, Jean Evrard, Gerry Skinner, Nikolai Abrosimov, Jose Alvarez, Pierre Bastie, Bernard Hamelin, Margarida Hernanz, Pierre Jean, Jürgen Knödlseder and Bob Smither / CLAIRE: First light for a gamma-ray lens

253–267

N. Barrière, P. von Ballmoos, H. Halloin, N. Abrosimov, J. M. Alvarez, K. Andersen, P. Bastie, S. Boggs, P. Courtois, T. Courvoisier, M. Harris, M. Hernanz, J. Isern, P. Jean, J. Knödlseder, G. Skinner, B. Smither, P. Ubertini, G. Vedrenne, G. Weidenspointner and C. Wunderer / MAX, a Laue diffraction lens for nuclear astrophysics

269–278

Craig Brown, Nicola Rando, Alexander Short, Aleksander Lyngvi and Tone Peacock / The gamma ray lens – an ESA technology reference study

279–288

G. K. Skinner / Gamma ray Fresnel lenses – why not?

289–298

John Krizmanic, Brian Morgan, Robert Streitmatter, Neil Gehrels, Keith Gendreau, Zaven Arzoumanian, Reza Ghodssi and Gerry Skinner / Development of ground-testable phase fresnel lenses in silicon

299–306

Laurent Koechlin, Denis Serre, Gerald K. Skinner, Peter Von Ballmoos and Thomas Crouzil / Multiwavelength focusing with the Sun as gravitational lens

307–315

Section III: Focal Plane Instrumentation Tadayuki Takahashi / A Si/CdTe Compton Camera for gamma-ray lens experiment

317–331

Ernst-Jan Buis, Marco Beijersbergen, Stefan Kraft, Alan Owens, Francesco Quarati, Sytze Brandenburg and Reint Ostendorf / New scintillators for focal plane detectors in gamma-ray missions

333–339

Ezio Caroli, Natalia Auricchio, Lorenzo Amati, Yuriy Bezsmolnyy, Carl Budtz-Jørgensen, Rui M. Curado da Silva, Filippo Frontera, Alessandro Pisa, Stefano Del Sordo, John B. Stephen and Giulio Ventura / A focal plane detector design for a wide-band Laue-lens telescope

341–351

Ezio Caroli, Rui M. Curado da Silva, Alessandro Pisa, John B. Stephen, Filippo Frontera, Matilde T. D. Castanheira and Stefano del Sordo / Polarisation measurements with a CdTe pixel array detector for Laue hard X-ray focusing telescopes

353–364

C. B. Wunderer, P. von Ballmoos, N. Barrière, S. E. Boggs, G. Weidenspointner and A. Zoglauer / Simulated performance of dedicated Ge-strip Compton telescopes as γ -lens focal plane instrumentation

365–373

G. Weidenspointner, C. B. Wunderer, N. Barrière, A. Zoglauer and P. von Ballmoos / Monte Carlo study of detector concepts for the MAX Laue lens gamma-ray telescope

375–386

Steven Boggs, Mark Bandstra, Jason Bowen, Wayne Coburn, Robert Lin, Cornelia Wunderer, Andreas Zoglauer, Mark Amman, Paul Luke, Pierre Jean and Peter von Ballmoos / Performance of the Nuclear Compton Telescope

387–394

Robert Andritschke, Andreas Zoglauer, Gottfried Kanbach, Peter F. Bloser and Florian Schopper / The Compton and pair creation telescope MEGA

395–403

Section IV: Ground Facilities and Flight Systems for Focusing Telescopes M. J. Freyberg, H. Bräuninger, W. Burkert, G. D. Hartner, O. Citterio, F. Mazzoleni, G. Pareschi, D. Spiga, S. Romaine, P. Gorenstein and B. D. Ramsey / The MPE X-ray test facility PANTER: Calibration of hard X-ray (15–50 kev) optics

405–412

Gianluca Loffredo, Filippo Frontera, Damiano Pellicciotta, Alessandro Pisa, Vito Carassiti, Stefano Chiozzi, Federico Evangelisti, Luca Landi, Michele Melchiorri and Stefano Squerzanti / The Ferrara hard X-ray facility for testing/calibrating hard X-ray focusing telescopes

413–420

Rodolphe Clédassou and Philippe Ferrando / SIMBOL-X: An hard X-ray formation flying mission

421–434

Emmanuel Hinglais (CNES) / Distributed space segment for high energy astrophysics: Similarities and specificites

435–445

Ph. Laporte, J. Evrard and A. Laurens / The CLAIRE gondola: Testing the first gamma-ray lens on a stratospheric balloon

447–454

Xavier Leyre, Michel Sghedoni, Francis Arbusti, Primo Attina, Peter von Ballmoos / Recent advances and low cost concept for the gammaray lens project MAX

455–464

J. Borde, P. von Ballmoos and R. Soumagne / Small-sat platforms and formation flying: An opportunity for the gamma ray telescope MAX

465–482

Paul Duchon / MAX: Formation flying for nuclear astrophysics

483–495

John Krizmanic, Gerry Skinner and Neil Gehrels / Formation flying for a Fresnel lens observatory mission

497–503

Exp Astron (2005) 20:1–2 DOI 10.1007/s10686-006-9073-y PREFACE

Preface P. von Ballmoos

C

Springer Science + Business Media B.V. 2006

Over the last decade, a small but growing community has been pursuing various techniques for the focusing of hard X-rays and gamma-rays. The workshop Focusing Telescopes in Nuclear Astrophysics provided a first opportunity for this young “gamma-wave” community to meet, exchange technological know-how, and discuss scientific objectives and synergies. The workshop took place in Bonifacio, Corsica, September 12–15, 2005. It brought together sixty participants with different horizons, and with competence in a wide range of disciplinesbut with the common interest in finding alternative instrumental approaches for use in nuclear astrophysics. Participants from the high energy astrophysics community emphasized the extraordinary scientific potential of nuclear astrophysics for the study of the most powerful sources and the most violent events in the Universe. Their contributions are collected in the first part of this volume and discuss science objectives on all levels: neutron stars, X-ray binaries, pulsars, novae, supernovae, AGN, blazars, cosmology . . . but also our sun! In order to achieve the ambitious scientific goals, experimental gamma-ray astronomy must find new ways to improve the performance of its instruments, with better sensitivity being unquestionably the foremost requirement. In the second part of this volume, the evolving “gamma-wave” community examines the options for focusing optics for hard-X and soft gamma rays. A few years back, there was no way to focus gamma-rays; today we have many: grazing incident mirrors and multilayer coatings, Laue- and Fresnel-lenses; even an optic using the curvature of space-time is proposed. In more than twenty articles various aspects of the techniques are discussed, from the theoretical basis to the ambitious mission concepts for future space observatories. A particular emphasis is on the progress in R&D for the various techniques, on results from prototypes and on first results obtained from stratospheric balloon flights. The goal of improving instrument sensitivities by up to two orders of magnitude which is the main incentive for developing focusing telescopes, also drives the development of new detector technologies. One of the focal points of the workshop was the consideration

P. von Ballmoos Centre d’Etude Spatiale des Rayonnements, Toulouse, France e-mail: [email protected] Springer

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of detectors matching the ambitious objectives of gamma ray optics and their capability of taking maximum advantage of the concentrated signal flux. In the third part of this volume, a number of innovative detector concepts for focusing telescopes are discussed. Besides offering high detection efficiencies, these focal plane instruments will provide imaging capabilities, perform high resolution spectroscopy and measure the polarization of the incident photons. The deflection of photons in focusing X/γ -ray optics is only by small angles. As a consequence, telescope systems have long focal lengths and require a new class of flight systems and ground facilities. Part four of this volume is dedicated to the associated challenges. Facilities for testing hard X-ray focusing telescopes on the ground and techniques for testing using stratospheric balloons are presented. The space missions that seem best adapted for X/γ -ray optics involve “formation flying” of two spacecraft. Photons are collected by an optics spacecraft and are focused onto a separate detector spacecraft. Formation flying missions present a number of complex challenges for spacecraft engineering which are discussed in this volume. Eleven years have past since the workshop on imaging in high energy astronomy in Capri (1994), which itself followed by the same interval a similar meeting in Southampton (1983). Eleven years is also roughly the time separating launches of successive major space missions in nuclear astrophysics – HEAO-3 (1979), GRO (1991) and then INTEGRAL (2002). One of the foremost objectives of the Gamma Wave 05 workshop was to consider the next generation of instrumentation required for nuclear astrophysics and consider implementation approaches within National and European Space Science programs. In sunny Bonifacio the Gamma-Wave community expressed their wish that the eleven year cycle continue with the launch of a major focusing X/γ -ray mission on a 2013 horizon. On behalf of the local and scientific organizing committees, we acknowledge the generous contributions of ESA, CNES, ASTRIUM and ALCATEL, which allowed the organisation of the workshop and the publication of the present volume. We thank Dolores Granat, Eric Deleage and Nicolas Barrière for their tireless effort behind the scenes to ensure the success of this workshop. Many thanks to Gerry Skinner, who has attempted to provide a scientific conscience for the present volume, and to Sylvia Iviglia from Springer for shepherding its completion. Finally, we thank the participants of the Gamma-Wave 05 workshop for their dedication to this project, and look forward to the exciting promise of the next phase of nuclear astrophysics instrumentation. Toulouse, July 2006 PvB

Springer

Exp Astron (2005) 20:3–13 DOI 10.1007/s10686-006-9031-8 ORIGINAL ARTICLE

Prospects in space-based gamma-ray astronomy J. Knödlseder

Received: 25 November 2005 / Accepted: 22 February 2006 C Springer Science + Business Media B.V. 2006

Abstract Observations of the gamma-ray sky reveal the most powerful sources and the most violent events in the Universe. While at lower wavebands the observed emission is generally dominated by thermal processes, the gamma-ray sky provides us with a view on the non-thermal Universe. Here particles are accelerated to extreme relativistic energies by mechanisms which are still poorly understood, and nuclear reactions are synthesizing the basic constituents of our world. Cosmic accelerators and cosmic explosions are the major science themes that are addressed in the gamma-ray regime. With the INTEGRAL observatory, ESA has provided a unique tool to the astronomical community revealing hundreds of sources, new classes of objects, extraordinary views of antimatter annihilation in our Galaxy, and fingerprints of recent nucleosynthesis processes. While INTEGRAL provides the global overview over the soft gamma-ray sky, there is a growing need to perform deeper, more focused investigations of gamma-ray sources. In soft X-rays a comparable step was taken going from the Einstein and the EXOSAT satellites to the Chandra and XMM/Newton observatories. Technological advances in the past years in the domain of gamma-ray focusing using Laue diffraction and multilayer-coated mirror techniques have paved the way towards a gamma-ray mission, providing major improvements compared to past missions regarding sensitivity and angular resolution. Such a future GammaRay Imager will allow to study particle acceleration processes and explosion physics in unprecedented detail, providing essential clues on the innermost nature of the most violent and most energetic processes in the Universe.

Keywords Gamma-ray astronomy astronomy · Cosmic accelerators · Cosmic explosions

J. Knödlseder () Centre d’Etude Spatiale des Rayonnements, 9, avenue du Colonel-Roche, B.P. 4346, 31028 Toulouse Cedex 4, France e-mail: [email protected] Springer

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1. Why gamma-ray astronomy? As introductory remark, it is worth emphasising some unique features of gamma-ray astronomy: the specific character of the emission processes, the diversity of the emission sites, and the penetrating nature of the emission. First, the emission process that leads to gamma-rays is in general very specific, and as such, is rarely observable in other wavebands. At gamma-ray energies, cosmic acceleration processes are dominant, while in the other wavebands thermal processes are generally at the origin of the emission. For example, electrons accelerated to relativistic energies radiate gamma-ray photons of all energies through electromagnetic interactions with nuclei, photons, or intense magnetic fields. Accelerated protons generate secondary particles through nuclear interactions, which may decay by emission of high-energy gamma-ray photons. At gamma-ray energies, nuclear deexcitations lead to a manifold of line features, while in the other wavebands, it is the bound electrons that lead to atomic or molecular transition lines. For example, the radioactive decay of tracer isotopes allows the study of nucleosynthesis processes that occur in the deep inner layers of stars. The interaction of high-energy nuclei with the gas of the interstellar medium produces a wealth of excitation lines that probe the composition and energy spectrum of the interacting particles. Finally, annihilation between electrons and positrons result in a unique signature at 511 keV that allows the study of antimatter in the Universe. Second, the sites of gamma-ray emission in the Universe are very diverse, and reach from the nearby Sun up to the distant Gamma-Ray Bursts and the cosmic gamma-ray background radiation. Cosmic acceleration takes place on all scales: locally in solar flares, within our Galaxy (e.g. in compact binaries, pulsars, supernova remnants), and also in distant objects (such as active galactic nuclei or gamma-ray bursts). Cosmic explosions are another site of prominent gamma-ray emission. They produce a wealth of radioactive isotopes, are potential sources of antimatter, and accelerate particles to relativistic energies. Novae, supernovae and hypernovae are thus prime targets of gamma-ray astronomy. Third, gamma-rays are highly penetrating, allowing the study of otherwise obscured regions. Examples are regions of the galactic disk hidden by dense interstellar clouds, or the deeper, inner, zones of some celestial bodies, where the most fundamental emission processes are at work. New classes of sources become visible in the gamma-ray domain, that are invisible otherwise. In summary, gamma-ray astronomy provides a unique view of our Universe. It unveils specific emission processes, a large diversity of emission sites, and probes deeply into the otherwise obscured high-energy engines of our Universe. The gamma-ray Universe is the Universe of particle acceleration and nuclear physics, of cosmic explosions and non-thermal phenomena. Exploring the gamma-ray sky means exploring this unique face of our world, the face of the evolving violent Universe.

2. Cosmic accelerators 2.1. The link between accretion and ejection As a general rule, accretion in astrophysical systems is often accompanied by mass outflows, which in the high-energy domain take the form of (highly) relativistic jets. Accreting objects are therefore powerful particle accelerators, that can manifest on the galactic scale as Springer

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microquasars, or on the cosmological scale, as active galactic nuclei, such as Seyfert galaxies and Blazars. Although the phenomenon is relatively widespread, the jet formation process is still poorly understood. It is still unclear how the energy reservoir of an accreting system is transformed in an outflow of relativistic particles. Jets are not always persistent but often transient phenomena, and it is still not known what triggers the sporadic outbursts in accreting systems. Also, the collimation of the jets is poorly understood, and in general, the composition of the accelerated particle plasma is not known (electron-ion plasma, electron-positron pair plasma). Finally, the radiation processes that occur in jets are not well established. Observations in the gamma-ray domain are able to provide a number of clues to these questions. Gamma-rays probe the innermost regions of the accreting systems that are not accessible in other wavebands, providing the closest view to the accelerating engine. Time variability and polarisation studies provide important insights into the physical processes and the geometry that govern the acceleration site. The accelerated plasma may reveal its nature through characteristic nuclear and/or annihilation line features which may help to settle the question about the nature of the accelerated plasma.

2.2. The origin of galactic soft γ -ray emission Since decades, the nature of the galactic hard X-ray (>15 keV) emission has been one of the most challenging mysteries in the field. The INTEGRAL imager IBIS has now finally solved this puzzle. At least 90% of the emission has been resolved into point sources, settling the debate about the origin of the emission (Lebrun et al., 2004) (c.f. Figure 1). At higher energies, say above ∼300 keV, the situation is less clear. In this domain, only a small fraction of the galactic emission has so far been resolved into point sources, and the nature of the bulk of the galactic emission is so far unexplained. That a new kind of object or emission mechanism should be at work in this domain is already suggested by the change of the slope of the galactic emission spectrum. While below ∼300 keV the spectrum can be explained by a superposition of Comptonisation spectra from individual point sources, the spectrum turns into a powerlaw above this energy, which is reminiscent of

Fig. 1 The hard X-ray sky resolved into individual point sources by the IBIS telescope aboard INTEGRAL Lebrun et al. (2004). Springer

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particle acceleration processes. Identifying the source of this particle acceleration process, i.e. identifying the origin of the galactic soft gamma-ray emission, is one of the major goals of a future European gamma-ray mission. One of the strategies to resolve this puzzle is to follow the successful road shown by INTEGRAL for the hard X-ray emission: trying to resolve the emission into individual point sources. Indeed, a number of galactic sources show powerlaw spectra in the gamma-ray band, such as supernova remnants, like the Crab nebula, or some of the black-hole binary systems, like Cyg X-1 (Mc Connell et al., 2000). Searching for the hard powerlaw emission tails in these objects is therefore a key objective for a future gamma-ray mission. 2.3. The origin of the soft γ -ray background After the achievements of XMM-Newton and Chandra, the origin of the cosmic X-ray background (CXB) is now basically solved for energies close to a few keV. However, whilst the CXB is ∼85% and 80% resolved in the 0.5–2 keV and 2–10 keV bands, respectively, it is only ∼50% resolved above ∼8 keV (Worsley et al., 2005). The situation is even worse in the hard X-ray and soft gamma-ray bands. Although about 20% of the sources detected in the second IBIS catalogue are of extragalactic nature (Bassani et al., 2006) they only account for ∼1% of the background emission seen in the 20–100 keV band, i.e. where the bulk of the energy density is found. Looking from another point of view, synthesis models, which are well established and tested against observational results, can be used to evaluate the integrated AGN contribution to the soft γ -ray background. Unfortunately, they lack some key information at high energies: the absorption distribution is currently biased against low column densities due to the lack of soft gamma-ray surveys, no AGN luminosity function is available above 10 keV nor has the input spectral shape of the different classes of AGN been firmly established at high energies. Furthermore, the integrated AGN contribution changes as a function of model input parameters. As an illustration, Figure 2 shows how different results can be obtained

Fig. 2 The 0.25–400 keV cosmic X-/γ −ray background spectrum fitted with synthesis models (Comastri, 2004). None of the models provides a satisfactory fit of the observations. Springer

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by varying the power law energy cut-off. A large region of this parameter space is virtually unexplored because we currently lack information on large AGN samples. Observations by BeppoSAX (Risaliti, 2002; Perola et al., 2002) of a handful of radio quiet sources, loosely locate this drop-off in the range 30–300 keV; furthermore these measurements give evidence for a variable cut-off energy and suggest that it may increase with increasing photon index (Perola et al., 2002). In radio loud sources the situation is even more complicated with some objects showing a power law break and others no cut-off up to the MeV region. In a couple of low luminosity AGN no cut-off is present up to 300–500 keV. The overall picture suggests some link with the absence (low energy cut-off) or presence (high energy cut-off) of jets in the various AGN types sampled, but the data are still too scarce for a good understanding of the processes involved. One method to tackle this issue is to measure the soft gamma-ray Spectra Energy Distribution (SED, which includes a power law continuum plus high energy cut-off as well as hard tails if present) in a sizeable fraction of AGN in order to determine average shapes in individual classes and so the nature of the radiation processes at the heart of all AGN. This would provide at the same time information for soft γ -ray background synthesis models. On the other hand, sensitive deep field observations should be able to resolve the soft γ -ray background into individual sources, allowing for the ultimate identification of the origin of the emission.

2.4. Particle acceleration in extreme B-fields The strong magnetic fields that occur at the surface of neutron stars in combination with their fast rotation make them to powerful electrodynamic particle accelerators, which may manifest as pulsars to the observer. Gamma-ray emitting pulsars can be divided into 3 classes: spindown powered pulsars, such as normal or millisecond pulsars, accretion powered pulsars, occurring in low-mass or high-mass binary systems, and magnetically powered pulsars, known as magentars. Despite the longstanding efforts in understanding the physics of spin-down powered pulsars, the site of the gamma-ray production within the magnetosphere (outer gap or polar cap) and the physical process at action (synchrotron emission, curvature radiation, inverse Compton scattering) remain undetermined. Although most of the pulsars are expected to reach their maximum luminosity in the MeV domain, the relatively weak photon fluxes have only allowed the study of a handful of objects so far. Increasing the statistics will allow the study of the pulsar lightcurves over a much broader energy range than today, providing crucial clues on the acceleration physics of these objects. Before the launch of INTEGRAL, the class of anomalous X-ray pulsars (AXPs), suggested to form a sub-class of the magnetar population, were believed to exhibit very soft X-ray spectra. This picture, however, changed dramatically with the detection of AXPs in the soft gamma-ray band by INTEGRAL (Kuiper et al., 2004). In fact, above ∼10 keV a dramatic upturn is observed in the spectra which is expected to cumulate in the 100 keV – 1 MeV domain. The same is true for Soft Gamma-ray Repeaters (SGRs), as illustrated by the recent discovery of quiescent soft gamma-ray emission from SGR 1806-20 by INTEGRAL (Molkov et al., 2005) (c.f. Figure 3). The process that gives rise to the observed gamma-ray emission in still unknown. No high-energy cut-off has so far been observed in the spectra, yet upper limits in the MeV domain indicate that such a cut-off should be present. Determining this cut-off may provide important insights in the physical nature of the emission process, and in particular, about the role of QED effects, such as photon splitting, in the extreme magnetic field that Springer

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Fig. 3 The quiescent energy spectrum of SGR 1806-20 (lower spectrum) and the summed spectrum of all detected bursts rescaled down by a factor of 1000 (upper spectrum) (Molkov et al., 2005).

occur in such objects. Strong polarisation is expected for the high-energy emission from these exotic objects, and polarisation measurements may reveal crucial to disentangle the nature of the emission process and the geometry of the emitting region. Complementary measurements of cyclotron features in the spectra provide the most direct measure of the magnetic field strengths, complementing our knowledge of the physical parameters of the systems.

3. Cosmic explosions 3.1. Understanding type Ia supernovae Although hundreds of Type Ia supernovae are observed each year, and although their optical lightcurves and spectra are studied in great detail, the intimate nature of these events is still unknown. Following common wisdom, Type Ia supernovae are believed to arise in binary systems where matter is accreted from a normal star onto a white dwarf. Once the white dwarf exceeds the Chandrasekhar mass limit a thermonuclear runaway occurs that leads to its incineration and disruption. However, attempts to model the accretion process have so far failed to allow for sufficient mass accretion that would push the white dwarf over its stability limit (Hillebrandt and Niemeyer, 2000). Even worse, there is no firm clue that Type Ia progenitors are indeed binary systems composed of a white dwarf and a normal star. Alternatively, the merging of two white dwarfs in a close binary system could also explain the observable Springer

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Fig. 4 Simulated gamma-ray spectrum of a Type Ia supernova (Gomez-Gomar et al., 1998).

features of Type Ia events (Livio and Riess, 2003). Finally, the explosion mechanism of the white dwarf is only poorly understood, principally due to the impossibility to reliably model the nuclear flame propagation in such objects (Hillebrandt and Niemeyer, 2000). In view of all these uncertainties it seems more than surprising that Type Ia are widely considered as standard candles. In particular, it is this standard candle hypothesis that is the basis of one of the fundamental discoveries of the last decade: that the expansion of the Universe is currently accelerating (Riess et al., 1998). Although empirical corrections to the observed optical lightcurves seem to allow for some kind of standardisation, there is increasing evidence that Type Ia supernovae are not an homogeneous class of objects (Mannucci et al., 2005). Gamma-ray observation of Type Ia supernovae provide a new and unique view of these events. Nucleosynthetic products of the thermonuclear runaway lead to a rich spectrum of gamma-ray line and continuum emission that contains a wealth of information on the progenitor system, the explosion mechanism, the system configuration, and its evolution (c.f. Figure 4). In particular, the radioactive decays of 56 Ni and 56 Co, which power the optical lightcurve which is so crucial for the cosmological interpretation of distant Type Ia events, can be directly observed in the gamma-ray domain, allowing to pinpoint the underlying progenitor and explosion scenario. The comparison of the gamma-ray to the optical lightcurve will provide direct information about energy recycling in the supernova envelope that will allow a physical (and not only empirical) calibration of Type Ia events as standard candles. In addition to line intensities and lightcurves, the shapes of the gamma-ray lines hold important information about the explosion dynamics and the matter stratification in the system. Measuring the line shapes (and their time evolution) will allow to distinguish between Springer

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the different explosion scenarios, ultimately revealing the mechanism that creates these most violent events in the Universe (Gomez-Gomar et al., 1998). 3.2. Understanding core-collapse explosions Gamma-ray line and continuum observations address some of the most fundamental questions of core-collapse supernovae: how and where the large neutrino fluxes couple to the stellar ejecta; how asymmetric the explosions are, including whether jets form; and what are quantitative nucleosynthesis yields from both static and explosive burning processes? The ejected mass of 44 Ti, which is produced in the innermost ejecta and fallback matter that experiences the alpha-rich freezeout of nuclear statistical equilibrium, can be measured to a precision of several percent in SN 1987A. Along with other isotopic yields already known, this will provide an unprecedented constraint on models of that event. 44 Ti can also be measured and mapped, in angle and radial velocity, in several historical galactic supernova remnants. These measurements will help clarify the ejection dynamics, including how common jets initiated by the core collapse are. Wide-field gamma-ray instruments have shown the global diffuse emission from long-lived isotopes 26 Al and 60 Fe, illustrating clearly ongoing galactic nucleosynthesis. A necessary complement to these are high-sensitivity measurements of the yields of these isotopes from individual supernovae. A future European gamma-ray mission should determine these yields, and map the line emission across several nearby supernova remnants, shedding further light on the ejection dynamics. It is also likely that the nucleosynthesis of these isotopes in hydrostatic burning phases will be revealed by observations of individual nearby massive stars with high mass-loss rates. For rare nearby supernovae, within a few Mpc, we will be given a glimpse of nucleosynthesis and dynamics from short-lived isotopes 56 Ni, and 57 Ni, as was the case for SN 1987A in the LMC. In that event we saw that a few percent of the core radioactivity was somehow transported to low-optical depth regions, perhaps surprising mostly receding from us, but there could be quite some variety, especially if jets or other extensive mixing mechanisms are ubiquitous. 3.3. Unveiling the origin of galactic positrons The unprecedented imaging and spectroscopy capabilities of the spectrometer SPI aboard INTEGRAL have now provided for the first time an image of the distribution of 511 keV electron positron annihilation all over the sky (Knödlseder et al., 2005) (c.f. Figure 5). The outcome of this survey is astonishing: 511 keV line emission is only seen towards the bulge region of our Galaxy, while the rest of the sky remains surprisingly dark. Only a weak glim of 511 keV emission is perceptible from the disk of the Galaxy, much less than expected from stellar populations following the global mass distribution of the Galaxy. In other words, positron annihilation seems to be greatly enhanced in the bulge with respect to the disk of the Galaxy. A detailed analysis of the 511 keV line shape measured by SPI has also provided interesting insights into the annihilation physics (Churazov et al., 2005). At least two components have been identified, indicating that positron annihilation takes place in a partially ionised medium. This clearly demonstrated that precise 511 keV line shape measurements provide important insights into the distribution of the various phases of the interstellar medium (ISM). While INTEGRAL has set the global picture of galactic positron annihilation, high angular resolution mapping of the galactic bulge region is required to shed light on the still Springer

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Fig. 5 First all-sky map of 511 keV electron-positron annihilation radiation as observed by the SPI telescope aboard INTEGRAL (Knödlseder et al., 2005).

mysterious source of positrons. So far, no individual source of positron emission could have been identified, primarily due to the expected low levels of 511 keV line fluxes. An instrument with sufficiently good sensitivity and angular resolution should be able to pinpoint the origin of the positrons, by providing detailed maps of the central bulge region of the Galaxy. With additional fine spectroscopic capabilities, comparable to that achieved by the germanium detectors onboard the SPI telescope, the spatial variations of the 511 keV line shape will allow to draw an unprecedented picture of the distribution of the various ISM phases in the inner regions of our Galaxy. Thus, with the next generation gamma-ray telescope, galactic positrons will be exploited as a messenger from the mysterious antimatter source in the Milky-Way, as well as a tracer to probe the conditions of the ISM that are difficultly to measure by other means.

4. Mission requirements The major mission requirement for the future European gamma-ray mission is sensitivity. Many interesting scientific questions are in a domain where photons are rare (say 10−7 ph cm−2 s−1 ), and therefore large collecting areas are needed to perform measurements in a reasonable amount of time. It is clear that a significant sensitivity leap is required, say 50–100 times more sensitive than current instruments, if the above listed scientific questions should be addressed. With such a sensitivity leap, the expected number of observable sources would be large, implying the need for good angular resolution to avoid source confusion in crowded regions, such as for example the galactic centre. Also, it is desirable to have an angular resolution comparable to that at other wavebands, to allow for source identification and hence multi wavelength studies. As mentioned previously, gamma-ray emission may be substantially polarised due to the non-thermal nature of the underlying emission processes. Studying not only the intensity but also the polarisation of the emission would add a new powerful scientific dimension to the observations. Such measurements would allow to discriminate between the different plausible emission processes at work, and would allow to constrain the geometry of the emission sites. Taking all these considerations into account, the following mission requirements derive (c.f. Table 1). The energy band should cover the soft gamma-ray band, with coverage down Springer

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Table 1 Mission requirements for the future European gamma-ray mission (sensitivities are for 106 seconds at 3σ detection significance)

Parameter

Requirement

Energy band Continuum sensitivity Narrow line sensitivity Energy resolution Field of view Angular resolution Polarisation

50 keV – 2 MeV 10−8 ph cm−2 s−1 keV−1 5 × 10−7 ph cm−2 s−1 2 keV at 600 keV 30 arcmin arcmin 1% at 10 mCrab

to the hard X-ray band (to overlap with future X-ray observatories), and coverage of the major gamma-ray lines of astrophysical interest. A real sensitivity leap should be achieved, typical by a factor of 50–100 with respect to existing gamma-ray instrumentation. For highresolution gamma-ray line spectroscopy a good energy resolution is desirable to exploit the full potential of line profile studies. A reasonably sized field-of-view together with arcmin angular resolution should allow the imaging of field populations of gamma-ray sources in a single observation. Finally, good polarisation capabilities, at the percent level for strong sources, are required to exploit this additional observable. Can these mission requirements be reached within the 2015–2025 time frame? We are convinced that the answer is yes. How can these mission requirements be reached? We think that the best solution is the implementation of a broad-band gamma-ray lens telescope based on the principle of Laue diffraction of gamma-rays in mosaic crystals (Von Ballmoos et al., 2004; Halloin et al., 2004; De Chiara et al., 2000). The Laue lens may eventually be complemented by a coded mask telescope or a multilayer-coated mirror telescope in order to achieve the hard X-ray coverage. The focal length of such a system would lie between a few tens and a few hundreds metres, requiring the technology of satellite formation flying. We note that such a gamma-ray lens telescope is currently under study at the French space agency CNES (project MAX (Von Ballmoos et al., 2004)) and at the ESA Science Payload & Advanced Concepts Office (project Gamma-Ray Lens), which both confirm the feasibility of such a scenario. We therefore believe that a gamma-ray lens telescope in formation flight configuration provides the most promising instrumental concept allowing advances in the field of space-based gamma-ray astronomy. The precise design of the gamma-ray lens telescope is currently under discussion (see http://gri.rm.iasf.cnr.it/). The artists view in Figure 6 gives an idea how the future Gamma-Ray Imager mission may look like. In this example, the lens spacecraft is composed of concentric rings of crystals, where each ring is focusing a specific narrow energy band on the (same) focal spot on the Fig. 6 Artists view of the Gamma-Ray Imager. A Laue lens, situated on the left spacecraft, is focusing gamma-rays onto a small detector, situated on the right spacecraft. Both spacecrafts are in formation flight with a typical focal length between a few tens and a few hundreds metres.

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detector spacecraft. Higher energies show smaller diffraction angles and therefore are situated closer to the optical axis (inner rings). Conversely, lower energies show larger diffraction angles and therefore are situated on the outer rings. The lowest energies may require radial distances from the optical axis that exceed the available space in launcher fairings, therefore deployable lens petals may eventually be employed.

5. Conclusions The gamma-ray band presents a unique astronomical window that allows the study of the most energetic and most violent phenomena in our Universe. With ESA’s INTEGRAL observatory, an unprecedented global survey of the soft gamma-ray sky is currently performed, revealing hundreds of sources of different kinds, new classes of objects, extraordinary views of antimatter annihilation in our Galaxy, and fingerprints of recent nucleosynthesis processes. While INTEGRAL provides the longly awaited global overview over the soft gamma-ray sky, there is a growing need to perform deeper, more focused investigations of gamma-ray sources, comparable to the step that has been taken in X-rays by going from the EINSTEIN satellite to the more focused XMM-Newton observatory. Technological advances in the past years in the domain of gamma-ray focusing using Laue diffraction techniques have paved the way towards a future European gamma-ray mission, that will outreach past missions by large factors in sensitivity and angular resolution. Such a future Gamma-Ray Imager will allow to study particle acceleration processes and explosion physics in unprecedented depth, providing essential clues on the intimate nature of the most violent and most energetic processes in the Universe.

References Bassani, L., et al.: ApJ 636, 65 (2006) Churazov, E., Sunyaev, R., Sazonov, S., et al.: MNRAS 357, 1377 (2005) Comastri: in: R. Maiolino and R. Mujica (eds.), Proceedings of ‘Multiwavelength AGN surveys’ (Cozumel, December 8–12 2003), (astro-ph/0406031) (2004) De Chiara, P., et al.: Proc. of SPIE/ESO Astronomical Telescopes and Instrumentation ICM, 27–31 March 2000 (2000) Gomez-Gomar, J., et al.: MNRAS 295, 1 (1998) Halloin, H., von Ballmoos, P., Evrard, J., et al.: SPIE 5168, 471 (2004) Hillebrandt, W., Niemeyer, J.C.: ARAA 38, 191 (2000) Knödlseder, J., Jean, P., Lonjou, V., et al.: A&A 441, 513 (2005) Kuiper, L., Hermsen, W., Mendez, M.: ApJ 613, 1173 (2004) Lebrun, F., et al.: Nature 428, 293 (2004) Livio, M., Riess, A.G.: ApJ 594, L93 (2003) Mannucci, F., Della Valle, M., Panagia, N., et al.: A&A 433, 807 (2005) McConnell, M.L., Bennett, K., Bloemen, H., et al.: in: M.L. McConnell & J.M. Ryan (eds.), Proc. 5th Compton Symposium, AIP 510, 114 (2000) Molkov, S., Hurley, K., Sunyaev, R., et al.: A&A 433, L13 (2005) Perola, G.C., et al.: A&A 389, 802 (2002) Riess, A.G., Filippenko, A.V., Challis, P., et al.: AJ 116, 1009 (1998) Risaliti, G.: A&A 386, 379 (2002) Von Ballmoos, P., Halloin, H., Paul, J., et al.: Proc. 5th INTEGRAL Workshop, Munich 16–20 February 2004, ESA SP-552, 747 (2004) Worsley, M.A., et al.: MNRAS 357, 1281 (2005)

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Annihilation of positrons in the Galaxy S. Sazonov · E. Churazov · R. Sunyaev · M. Revnivtsev

Received: 17 January 2006 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract Observations of electron-positron annihilation radiation from the Galactic Center region with the SPI instrument aboard INTEGRAL are summarized. The measured width of the 511 keV line and inferred fraction of positrons annihilating through positronium formation are consistent with the annihilation taking place in the warm ISM phase, although combinations of several ISM phases are also allowed by the data. The spatial distribution of 511 keV emission suggests that positron sources are concentrated toward the Galactic bulge and avoid the Galactic disk. Keywords Galaxy: Center . Gamma rays: Observations . ISM: General

1. Introduction The electron–positron annihilation line at 511 keV is the brightest line in the electromagnetic spectrum of the Galaxy at energies above 10 keV. It was discovered during balloon flights more than 30 years ago as emission at roughly ∼476 keV from the general direction of the Galactic Center (GC) [6], and later clearly identified as a narrow e− − e+ annihilation line at 511 keV in observations by high-resolution germanium detectors [8]. Although the Galactic annihilation radiation has since then been observed by many experiments, its origin remains unclear. Several mechanisms of positron production have been proposed, including: – Radioactive β + decay of unstable isotopes, e.g. 26 Al or 56 Co, produced in supernovae or novae – Decay of π + mesons produced by interaction of cosmic rays with the ISM

S. Sazonov · E. Churazov · R. Sunyaev · M. Revnivtsev Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching,Germany S. Sazonov () Space Research Institute, Profsoyuznaya 84/32, 117997 Moscow, Russia e-mail: [email protected] Springer

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– Generation of e− − e+ pairs by interaction of high-energy photons or in strong magnetic fields near black holes or radiopulsars – Annihilation of dark matter particles Although not complete, this list demonstrates the very broad range of possible mechanisms, from widely accepted (nucleosynthesis in supernovae) to more exotic (dark matter annihilation). To find out the origin of the Galactic annihilation radiation it is crucial to (a) compare its spatial distribution with that of possible positron sources and (b) obtain constraints on the properties of the annihilation medium from the observed annihilation spectrum. The INTEGRAL observatiory with its high-resolution spectrometer SPI is designed to pursue these goals.

2. Observations and data analysis INTEGRAL is the ESA’s project with participation of Russia and the USA. The SPI instrument (Vedrenne et al., 2003) consists of 19 Ge crystals, providing energy resolution ∼2 keV near 511 keV. A 3-cm thick tungsten coded mask located 1.7 m above the detector modulates the incoming flux. The field of view is ∼16◦ -radius. We analyzed observations from February–November 2003, with a total exposure of 3.9 Ms [2]. The absolute energy scale was for each observation calibrated to better than 10 eV near 511 keV using a set of background lines (71 Ge at 198.4 keV, 69 Zn at 438.6 keV, 69 Ge at 584.5 keV, and 69 Ge at 882.5 keV). The energy resolution at 511 keV was found to be 2.1 keV (FWHM) by interpolating the observed widths of two bracketing lines, 438.6 keV and 584.5 keV. Since the instrument background contribution to the 511 keV line exceeds the useful signal from the GC region by 50–100 times, it is necessary to predict the background to better than 1 percent accuracy. To construct a model of background spectrum we used observations of the sky >30◦ away from the GC, with a total exposure of 3.7 Ms. 2.1. Galaxy map in the 511 keV line Figure 1 shows the surface brightness map of the Galaxy in the 511 keV line. By construction, only large-scale structure exceeding the size of the instrument’s FOV has been retained on this map, while any small-scale structure is strongly suppressed. Nevertheless, the global pattern of annihilation radiation is evident: the central region of the Galaxy is a powerful source of 511 keV radiation, while there is no statistically significant annihilation signal outside this region. One can obtain better constraints on the surface brightness distribution by specifying a model distribution with several free parameters, convolving it with the angular response of the instrument, and comparing the outcome with the measured distribution. In the simplest model, the surface brightness is described by a two-dimensional Gaussian around the GC. A more flexible model includes a constant component. The best agreement with the data is achieved for a Gaussian with FWHM = 6◦ . The inferred flux is ∼7.6 × 10−4 phot/s/cm2 and ∼10−3 phot/s/cm2 for the model with and without a constant component, respectively. This flux difference indicates that the true spatial distribution may be more complex than assumed in these simple models. Using more complicated models [7, 10] of 511 keV surface brightness distribution, in particular including components associated with the Galactic disk and bulge, leads to qualitatively the same results – the flux of the central component (∼10−3 phot/s/cm2 ) is much higher than that of the disk one, unless the disk thickness exceeds a few ten degrees. Springer

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Fig. 1 Surface brightness distribution of 511 keV emission in Galactic coordinates. The effective angular resolution of the map is ∼15◦ . The apparent structure outside the central ∼25◦ region is not statistically significant

2.2. Annihilation spectrum Figure 2 shows the measured spectrum near 511 keV. It is well fit by a model consisting of a Gaussian line and a 3-photon (ortho-positronium) annihilation continuum. The flux ratio of these components yields the fraction of annihilations proceeding through positronium formation: FPS =

2 , 1.5 + 2.25(F2γ /F3γ )

where F2γ and F3γ are the flux in the line and in the 3-photon continuum, respectively. This expression accounts for the fact that ortho- and parapositronium are produced in 3:1 proportion and generate 3 and 2 photons, respectively. Table 1 summarized the results of our spectral analysis.

3. Constraints on the ISM parameters The two measured quantities, the line width and the flux ratio of the line and 3-photon continuum, place constraints on the temperature and ionization degree of the annihilation Table 1 Best-fit parameters of the annihilation spectrum in the energy range 450–550 keV. The quoted uncertainties are 1σ for a single parameter of interest. Adapted from [2]

Parameter

Value and uncertainty

E, keV FWHM, keV F2γ 10−4 phot s−1 cm−2 F3γ 10−4 phot s−1 cm−2 F3γ /F2γ FP S χ2 (d.o.f.)

510.954 [510.88–511.03] 2.37 [2.12–2.62] 7.16 ± 0.36 26.1 ± 5.7 3.65 ± 0.82 0.94 ± 0.06 192.7 (193) Springer

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Fig. 2 Spectrum of the GC annihilation radiation measured by INTEGRAL/SPI. The curves show the contributions of the 511 keV line and 3-photon continuum (not convolved with the energy response of the instrument)

medium. Using a Monte-Carlo code we simulated the formation of the annihilation spectrum in a pure hydrogen, dust-free plasma. The positrons are assumed to be born hot (with an energy higher than several hundred keV), then decelerate due to Coulomb losses in an ionized plasma or due to photoionization and atom excitation in a neutral gas, and eventually thermalize with the ambient medium. After the positron energy falls below several eV, charge exchange with neutral atoms, radiative recombination or direct annihilation with free or bound electrons occurs [1]. The predicted annihilation line has a non-Gaussian shape and contains a broad and a narrow components. In Figure 3 the effective line width and positronium fraction are shown as functions of temperature and ionization degree. These theoretical curves are compared with the constraints on the effective line width and positronium fraction provided by INTEGRAL observations. There are two families of theoretical curves. One regime corresponds to a gas with temperature below ∼6,000 K. In a cold and neutral medium about 94% of positrons form positronium in flight. The remaining 6% fall below the threshold for positronium formation (6.8 eV) and then annihilate with bound electrons, forming a narrow line (FWHM = 1.7 keV, [4]. The effective width of the line arising from in-flight annihilation through positronium formation is 5.3 keV, and that of the net line (sum of the broad and narrow components) is ∼4.6 keV. If the ionization degree exceeds ∼10−3 , Coulomb losses start to play an important role, decreasing the fraction of positrons forming positronium in flight. For positrons falling below 6.8 eV, three processes are important: radiative recombination with free electrons and annihilation with free and bound electrons. For an ionization degree ∼10−2 and temeperatures ∼1,000 K, annihilation with bound electrons leads to a decrease of the net positronium fraction to 80–90 percent. If the ionization degree exceeds several per cent, only radiative recombination and annihilation with free electrons Springer

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Fig. 3 Positronium fraction vs. effective width of the 511 keV line for different temperatures and ionization degrees of the medium. There are two groups of theoretical curves: low-temperature (T < 5,000 K, dotted lines), and high-temperature (T > 7,000 K, solid lines). The temperature is fixed for each curve and the ionization degree varies from 0 to 1 along the curves. For the low-temperature curves and for the 8,000 K one, an ionization degree of 0.01 is indicated by empty squares, and 0.1 by dark squares. Each high-temperature curve has two regimes: thin (thick) lines correspond to the ionization degrees lower (higher) than expected for collision dominated plasma. The dashed line shows the prediction for a fully ionized plasma. The rectangle represents the range of parameter values allowed by INTEGRAL data. Adapted from [2]

are important, and both the positronium fraction and line width approach the values expected for a fully ionized plasma. The second family of curves corresponds to temperatures above 7,000 K. In this regime, thermalized positrons can form positronium by charge exchange with hydrogen atoms. This process dominates over radiative recombination and direct annihilation if the plasma is not strongly ionized. The positronium fraction approaches unity. Only for a significantly ionized plasma (∼6–10 percent) at T ≥ 8,000 K does annihilation with free electrons become important and the positronium fraction decreases with increasing ionization degree. According to the standard model [9] there are several abundant ISM phases: hot (T > a few 105 K) ionized, warm (T ∼ 8,000 K), and cold (T < 100 K) neutral. It is clear from Figure 3 that the hot phase cannot provide a dominant contribution to the observed annihilation spectrum, since the width of the line would be too large (e.g. ∼11 keV for T = 106 K, Cranell et al., 1976) while the positronium fraction too low. A similar conclusion can be drawn with respect to the cold, neutral ISM phase. In this case, the expected positronium fraction is consistent with the observed one but the expected line width (∼4.5 keV) is too large. The line width can be reduced by raising the ionization degree above 10−2 , i.e. much higher than is typical of molecular and cold HI clouds, making such a solution unlikely. Springer

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Fig. 4 Expected annihilation spectrum for an ISM with T = 8, 000 K and ionization degree of 0.1 (thick solid line). Separately shown are the contributions of the 3-photon continuum (dotted), in-flight annihilation line (short-dashed), annihilation through para-positronium formation upon thermalization (thin solid), and direct annihilation of thermalized positrons (long-dashed). Adapted from [2]

On the other hand, in the warm (T ∼ 8,000–10,000 K) ISM phase, the ionization degree can vary from less than 0.1 to more than 0.8. This phase alone can therefore explain the observed line width and positronium fraction. The required ionization degree is several per cent. This conclusion is in qualitative agreement with early observations of the Galactic annihilation radiation [1]. The spectrum predicted for the annihilation in a plasma with temperature 8,000 K and ionization degree 0.1 is shown in Figure 4. This spectrum is consistent with the INTEGRAL data. Although the warm ISM model can reproduce the observations, this does not rule out more complicated solutions in which annihilation takes place in several ISM phases. For example, the observations can be explained by a combination of the cold and warm ISM phases in comparable proportions (see [2, 5]).

4. Discussion INTEGRAL has enabled the most accurate to date measurement of the spectrum of positron annihilation radiation from the GC region. The surface brightness of annihilation radiation is high in the central 5–10 degrees of the Galaxy and low outside this region. The total flux from the GC region is ∼10−3 phot/s/cm2 , with a significant uncertainty due to uncertainty in the spatial distribution of the radiation. Assuming a distance of 8.5 kpc to the annihilation site and taking into account that the fraction of annihilations occuring through positronium formation is close to unity, the observed flux implies a rate of ∼2 × 1043 positron annihilations per second in the Galaxy. The Springer

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corresponding luminosity is L e+ ∼1.6 × 1037 erg/s. This imposes strong energetic constraints on the mechanisms of positron production. For an initial positron Lorentz-factor γ the minimum energy supply is γ L e+ . If positrons are generated by more energetic (or massive) particles, the minimum power required to produce the necessary number of positrons can be estimated as (E o /m e c2 )L e+ , where E 0 is the initial energy of the particles. For example, if positrons are generated by cosmic rays (through π + formation), the required energy supply is 3 × 273 × L e+ ∼1040 erg/s (this takes into account that π − and π 0 mesons are also produced). The decay of π 0 mesons should also lead to gamma radiation at energies 50–100 MeV with a luminosity ∼3 × 1039 erg/s. The Galactic disk produces less annihilation flux than the GC region [7, 10], although the ratio of the two luminosities is a model-dependent quantity and in paricular strongly depends on the thickness of the disk component. The energy of the annihilation line coincides with the rest energy of electrons/positrons: E/m e c2 = 0.99991 ± 0.00015, implying that the average radial velocity of the annihilation medium relative to the Earth is less than 44 km/s. The observed width of the annihilation line implies that the velocity dispersion in the annihilation medium is less than 800 km/s. The combination of the observed line width (2.37 ± 0.25 keV) and positronium fraction (0.94 ± 0.06) can be explained by an annihilation in the warm ISM phase, with T ∼ 8,000 K and ionization degree ∼0.1. Annihilation in neither the cold (T ≤ 103 K) nor hot (T ≥ 105 K) ISM phase is consistent with the observations. A combination of several ISM phases is also allowed by the data. The limit on the fraction of annihilations occuring in a very hot (T ≥ 106 K) ISM is < 8%. We note however that positrons injected into the hot ISM can live long enough to (a) leave the Galaxy or (b) propagate into a denser ISM phase to annihilate there. Therefore, the inferred low fraction of annihilations taking place in the hot ISM phase does not necessarily imply that positrions are not produced in that phase. The above characteristics witness against a positron origin associated with Type 2 supernovae or massive stars, since these classes of object are concentrated toward the Galactic disk rather than the bulge. A positron origin due to interaction of cosmic rays with the ISM is also unlikely, in particular due to energetic considerations. The INTEGRAL data strongly favor bulgedominated populations of positron sources, such as Type la supernovae, lowmass X-ray binaries or dark matter. The continuing INTEGRAL observations will provide more stringent limits on the surface brightness distribution and spectral variations of the annihilation radiation along the Galactic plane and across it, allowing one to considerably narrow the range of physical processes responsible for positron production in the Galaxy.

References 1. Bussard, R.W. et al.: The annihilation of galactic positrons. ApJ 228, 928 (1979) 2. Churazov, E. et al.: Positron annihilation spectrum from the Galactic Centre region observed by SPI/INTEGRAL. MNRAS 357, 1377 (2005) 3. Crannell, C.J. et al.: Formation of the 0.511 MeV line in solar flares. ApJ 210, 582 (1976) 4. Iwata, K., Greaves, R.G., Surko, C.M.: γ -ray spectra from positron annihilation on atoms and molecules, PhRvA 55, 3586 (1997) 5. Jean, P. et al.: Spectral analysis of the Galactic e+ − e− annihilation emission. A& A 445, 579 (2006) 6. Johnson, W.N. et al.: The spectrum of low-energy gamma radiation from the Galactic-Center region. ApJ 172, L1 (1972) 7. Knödlseder, J. et al.: The all-sky distribution of 511 keV electron-positron annihilation emission. A& A 441, 513 (2005) 8. Leventhal, M. et al.: Detection of 511 keV positron annihilation radiation from the galactic center direction. ApJ 225, L11 (1978) Springer

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9. McKee, C.F., Ostriker, J.P.: A theory of the interstellar medium – three components regulated by supernova explosions in an inhomogeneous substrate. ApJ 218, 148 (1977) 10. Teegarden, B.J. et al.: INTEGRAL SPI limits on electron – positron annihilation radiation from the Galactic plane. ApJ 621, 296 (2005) 11. Vedrenne, G. et al.: SPI: The spectrometer aboard INTEGRAL. A& A 411, L63 (2003)

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Prospects and requirements for measurements of extragalactic γ -ray lines Richard E. Griffiths

Received: 16 January 2006 / Accepted: 6 June 2006 C Springer Science + Business Media B.V. 2006

Abstract A brief summary is presented of requirements for the measurements of extragalactic γ -ray lines. The electron-positron annihilation line at 511 keV represents the best prospect, and although this line is greatly broadened in active galactic nuclei, a narrow line should be present in clusters of galaxies and radio lobes as a result of prior AGN activity. The strongest fluxes should be of the order of 10−4 photons cm−2 s−1 from the closest extended sources. Keywords Extragalactic . Gamma-rays . AGN . Clusters of galaxies

1. Introduction The status of γ -ray astronomy today is quite similar to the situation in X-ray astronomy in the early to mid-1970’s following the collimated rocket experiments and the early sky survey satellites UHURU, Ariel V and EXOSAT, i.e. the X-ray astronomy era before the advent of focussing X-ray optics. Before the launch of INTEGRAL, about 400 high-energy X-ray sources were known from the previous experiments such as COS-B and the Compton Gamma-Ray Observatory carrying COMPTEL and BATSE. These all-sky or Galactic plane γ -ray experiments have located the strongest γ -ray sources to a typical precision of about a degree. Source identifications have generally depended on correlated detections in the energy range of 10–100 keV (the INTEGRAL reference catalogue – see Figure 1, from Ebisawa et al. [7]), where the corresponding detection at lower energy with X-ray telescopes has resulted in optical identification. These γ -ray missions have not had the advantage of focussing and have therefore operated in the background-limited regime, with very little spectroscopy. With such missions, the sensitivity increases as the square root of the aperture, because the detector size is comparably large. The development of future missions of this kind is thus completely inappropriate – there cannot be order-of-magnitude improvements in sensitivity

R. E. Griffiths Carnegie Mellon University e-mail: griffi[email protected] Springer

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Fig. 1 INTEGRAL reference catalog [7]

by pursuing such techniques and spectroscopic studies would stagnate. The development of gamma-ray astronomy can only proceed by following the lead of X-ray astronomy, and for the same reasons. In order for γ -ray astronomy to flourish, especially in extragalactic work, methods of focussing or concentrating γ -rays need to be developed, so that background is drastically reduced even if the experiments remain background-limited for most targets. This reduction in background will mean that gamma-ray astronomy will finally be opened up for spectroscopic studies. Considerable progress in this direction has already been made with non-focussing instruments, and these developments will be the starting point for the science requirements summarized below. The primary targets for future γ -ray astronomy payloads are thus already generally known from the large area surveys, including the BAT instrument on the Swift satellite, or they are otherwise Targets of Opportunity within known classes of objects such as SuperNovae (SN) and Gamma Ray Bursters (GRB). With the sensitivities of previous experiments, the requirements below will show that exposure times would need to be very long (typically 106 –107 s) in order to conduct any significant astrophysics, e.g. to search for and measure nuclear lines rather than just object detection. Measurements of line strengths are needed for comparison with astrophysical models, so that the lines need to be detected at high significance (at least 5σ ) rather than just a marginal detection. Further, the sensitivities of future instruments need to be such that variability in the nuclear lines from transient objects (novae, supernovae and γ -ray bursts) can be observed – this implies that the required sensitivity to line flux needs to be reached within a typical exposure time of 105 s, rather than 106 or 107 s. These are compelling arguments in favour of a pointed, focussing mission and an argument which eliminates future surveys of large sky areas with limited sensitivity. Observations with the Integral satellite have now set the stage for future requirements on nuclear line spectroscopy in the high energy X-ray region and at gamma-ray energies. These observations are summarised in the Integral papers collected in a special issue of Astronomy & Astrophysics (INTEGRAL Special Issue [12]). The source classes with potential γ -ray lines are as follows: (i) supernovae, especially Type Ia, (ii) galactic novae and X-ray bursters, (iii) microquasars, (iv) Galactic X-ray binaries, (v) Galactic Center, (vi) Active Galactic Nuclei (AGN), (vii) Springer

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Clusters of Galaxies, (viii) Gamma-Ray Bursters, and (ix) GRB remnants. In this paper, the expected line fluxes will be reviewed for extragalactic objects, especially AGN and clusters of galaxies. 2. Extragalactic supernovae Ia For a detailed review of the γ -ray lines predicted from Type Ia supernovae, see the paper by Leising (this volume). For the availability of at least one target at all times, the requirement is to reach SN Ia at distances of 50–100 Mpc (Cappellaro and Turatto [5]), because there are about 25 SNIa’s within 100 Mpc per year, each brighter than Vmag = 16 so that they will be found with the planned large-area synoptic sky surveys. Recent estimates of the rates of SN Ia have been made by Scannapieco and Bildsten [21] and Mannucci et al. [17]. The predicted absolute line fluxes have been calculated by Hoeflich as a function of time following the explosion. For a SNIa the expected line flux in 56 N i 158keV at 20 days past onset is φ(56 N i 158keV ) = 10−2 /D 2

ph cm−2 s−1

where distance D is in Mpc. The required sensitivity to reach objects at 100 Mpc is thus better than 10−7 and approaching 10−8 ph cm−2 s−1 in this line, for integration periods not exceeding 1 day (so that the decay can be followed). Similarly, at 70 days past onset φ(56 Co847keV ) = 5 × 10−3 /D 2

ph cm−2 s−1

Relative to the peak visual magnitude m V , log(φ(56 Co847keV ) × 104 ) = 0.4[10.9 − m V ] so that for m V ∼ 16, φ(56 Co847keV ) ∼ 10−6 ph cm−2 s−1 . A sensitivity of 10−7 ph cm−2 s−1 would mean that a SNIa at V mag. 18 would have detectable nuclear line flux. The astrophysics resulting from line detection alone is, of course, very limited. The optical decay curves of SN Ia already show unambiguously that radionucleides of Ni56 and Co56 are the source of energy. In order to distinguish between the various models for the supernova explosion (see [11]), line widths and ratios need to be measured as a function of time (in days). As an additional cautionary note on the use of nuclear lines for the astrophysics of SNIa, it is possible in principle to use higher energy lines to distinguish between the detonation and deflagration models for the initial event. However, this is very difficult to achieve in practice – the emission spectra calculated in Hoeflich et al. show that large numbers (thousands) of counts are needed in the lines in order to make progress, and the requirements then become prohibitively difficult.

3. Annihilation line from nearby galaxies Results obtained with INTEGRAL have shown the presence of extended 511 keV emission from a region around the Galactic Center [14]. There may be individual compact sources Springer

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present within the region, or it may be completely diffuse. If it is mainly diffuse, then a region of size 1 sq. deg. would contain a flux of about 10−7 ph cm−2 s−1 . Apart from the intrinsic interest in the GC that this result has generated, it is also a very encouraging pointer to further possibilities for observations of the 511 keV line in the nuclear regions of other galaxies. Although the Milky Way is a giant galaxy, it is much smaller in mass than the cD galaxies at the cores of large clusters of galaxies. These can have masses a hundred times as large, and it is a reasonable assumption that the strength of the annihilation line will probably scale as the mass of the galaxy. The local-group galaxy, M31, is similar in mass to the Milky Way, but has a more massive central black hole with mass of order 1–2 ×108 M (Bender et al. [3]). If the intrinsic flux from the 511 keV line is (conservatively) similar to that from the GC, then the observed flux −1 from the nuclear region of M31 would be about 10−7 ph cm−2 s (the distance to the GC is 8.5 kpc; the distance to M31 is about 700 kpc or about 2 million lt-yrs.). A direct scaling with MBH mass would lead to an intrinsic flux from M31 about 50 times higher than that −1 from the GC, i.e. 5 × 10−6 ph cm−2 s . If the 511 keV emission from the core of M31 has a similar intrinsic size to that in the G.C., then the line in M31 would have an angular extent of about 0.1 degs.

4. Annihilation lines from nearby AGN Firstly, much work remains to be done in the study of the high-energy continuum radiation from AGN. The Hard X-ray Detector (HXD) on the Japanese/US satellite Suzaku should accomplish much of this over the next several years (see Kawaharada et al. [13] for a description of the instrument). The Suzaku HXD has the sensitivity shown in Figure 2 and is compared with previous instruments. Before Suzaku, Beppo-SAX was exemplary for its wide spectral coverage (0.1–200 keV) with the PDS sensitivity reaching to 0.1 times the flux from the nearest quasar 3C273 in the energy range 10–100 keV. Other highly successful satellites and instruments which have explored this energy range have included the X-ray Transient Explorer (XTE), the IBIS instrument on INTEGRAL and the OSSE instrument on the Gamma-Ray Observatory. The

Fig. 2 Suzaku HXD sensitivity [13]. For an updated version, see [22] – this volume Springer

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Fig. 3 Spectral energy distribution from a cluster following positron injection by an AGN at various times. The cases labelled s = 2 and 3 are for different power-law indices for positron injection spectra. From Furlanetto and Loeb [8]

HXD instrument on Suzaku has a smaller field of view than previous instruments, and this reduces the sky fluctuation noise, so that the sensitivity should be better than IBIS or SAX by a factor of about 2 or 3 when the background is well understood [9]. As described by Takahashi (this volume), the HXD will be able to measure the reflection spectra (in the energy range of tens of keV) in several tens of AGN, out to a redshift of ∼0.1 and high-energy cut-offs in a similar number of objects, depending on the cut-offs themselves (Perola et al. [19]). The BAT instrument on Swift will provide a few hundred possible targets for these detailed studies with Suzaku. These studies will provide a further step in the overall synthesis of the X-ray background, as described by Andrea Comastri in this volume [6]. Although the prospects are good for the measurement of AGN high-energy continua, the prospects for detection of annihilation lines are rather poor. AGN jets are strongly suspected to be sources of relativistic positrons, but the annihilation lines from the jets themselves are expected to be greatly broadened [10]. The jets are emitted at high Doppler factors δ of 10–100 where

δ=

1 γ (1 − β cos θ)

and where γ = (1−β12 )0.5 and the jet is moving with velocity v = cβ at angle θ to the line of sight (see the review by Bicknell, Wagner and Groves (2001)). Springer

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The 511 keV line is blue-shifted to:

E=

δ γth × 511 keV 1+z

where γth is the Lorentz factor representing the low-energy cutoff in the power-law energy distribution of the particles [1]. A line width of 2–3 MeV is anticipated and has probably been observed as the “MeV bump” in blazars (e.g. [4, 18]) The positrons eventually lose energy and finally annihilate in the ambient ISM where the remainder should produce a narrow line in the circumnuclear region around an AGN which has been active over the previous, say, 108 yrs. Nearby AGN such as Cen A, 3C 273, NGC 1275, and NGC 4151 represent the best prospects for line detection and the historical positron flux depends on the mass and spin of the central MBH. The bulk of the positrons will presumably be annihilated in close proximity because of the ISM density near the MBH. This annihilation line radiation will thus be confined to the nuclear region of the galaxy, typically less than an arcminute in size, or could also be present in radio lobes, as in the case of Cen A (see below).

5. Annihilation line from clusters of galaxies Although the observation of the annihilation line arising from the positrons from active AGN jets may be impossible, the relic positrons from inactive AGN in clusters of galaxies produce enrichment of the ICM and the resulting annihilation line from cooled positrons may be more readily observable, though spatially extended. At the ambient ICM temperature, most annihilations result in the 511 keV line, rather than in the production of positronium and a continuum, as in the case of positron emission from Galactic black holes. A detailed analysis of the annihilation lines that may be anticipated from clusters of galaxies has been performed by Furlanetto and Loeb [8] and their results are summarised here (see also Figure 3): The intrinsic widths of the 511 keV lines from clusters is predicted to be roughly 32 (TkeV )1/2 , i.e. in the range of tens to about a hundred keV. The flux from a cluster of galaxies is predicted to be:

Fcl = 8 × 10−7

rmix 200kpc

3

D 100Mpc

−2 ×

n˙ lines ph cm−2 s−1 10−24 cm3 s−1

where rmix is the positron mixing radius, typically 200 kpc and n˙ line is the emissivity in the −1 511 keV line, expected to be roughly 10−24 cm3 s . Typical integrated 511 keV line fluxes from clusters of galaxies might therefore be of order 10−6 (D/100Mpc)−2 ph cm−2 s−1 . At a distance of 100 Mpc, a typical cluster has an angular extent of about 3 arcmins., effectively a point source for any collecting or focussing instrument at this energy. The sensitivity requirement is thus of order 10−6 ph cm−2 s−1 . For nearby large clusters, i.e. the Virgo cluster at 20 Mpc, the possibility arises of mapping the cluster in 511 keV emission. Springer

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The integrated flux from Virgo is expected to be: ne ζAGN 3 × 10−3 cm−3 0.1 τ −1 ph cm−2 s , 108 yr

FVirgo = 1.3 × 10−6 X sAGN η−1 ×

LK 1044 ergs s−1

where X sAGN is a factor varying between 1 and 10 for positron injection spectra having power law indices (s) between 2 and 3; η−1 is the contribution from past AGN activity, and may be up to a factor of ten; ζAGN is the fraction of the injected kinetic energy contained in the positron component, estimated to be typically 0.1; L K is the total mechanical (kinetic) luminosity; and τ is the lifetime of an AGN in a single duty cycle, typically about 108 yr. Similarly, the flux from CenA is estimated to be: ne ζAGN 10−2 cm−3 0.1 τ LK phcm−2 s−1 , × 43 −1 10 ergs s 1.4 × 108 yr

FCenA = 10−5 X sAGN η−1

where the symbols have the same meanings as above and the unknown factors have values comparable to the quantities in the denominators beneath them. The arguments for CenA are less compelling, since this is still an active nucleus and the positrons have not had time to cool, and CenA is not in a rich cluster like Virgo with many extinct AGN.

6. Conclusions The prospects for the detection and study of extragalactic γ -ray lines are strongest for the e+ − e− annihilation line at 511 keV, but only in sources where the positrons ejected from black holes have had time to cool to ambient temperatures (the intracluster medium). This means that cD galaxies, radio lobes and clusters of galaxies are more likely to produce detectable fluxes than those AGN which are still currently active. The fluxes from large nearby clusters of galaxies, and also from CenA, may approach 10−4 photons cm−2 s−1 in the 511 keV line. In order to detect such lines, a careful trade-off study needs to be made between high-energy Wolter-type mirrors and Laue crystal spectrometers. Acknowledgements It is a great pleasure to acknowledge many discussions with members of the Science Payloads and Advanced Concepts Office at the European Space & Technology Center in Noordwijk: and in particular Tony Peacock, Marcos Bavdaz, Nicola Rando, Dave Lumb and Craig Brown. This work was supported in part by the European Space Agency.

References 1. Abraham, Z., Romero, G. E., Durouchoux, P.: Proc. Fourth Integral Workshop “Exploring the Gamma-Ray Universe”, ESA-SP 459, p.131 2. Barris, B.J., Tonry, J.L.: Astrophys. J. 637, 427 (2006) 3. Bender, R. et al.: Astrophys. J. 631, 280 (2005) Springer

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4. Bottcher, M., Schlickeiser, R: Astron. Astrophys. Supp. Ser. 120, 575 5. Cappellaro, E., Turatto, M.: The influence of binaries on stellar population studies, (Dordrecht: Kluwer Academic Publishers). Astrophys. Space Sci. Library 264, 199 (2001) 6. Comastri, A.: DOI: 10.1007/s10686-006-9041-6 (2006) 7. Ebisawa, K., Bourban, G., Bodaghee, A., Mowlavi, N., Courvoisier, T. J.-L.: Astron. Astrophys. 411, L59; see also vizieR On-line Data Catalog J/A+A/411/L59 (2004) 8. Furlanetto, S.R., Loeb, A.: Astrophys. J. 572, 796 (2002) 9. Fukuzawa and the Suzaku HXD Team, 2006, in press 10. Begelman, M., Blandford, R. Rees, M.J.: Rev. Mod. Phys. 56, 255 (1984) 11. Hoeflich, P., Wheeler, J.C., Khokhlov, A.: Astrophys. J. 492, 228; ibid. 2004, 605, 573 (1998) 12. INTEGRAL Special Issue: Astron. Astrophys. 411, L1–L460 (2003) 13. Kawaharada, M., et al.: Proc. Soc. Photo-Optical Eng. 5501, 286 (2004) 14. Knoedlseder, J., et al.: Astron. Astrophys. 441, 513 (2005) 15. Leising, M.: DOI: 10.1007/s10686-006-9052-3 (2006) 16. Maciolek-Niedzwiecki, A., Zdziarski, A. Coppi, P.: MNRAS 276, 273. 17. Mannucci, F., Della Valle, M., Panagia, N., Cappellaro, E., Cresci, G., Maiolino, R., Petrosian, A., Turatto, M.: Astron. Astrophys. 433, 807 18. Marcowith, A., Henri, G., Pelletier, G.: MNRAS 277, 681 19. Perola, G.C., Matt, G., Cappi, M., Fiore, F., Guainazzi, M., Maraschi, L., Petrucci, P.O., Piro, L.: Astron. Astrophys. 389, 802 (2002) 20. Roland, J., Hermsen, W.: Astron. Astrophys. 297, L9 21. Scannapieco, E., Bildsten, L.: Astrophys. J. 629, L85 22. Takahashi, T., et al.: DOI: 10.1007/s10686-006-9059-9 (2006)

Springer

Exp Astron (2005) 20:31–40 DOI 10.1007/s10686-006-9061-2 O R I G I NA L A RT I C L E

Non-thermal cosmic backgrounds and prospects for future high-energy observations of blazars P. Giommi · S. Colafrancesco

Received: 27 January 2006 / Accepted: 17 July 2006 C Springer Science + Business Media B.V. 2006

Abstract We discuss the contribution of the blazar population to the extragalactic background radiation across the electromagnetic (e.m.) spectrum with particular reference to the microwave, hard-X-ray and γ -ray bands. Our estimates are based on a recently derived blazar radio LogN-LogS that was built by combining several radio and multi-frequency surveys. We show that blazar emission integrated over cosmic time gives rise to a considerable broad-band non-thermal cosmic background that dominates the extragalactic brightness in the high-energy part of the e.m. spectrum. We also estimate the number of blazars that are expected to be detected by future planned or hypothetical missions operating in the X-ray and γ -ray energy bands. Keywords Galaxies:active . Galaxies: blazar: BL Lacertae surveys

1. Introduction Active Galactic Nuclei (AGN) are well known to dominate the high-energy (soft-X-ray and beyond) high Galactic latitude sky. Their radiation integrated over cosmic time can explain most, if not all, the extragalactic background radiation (e.g. [4, 7, 17, 24]). Historically, AGN have been classified in many – sometime inconsistent or confusing – ways, depending on how they appeared in surveys performed in different energy bands and with different flux limits (such flux limits are often determined by the technology available at the time of the survey, or depending on some specific observational parameter, like, e.g., the flux ratio between radio and optical emission, the equivalent width of their emission lines, etc.).

P. Giommi () ASI Science Data Center, C/O ESA-ESRIN, Frascati, Italy e-mail: [email protected] S. Colafrancesco INAF, Osservatorio Astronomico di Roma e-mail: [email protected] Springer

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In the following we use the widely accepted standard paradigm where AGN are powered by accretion onto a super-massive black hole, e.g. [30, 31, 33], to divide this class of sources into two broad categories defined by their intrinsic emission mechanism: – AGN whose power is dominated by radiation of thermal origin produced by matter that is strongly heated in the inner parts of a disk of matter falling onto the supermassive black hole and illuminating the circumnuclear matter that is responsible for the broad line emission. We call these objets Thermal Emission Dominated AGN or TED-AGN. – AGN whose power is dominated by Non-Thermal radiation (or NTED-AGN) where most of the emission is generated through non-thermal processes, like the synchrotron and the inverse Compton mechanism, by particles accelerated in a jet of material that moves at relativistic speed away from the central black hole. The jet itself is formed converting part of the accretion energy in a way that is presently not well understood. Within this general definition the class of blazars corresponds to the small subset of NTED-AGN that are viewed at a small angle w.r.t. the jet axis (for this reason their emission is strongly amplified by relativistic effects [2, 30]), whereas Radio Galaxies are those NTED-AGN that are viewed at a large angle w.r.t. the jet axis. Here we do not distinguish between line-less objects, or BL Lacs, and broad-line Flat-Spectrum Radio Quasars, or FSRQs. When the accretion and jet emission coexist in the same object and produce similar amounts of radiation we have AGN that are a mixture of the TED and NTED type that appear like broad-line radio galaxies (e.g. 3C 120). The overall cosmic background radiation has two well understood components: the primordial black body emission peaking at microwave frequencies (the cosmic microwave background, CMB), and the X-ray apparently diffuse emission arising from the accretion onto super-massive black holes in AGN integrated over cosmic time (the cosmic X-ray background, CXB). We will show that blazars add a third non-thermal component that at low frequencies contaminates the CMB fluctuation spectrum and complicates its interpretation [5], while at the opposite end of the e.m. spectrum it dominates the extragalactic background radiation [7]. In the following, we estimate the contribution of blazars to non-thermal cosmic backgrounds starting from a recently derived deep radio LogN-LogS [7]. The broad-band e.m. spectrum of a blazar is composed of a synchrotron low-energy component that peaks [in a Log(ν) − Log(ν f (ν)) representation] between the far infrared (i.e. ∼300 GHz–10 THz, corresponding to ∼ (0.12–4)10−2 eV) and the X-ray band (∼2–10 keV), followed by an Inverse Compton component that has its maximum in the hard X-ray band (∼20–100 KeV) or at higher energies, depending on the location of the synchrotron peak, and extends into the γ -ray or even the TeV band. Those blazars where the synchrotron peak is located at low energy are usually called Low energy peaked blazars or LBL, while those where the synchrotron component reaches the X-ray band are called High energy peaked blazars or HBL [19]. LBL sources are the large majority among blazars [20] and are usually discovered in radio surveys, while HBL objects are preferentially found in X-ray flux limited surveys, since at these frequencies they are hundreds, or even thousands, of times brighter than LBLs of similar radio power. Springer

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Fig. 1 The blazars radio (5 GHz) LogN-LogS of [7] who built it combining several surveys as indicated in the top right part of the plot (see [7] for details)

2. The radio LogN-LogS of blazars and their contribution to extragalactic cosmic backgrounds The deep blazar radio (5 GHz) LogN-LogS shown in Figure 1 has been recently derived by [7] who showed that it can be described by a broken power law with parameters defined in Equation (1): N (>S) =

5.95 10−3 × S −1.62 0.125 × S −0.9

S > 0.015 Jy S < 0.015 Jy

(1)

Once the LogN-LogS of a population of sources is known in a given energy band, it is possible to estimate their emission in other parts of the e.m. spectrum, provided that the flux ratio between the two bands is known. Here we deal with flux ratios and Spectral Energy Distributions (SEDs) of blazars that will be used to estimate the contribution to cosmic backgrounds at microwave frequencies and in the X-ray and γ -ray bands (see Figure 3). The distribution of f x / f r flux ratios shown in Figure 2 (see [7] for details) spans about four orders of magnitudes implying that the X-ray flux of blazars with the same radio flux can be different by a factor up to ≈10,000! In the following we estimate the blazar contribution to the cosmic backgrounds (see Figure 3) basing our calculation on the radio LogN-LogS shown in Figure 1 and on flux ratios determined in different bands, or on observed blazar SEDs. 2.1. The cosmic microwave background The contribution of blazars to the CMB has been estimated in the past from different viewpoints (e.g. [5, 29]). Here we calculate the integrated microwave background intensity as Springer

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Fig. 2 The f x / f r distribution of blazars estimated by [7]

Fig. 3 The extragalactic Cosmic Background Energy distribution at microwave, X-ray and γ -ray energies. The CMB is represented by a black-body spectrum with temperature of 2.725◦ K [16]; the CXB is taken from HEAO-1 measurements [9, 15] and has been scaled to match the more recent BeppoSAX, ASCA, and XMMNewton results in the 2–10 keV band [12,14,32]. The gamma ray background is derived from the COMPTEL data in the range 0.8–30 MeV [11] and from EGRET data in the range 30 MeV–50 GeV. We report here the results of two different analyses of the EGRET data: open circles from [26] and filled circles from [27], which uses an improved model of the Galactic diffuse gamma-ray continuum. As for the TeV diffuse background, we report the upper limits derived in the 20–100 TeV region from the HEGRA air shower data analysis [1]. In the TeV–PeV energy range, other experiments give only upper limits and there is no clear observation of a diffuse photon signal yet (see [7] for more detail)

follows Iblazars =

1 Jy

S 0.1 mJy

Springer

dN dS , dS

(2)

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35

where dN/dS is the differential of Equation (1). The minimum integration flux Smin = 0.1 mJy is likely to be conservative, since blazars with radio flux near or below 1 mJy are already included in the Einstein Medium Sensitivity Survey BL Lac sample [23]. The integrated intensity Iblazars is converted from 5 GHz to microwave frequencies by convolving the flux value with the observed distribution of spectral slopes between 5 GHz to microwave frequencies, as estimated from the 1Jy-ARN sample (see [5] for details). The fractional contamination Iblazars /ICMB of blazars to the CMB intensity ICMB and the corresponding apparent temperature increase in the frequency range 90–300 GHz has been derived by [7]. Blazars also contribute to the CMB temperature anisotropies with a spectrum ( T )blazar = [(2π)−1 C ( + 1)]1/2 ,

(3)

where C,blazar =

Smax

dS Smin

dN 2 S . dS

(4)

The quantity on the right hand side of Equation (4) is the usual Poisson shot-noise term, [21, 28] and we neglect here the clustering term ω(I )2 (which adds to the Poissonian term) since there is not a clear estimate of the blazar clustering yet. Note, however, that the inclusion of clustering significantly increases the amount of contamination, especially at large angular scales [8]. For the blazar population described by the LogN-LogS given in Figure 1, we found C,blazar ≈ 54.4 Jy2 sr−1 at 41 GHz and C,blazar ≈ 51.6 Jy2 sr−1 at 94 GHz. When translated into temperature units (see [5]), we found a value C,blazar ≈ 2.22 × 10−2 µK2 sr at 41 GHz and C,blazar ≈ 1.09 × 10−3 µK2 sr at 94 GHz. We show in Figure 4 the quantity ( T )blazar and

Fig. 4 The contribution of blazars to the CMB fluctuation spectrum in the WMAP 41 GHz (left panel) and 94 GHz (right panel) channels, as evaluated from the LogN-LogS given in Figure 1 (solid line). We also show the angular power spectrum for the blazar population by adding an estimate of the possible contribution of radio sources with steep-spectrum at low radio frequencies which flatten at higher frequencies (dashed line). The dotted line also includes the effect of spectral and flux variability. Although this additional contamination may be substantial a precise estimation can only be done through simultaneous high resolution observations at the same frequency. A typical CMB power spectrum evaluated in a CDM cosmology with m = 0.3, = 0.65, b = 0.05 which best fits the available data is shown for comparison Springer

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compare it to the CMB fluctuation power spectrum which best fits the available data. These values (shown as solid lines) have to be considered as a definite lower limit for C,blazar , since they neglect the contribution of steep-spectrum sources at low frequencies which flatten at these frequencies (41 and 94 GHz, dashed lines) and the effect of flux variability (dotted lines). The blazar flux variability at millimeter wavelengths may be substantial (higher than factors 3–10 on time scales of weeks to years w.r.t. those seen at cm wavelengths) and could increase the amount of contamination of CMB maps when these are built over long integration periods. The contamination level shown in Figure 4 is the one expected in the case where no blazars are removed from the CMB data. We expect that a correct procedure for the derivation of the CMB power spectrum that takes into account the full point-like source contribution implied by our LogN-LogS, would both influence the shape of the expected power spectrum and increase the statistical uncertainties of the WMAP data points, especially at high multipoles, where the blazar contribution is larger. The calculations shown in Figure 4 are performed neglecting the blazar clustering and thus they must again be considered as a lower limit to the realistic angular power spectrum contributed by these sources. The effects of clustering on the CMB fluctuation spectrum has been partially estimated by some authors: (e.g. [8, 25]) and they depend both on the adopted model for the source counts and on their clustering model. Based on the correlation function of [13], on that for the SCUBA sources [25] and on our blazar LogN-LogS, we expect that the contamination of the first peak of the CMB fluctuation spectrum (at the WMAP 41 GHz channel) is at a level of 20–25%. This estimate does not include possible variability effects and additional core-dominated radio sources. 2.2. The soft X-ray background We estimate the contribution of blazars to the CXB at 1 keV using two methods: (i) converting the integrated radio flux calculated with Equation (2) into X-ray flux using the observed distribution of f x / f r flux ratios in Figure 2; and (ii) converting the integrated blazar contribution to the CMB (at 94 GHz) to X-ray flux using the distribution of αµx [the microwave (94 GHz) to X-ray (1 keV) spectral slope] estimated from the subsample of blazars detected by WMAP in the 94 GHz channel, for which an X-ray measurement is available (see Figure 9 in [7]). The first method gives a total blazar contribution to the X-ray background of 2.7 × 10−12 erg cm−2 s−1 deg−1 (about 70% of which is due to HBL sources with f x / f r > 5 × 10−12 erg cm−2 s−1 Jy−1 ) in the ROSAT 0.1–2.4 keV energy band. Assuming [7] an average blazar X-ray energy spectral index of αx = 0.7, this flux converts to 2.6 × 10−12 erg cm−2 s−1 deg−1 in the 2–10 keV band, i.e. 11% of the CXB which is estimated to be 2.3 × 10−11 erg cm−2 s−1 deg−1 [22]. The distribution of αµx has an average αµx = 1.07 and a standard deviation of 0.08, corresponding only to about a factor 3 in flux. This distribution is much narrower than the one of the average spectral slope between the radio and X-ray band (Figure 2), while its dispersion is comparable to that expected from blazar variability at radio and especially at X-ray frequencies. The X-ray flux can therefore be estimated simply as f 1 keV =1.4×10−7 f 94 GHz (see, e.g., [7]). Since the blazar integrated emission at 94 GHz is 7.2 × 10−6 CMB94 GHz (or 0.64 Jy/deg2 ) and the cosmic X-ray background is 2.3 × 10−11 erg cm−2 s−1 [22] in the 2–10 keV band (equivalent to 2.31 µJy/deg2 at 1 keV), we have that f1 keV = 0.09 µJy/deg2 , i.e. 3.9% of the CXB for f 94 GHz = 0.64 Jy/deg2 . Considering that the αµx distribution of [7] only includes LBL objects and that HBL sources make up ≈ two thirds of the total contribution to the CXB, the percentage scales to about 12%, which is very close to the value 11% obtained with the Springer

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Fig. 5 Left: The possible contribution of LBL blazars to the cosmic background. Simple SSC energy distributions fail to reproduce the observed intensity and slope of the γ -ray background. The observed range of γ -ray emission with EGRET, normalized to radio flux, indicates that the duty cycle at these energies must be low (see text for details). Right: The spectral slopes between the 5 GHz emission and the 100 keV and 1 MeV high energy fluxes in the SSC distribution of LBL blazars that reproduces the observed X and γ -ray cosmic background

previous method. Both our results are in good agreement with the independent estimate of [3], who find that the radio loud AGN content of the CXB is 13% in the XMM-Newton bright serendipitous survey. 2.3. Hard X-ray – soft γ -ray background The number of sources detected at energies larger than soft X-rays is still rather low; hence, deriving reliable distributions of flux ratios between radio or microwaves and the Hard X-ray/γ -ray fluxes is not currently possible. Thus, in order to estimate the blazar contribution to the high energy Cosmic Backgrounds (at E > 100 keV), we followed a different approach: we extrapolated the predicted blazar integrated intensity at microwave frequencies (Equation 2) to the hard X-ray and soft γ -ray band using a set of hypothetical SSC spectral energy distributions. Figure 5 (left panel) shows the CMB, CXB, and CGB together with three predicted SEDs from a simple homogeneous SSC models with parameters constrained to: (1) be consistent with the expected integrated flux at 94 GHz; 2) have αµx equal to the mean value of the WMAP blazars ( αµx = 1.07); 3) have a radio spectral slope equal to the average value found in the WMAP sample. The three curves so constrained are characterized by synchrotron peak frequencies of νpeak = 1012.8 , 1013.5 , and 1013.8 Hz. A high value of νpeak largely overestimates the observed hard-X-ray to soft γ -ray (≈1020 − 2 × 1022 Hz or ≈500 keV–10 MeV) cosmic background, whereas a too low value of νpeak predicts a negligible contribution (see Figure 5, left panel). The case νpeak = 1013.5 Hz predicts 100% of the hard X-ray/soft gamma-ray cosmic background. Since the Log(νpeak ) values of blazars in the WMAP and other catalogs peak near 13.5, ranging from 12.8–13.7 within one sigma from the mean value, we conclude that blazars may be responsible for a large fraction (and possibly 100%) of the hard-Xray/soft γ -ray cosmic background. 2.4. γ -ray background The SSC distributions of Figure 5 predict a negligible blazar contribution to the extragalactic γ -ray background above 100 MeV. Nevertheless, it is well known that blazars are the large Springer

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majority of the extragalactic γ -ray (E > 100 MeV) identified sources detected by the EGRET experiment [10]; therefore they are likely to contribute to the γ -ray background in a significant way. Indeed, [18] concluded that blazars should make a large fraction, if not the totality, of the extragalactic γ -ray background. However, these early calculations relied upon a very small blazar sample and had to assume no strong variability, a characteristic that was later demonstrated to be extremely common in γ -ray detected blazars. Figure 11 in [7] compares the energy distribution of the CMB, CXB, and CGB to the SED of 3C 279 (a well-known bright blazar detected by EGRET) scaled to the integrated blazar flux intensity as calculated with Equation (2). Taking into account the strong variability of blazars seen across the whole e.m. spectrum, it has been shown [7] that, while the contribution to the CXB can range from a few percent to over 10% in the higher states, the predicted flux at γ -ray frequencies ranges from about 100% to several times the observed cosmic background intensity. Such large excess implies that (i) either sources like 3C279 are not representative of the class of blazars or (ii) their duty cycles at γ -ray frequencies are very low. A way of quantifying the ratio between the γ -ray intensity predicted by assuming that the source is representative of the entire population and the actual background intensity is to use the f 94 GHz / f 100 MeV ) microwave (94 GHz) to γ -ray (100 MeV) slope αµγ = −Log( . Log(ν94 GHz /ν100 MeV )

For comparison, we define αµγ 100%CGB = 0.994 as the αµγ of a hypothetical source that would produce 100% of the CGB, if representative of the entire class. Any realistic source with αµγ flatter than αµγ 100%CGB = 0.994 would then predict – if representative of the entire population – an integrated flux in excess of the observed γ -ray background. Alternatively, its duty cycle must be lower than 100%. Figure 5 (left) shows the minimum and maximum values of αµγ among the sources detected by the EGRET experiment. 2.5. TeV background All blazars detected so far at TeV energies are of the HBL type. Therefore we estimate the blazar contribution to the TeV background as in the case of the soft γ -ray background but only considering the HBL component, and not the entire blazar population. These extreme objects have been estimated to be about 0.1% of the blazar population [7]. Using the SED of the well known TeV blazar MKN421 normalized at 94 GHz (see Figure 13 in [7]) – so that the flux is scaled to 0.1% of the intensity produced by the entire population of blazars – we see that, despite HBLs are a tiny minority, their integrated X-ray flux makes up a fairly large fraction of the CXB, and that their TeV emission may produce a significant amount of extragalactic light. We note, however, that since extreme HBLs (such as those of the Sedentary survey) are very rare (one object in several thousand degrees with flux above a few mJy), the extragalactic light at TeV energies should be very patchy (i.e. associated to single sources) rather than a diffuse light resulting from the superposition of many unresolved discrete sources.

3. Prospects for future high-energy observations of blazars We have seen that blazars, and in general NTED-AGN, emit non-thermal radiation across the entire e.m. spectrum. A clear understanding of the blazar content of the extragalactic high-energy sky is necessary, as new missions are planned or are under study by European and other space agencies to explore in more detail the hard X-ray and γ -ray bands. These missions will open the last energy windows (e.g. the few hundred keV-few MeV region) Springer

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Table 1 The number of blazars in the high Galactic latitude sky at different sensitivities and energy bands

Energy band Micro-wave (100 GHz) Soft X-ray (0.1−2.4 keV) Hard X-ray 50–150 keV Soft γ -ray 3–10 MeV γ -ray 100 MeV–100 GeV

Flux limit (energy band)

Flux limit (5 GHz)

No. of sources at high b (25,000 deg2 )

70 mJy 7 mJy 10−15 erg cm−2 s−1

100 mJy 10 mJy ∼0.1–10 mJy

5000 >100,000 >100,000

5 × 10−12 erg cm−2 s−1 1 × 10−13 erg cm−2 s−1 5 × 10−7 ph cm−2 s−1 1 × 10−7 ph cm−2 s−1 1 × 10−7 ph cm−2 s−1 3 × 10−9 ph cm−2 s−1

1000 mJy 20 mJy 1000 mJy 200 mJy Monte Carlo simulation

130 ≈70,000 130 2000 ≈100 ≈3000

that, for technical difficulties, have so far remained almost unexplored but that are extremely important for understanding the physical processes powering NTED-AGN. In the following we apply the same method used in the previous sections to estimate the number of blazars that could be detected by future microwave, X-ray and γ -ray observatories. We report the results in Table 1 where column 1 gives the energy band considered, column 2 gives the limiting sensitivity reached in that energy band, column 3 gives the corresponding 5 GHz flux, and column 4 gives the number of blazars expected in the high Galactic latitude sky (≈25,000 deg2 ). Figure 2 shows that the distribution of f x / f r ratios is extremely broad reflecting the fact that the flux in the X-ray region is deeply affected by the position of the synchrotron peak in Log(ν)−Log(ν f (ν)) plots. Blazars where the peak is located in the far infrared (i.e. LBL) have very little X-ray flux, whereas extreme HBL objects can be thousands of times brighter at X-ray frequencies than LBLs of the same radio flux. Figure 2 implies that a survey as deep as 10−15 erg cm−2 s−1 would detect the whole f x / f r distribution of blazars with 5 GHz flux larger than 10 mJy, corresponding to well over 100,000 sources in the high Galactic latitude sky. From Figure 5 (right panel) we can see that the average slope between the 5 GHz radio flux and the hard-X-ray band or the soft γ -ray band is 0.85 and 0.84, respectively. Since the ratio between the radio flux and these energy bands is not expected to have a large spread around the mean value (like f x / f r ), the average slopes can be directly converted to predict the hard-X-ray and the soft γ -ray fluxes. We have reported these predictions in column 2 of Table 1 A deep all sky survey in the soft X-ray band: 0.1–10 keV. From Table 1 we see that a deep all-sky X-ray survey in the soft X-ray band would allow to build a sample of >100,000 blazars that are expected to be above the limiting sensitivity of PLANCK (operating in the microwaves). Given the significant impact of the blazar foreground emission on the CMB power spectrum, it is important to remove accurately this foreground component from the CMB. An efficient way to achieve this goal is to exploit the fact that the spectral slope distribution between microwave and soft X-ray flux of LBLs is very narrow (see Figure 9 of [7]) with a dispersion that is probably mostly due to intrinsic variability. The soft X-ray > flux of LBLs (that are ∼ 90% of the blazar population) is therefore a very good estimator of the flux at microwave frequencies and could then be used to locate and remove foreground blazars from the PLANCK and other CMB esperiments. Springer

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The extremely large sample of blazars produced by such a survey could also be used to study the statistical properties of blazars in great detail (including the spatial correlation function) and would identify a very large number of targets for the next generation γ -ray observatories (such as AGILE or GLAST), as well as for the future instruments operating in the still poorly explored MeV spectral region. The expected number of blazars at γ -ray energies above 100 MeV cannot be estimated with a simple extrapolation of the 5 GHz flux (see Section 2.4), and therefore we have listed the preliminary expectations (see last row of Table 1) evaluated through a Monte Carlo method that makes use of the radio luminosity distribution of blazars and predicts γ -ray fluxes taking into account the αµγ distribution of EGRET detected blazars. This method is currently under development as part of our contribution to the GLAST project. Acknowledgements It is a pleasure to thank the Organizing and Advisory Committee of this meeting for the invitation to present our results in the context of the planned and future gamma-ray experiments.

References 1. Aharonian, F.A., Akhperjanian, A.G., Barrio, J.A., et al.: APh 17, 459 (2002) 2. Blandford, R.D., Rees, M.J.: in: Pittsburgh Conference on BL Lac Objects, Wolfe, A.M. (ed.), University of Pittsburgh, Pittsburgh, p. 328 (1978) 3. Galbiati, E., Caccianiga, A., Maccacaro, T., et al.: A&A, in press, astro-ph/0410432 (2004) 4. Giacconi, R., Gursky, H., Paolini, F., Rossi, B.: Phys. Rev. Lett. 9, 439 (1962) 5. Giommi, P., Colafrancesco, S.: A&A 414, 7 (2004) 6. Giommi, P., Menna, M.T., Padovani, P.: MNRAS 310, 465 (1999) 7. Giommi, P., Colafrancesco, S., Cavazzuti, E., Perri, M., Pittori, C.: A&A 445, 843 (2006) 8. Gonzales-Nuevo, J., Toffolatti, L., Argueso, F.: ApJ 621, 1 (2005) 9. Gruber, D.E., Matteson, J.L., Peterson, L.E., Jung, G.V.: ApJ 520, 124 (1999) 10. Hartman, R.C., Bertsch, D.L., Bloom, S.D., et al.: ApJS 123, 79 (1999) 11. Kappadath, S.C.: ph. D. Thesis, University of New Hampshire, USA (1998) 12. Kushino, A., Ishisaki, Y., Morita, U., et al.: PASJ 54, 327 (2002) 13. Loan, A.J., Wall, J., Lahav, O.: MNRAS 286, 994 (1997) 14. Lumb, D.H., Warwick, R.S., Page, M., De Luca, A.: A&A 389, 93L (2002) 15. Marshall, F.E., Boldt, E.A., Holt, S.S., et al.: ApJ 235, 4 (1980) 16. Mather, J., Fixsen, D., Shafer, R.A., Mosier, C., Wilkinson, D.T.: ApJ 512, 511 (1999) 17. Moretti, A., Campana, S., Lazzati, D., Tagliaferri, G.: ApJ 588, 696 (2003) 18. Padovani, P., Ghisellini, G., Fabian, A., Celotti, A. MNRAS 260, L21 (1993) 19. Padovani, P., Giommi, P.: ApJ 444, 567 (1995) 20. Padovani, P., Perlman, E., Landt, H., Giommi, P., Perri, M.: ApJ 58, 128 (2003) 21. Peebles, P.: The large scale sturcture of the universe, in: Priceton, P.U.P. (ed.) (1980) 22. Perri, M., Giommi, P.: MNRAS 362, L61 (2000) 23. Rector, T.A., Stocke, J.T., Perlman, E.S., Morris, S.L., Gioia, I.M.: AJ 120, 1626 (2000) 24. Rosati, P., Tozzi, P., Giacconi, R., et al.: ApJ 566, 667 (2002) 25. Scott, D., White, M.: A&A 346, 1 (1999) 26. Sreekumar, P., Bertsch, D.L., Dingus, B.L., et al.: ApJ 494, 523 (1998) 27. Strong, A., Moskalenko, I., Reimer, O.: ApJ 613, 956 (2004) 28. Tegmark, M., Efstathiou, G.: MNRAS, 281, 1297 (1996) 29. Toffolatti, L., Argueso Gomez, F., de Zotti, G., et al.: MNRAS 297, 117 (1998) 30. Urry, C.M., Padovani, P.: PASP 107, 803 (1995) 31. Urry, C.M.: ASPC 290, 3 (2003) 32. Vecchi, A., Molendi, S., Guainazzi, M., Fiore, F., Parmar, A.N.: A&A 349, L73 (1999) 33. Vellieux, S.: ASPC 290, 11 (2003)

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Exp Astron (2005) 20:41–47 DOI 10.1007/s10686-006-9041-6 O R I G I NA L A RT I C L E

Rolling down from the 30 keV peak: Modelling the hard X-ray and γ -ray backgrounds Andrea Comastri · Roberto Gilli · Gunther ¨ Hasinger

Received: 7 February 2006 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract We will briefly discuss the importance of sensitive X-ray observations above a few tens of keV for a better understanding of the physical mechanisms associated to the Supermassive Black Hole primary emission in both radio quiet and radio loud AGN and to the cosmological evolution of the most obscured sources. Keywords X-rays . Background radiation . AGN

1. Introduction The fraction of the hard X-ray background (XRB) resolved into discrete sources by deep Chandra and XMM-Newton observations smoothly decreases from essentially 100% below 2–3 keV to about 50% in the 7–10 keV energy range [1]. The resolved fraction averaged on the standard 2–10 keV band is of the order of 80% (see Hickox and Markevitch [2] for a recent estimate). At energies greater than 10 keV, where the bulk of the background energy density is produced, the resolved fraction is negligible, being strongly limited by the lack of imaging X-ray observations. The energy dependence of the resolved fraction goes almost hand in hand with the selfconsistency of AGN synthesis models. While at relatively low energy (say below 8–10 keV) a robust model, build over the AGN unified scheme, precisely account for a large body of observational data (XRB spectral intensity, X-ray source counts, redshift distribution, etc.) at higher energies the predictive power is strongly limited by the lack of observational constraints. At present the best estimates of the key parameters, responsible of the XRB spectral intensity around and above the 30 keV peak, mainly rely on the observations obtained with the PDS A. Comastri () · R. Gilli INAF-Osservatorio Astronomico di Bologna, Italy e-mail: [email protected] G. Hasinger Max Planck für Extraterrestrische Physik, Garching, Germany Springer

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instrument onboard BeppoSAX [3, 4] and are thus limited to nearby bright (S10−100keV > 10−11 erg cm−2 s−1 ) objects. As a consequence a relatively wide portion of the model parameter space remains so far unexplored [5].

2. XRB modelling Within the framework of AGN synthesis models the key parameters responsible for the shape and intensity of the >10 keV XRB spectrum are: – the covering fraction and geometrical distribution of the cold dense gas responsible of the reflection “hump” peaking at 20–30 keV and observed in both type 1 and type 2 AGN. – the relative fraction of heavily obscured sources with column densities of the order of a few 1024 cm−2 (the so called “mildly” Compton thick AGN; see Comastri [6] for a review). – the high energy cut-off of the primary emission which is usually parameterized as an exponential roll-over with an e-folding energy of a few hundreds of keV. The reflection of hard X-rays by cold dense circumnuclear gas is a well established property of nearby Seyfert galaxies (see Pounds et al. [7] for the discovery Ginga observations and Perola et al. [8] for a spectral survey of bright AGN with BeppoSAX). For unobscured or relatively unobscured AGN the reflecting material is covering about 2π sr. Several independent observational evidences suggest that a fraction as large as 50% (or even higher) of the Seyfert 2 galaxies in the local Universe are obscured by Compton-thick material [3, 6, 9]. A population of Compton thick (hereinafter CT) sources has to be included in AGN synthesis models for the XRB in order to match the 30 keV intensity peak and at the same time to avoid an excessive number of Compton thin AGN which are not detected in Chandra and XMM-Newton deep surveys (see the discussion in Comastri [6]). Their relative fraction and cosmological evolution are free parameters which are tuned until a good fit to the XRB spectrum is obtained. Assuming the same cosmological evolution of soft X-ray selected type 1 AGN of Hasinger et al. [10], the best fit model shown in Figure 1 is obtained with a relative fraction of CT AGN which is the same of Compton thin (N H in the range 1022 –1024 cm−2 ) and twice than unobscured (N H < 1022 cm−2 ) AGN (see Gilli et al. [11] for further details). The peaked shape of the CT spectrum in a ν Fν − ν plot is due to heavy absorption at low energies and the high energy cut-off (E cut ). The latter, fixed at 320 keV in Figure 1, has to be present in the high energy spectrum of all the sources (regardless of the absorption column density) otherwise the observed XRB flux above about 100 keV would be exceeded. The high energy cut-off e-folding energy has been unambiguosly measured only for a bunch of nearby Seyfert galaxies. The best fit values are loosely constrained in the 150–350 keV range [4, 12]. Both BeppoSAX [13] and more recent INTEGRAL observations [14] suggest a large scatter in the E cut values which span from about 50 keV up to lower limits of the order of 500 keV. While a clear bias against large values of the high energy cut-off is present, the available observations seem to indicate that such a parameter might not be the same in all the sources at variance with the assumptions of most of the synthesis models. The properties of the sources of the “unresolved” background may be inferred by subtracting from the observed broad band spectrum the energy dependent fraction of the “resolved” XRB. Such an approach has been pursued both making use of present observations [1] and exploiting the XRB synthesis models [5, 6]. In the former case the spectral shape of the ”unresolved” background is consistent with that expected from a population of obscured (N H 1023−24 cm−2 ) AGN at redshifts ∼ 0.5 − 1.5. In the latter, following a model Springer

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Fig. 1 The cosmic XRB spectrum and predicted AGN contribution (magenta solide line which includes also galaxy clusters) splitted between unobscured (red dashed line), Compton thin (blue thin line) and Compton thick (black line). For unobscured and Compton thin AGN the effect of including iron line emission is also reported and corresponds to the upper red and blue dashed curve [23]. The different XRB measurements are explained on the top left. Also shown are the resolved XRB fractions in different surveys by Worsley et al. [1]: Lockman Hole = red diamonds; CDFS = cyan crosses; CDFN = black crosses.

dependent approach, the shape of the unresolved fraction can be predicted over a much wider energy range. More specifically assuming a set of model parameters tuned to match the 2–10 keV resolved fraction and to reproduce the observed absorption distribution in deep fields the predicted XRB flux and spectral shape above 10 keV are strongly dependent from the adopted of E cut value (see Figure 2 in Comastri [5]). 3. Exploring the parameter space An additional source of uncertainties comes from the possible contribution to the hard XRB / soft γ -ray backgrounds (above about 100 keV) of the population of radio-loud sources which includes, for the purposes of the present exercise, both flat spectrum radio quasars (e.g. 3C 273) and BL Lac objects. We refer to Giommi et al. ([15] and these proceedings) for a detailed discussion of their contribution to the extragalactic X-ray and γ -ray bands. In the very first approximation radio-loud sources are expected to provide the bulk of the γ -ray background above a few tens of MeV, while radio-quiet AGN dominate below 100 keV. In between their relative contribution is expected to be comparable. An attempt to estimate the contribution of radio-loud quasars to the X-ray/soft γ -ray background (from 1 keV to a few MeV) is presented here. The assumed template spectrum and cosmological evolution are as follows: – the average X-ray/γ -ray spectrum is parameterized with a single power law plus a high energy cut-off. – the input spectrum is then folded with the same luminosity function of radio-quiet AGN assuming a pure luminosity evolution of the form L(z) L(0) × (1 + z)3 normalized to account for 10% of the XRB flux at 1 keV in agreement with Giommi et al. [15] and Galbiati et al. [16]. Springer

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Fig. 2 An estimate of the radio loud AGN contribution to the XRB computed for a range of slopes and high energy cut-offs (red long-dashed lines; see details in the text). The blue short dashed line represents the so far resolved fraction modeled following the prescriptions of Gilli et al. [11]. The solid black lines are the sum of the above mentioned components.

The power law slope energy index α is varied in the range 0.5–0.7 consistent with the averaged value observed in the X-ray band over a large range of redshifts [17–19] while the choiche of the E cut value is driven by the requirement of not exceeding the background flux. The results for three representative pairs of α and E cut : (0.5, 800 keV); (0.6, 1 MeV) and (0.7, 2 MeV) are shown in Figure 2 (long dashed lines from top to bottom respectively). In our approach, almost by definition, the two parameters are not completely independent, the flatter the power law slope, the lower the cut-off energy is. The contribution of radio loud AGN is then summed to the observationally resolved fraction in the 2–10 keV range, extrapolated to high energies following the prescriptions of the Gilli et al. [11] model (short dashed line in Figure 2). Finally the total contribution for the three α, E cut pairs is computed (solid lines). The residual unresolved background obtained by subtracting the models previously described from the total XRB flux, modeled using the [20] analytical approximation, is shown in Figure 3. A comparison with the contribution of a population of CT AGN, assumed to evolve as unobscured sources [10], for two different values (100 and 320 keV) of the high energy cutoff is shown in Figure 4. The model spectra agree extremely well below the peak energy while at higher energies, depending from the E cut and α values adopted to model the contribution of radio-loud AGN, the predicted residual spectrum falls more rapidly with an over-exponential shape which is more pronounced for α = 0.5, E cut = 800 keV. At the face value these results suggest that the sources of the unresolved background are characterized by either a very peaked spectrum or are clustered over a smaller redshift range or a combination of the two. 4. Conclusions The above described exercise confirm and somewhat extend the findings of Worsley et al. [1] and Comastri [5]. Even though the model dependent approach does not allow to break the Springer

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Fig. 3 The unresolved background as obtained by subtracting the contribution of both radio-quiet and radioloud AGN (long-dashed black lines) along with that predicted by the CT AGN in the Gilli et al., 2006 model for two different E cut values (magenta solid lines). The XRB spectral data in the 0.3–3 MeV range are from SMM [24], while in the 2–30 MeV from COMPTEL [25].

degeneracy between the spectral parameters and in particular among the cut-off energy and the source red-shift some preliminary conclusions may be already drawn. A population of CT AGN with a space density and cosmological evolution comparable to that of less obscured, Compton thin sources provide an excellent description of the residual XRB spectrum up to about 10–20 keV. At higher energies the residual spectrum is no longer well approximated by an exponentially cut-offed power law model folded with the redshift distribution observed in deep Chandra, and XMM-Newton fields. It can be argued that a suitable fine tuning of cut-off energy and redshift distributions along with a more extended treatement of the contribution of radio-loud AGN may provide a much better fit to the unresolved XRB above 30 keV. However it should be also stressed that the observational constraints used to compute the residual XRB are still subject to significant uncertainties. Recent measurements of the XRB spectral intensity below 10 keV obtained with imaging instrument are systematically higher than the intensity originally measured by HEAO1-A2 (see Figure 1 and [21] for a recent reanalysis of the HEAO1 data), Given that the the only available observation of the intensity and location of the XRB peak is from the same A2 experiment, some doubts have been raised on the absolute flux and intensity of the XRB above 10 keV. In the hard X-rays/ soft γ -rays the statistical errors as well as the relative calibration between different experiments are even larger. Before attempting a more sophisticated modelling of the broad band background spectrum from its peak down to MeV and GeV region a more robust determination of the observational framework is needed. Sensitive imaging observations down to about 10−14 erg cm−2 s−1 in the approximately 10–50 keV energy range would resolve about half of the background in that band to be compared with the present less than a few percent. A major breakthrough in the census and the study of obscured accreting black holes is expected by future hard X-ray missions and especially by Simbol-X [22]. A mission capable to explore the 100–1000 keV decade with comparably good sensitivity (i.e.the Gamma Ray Imager mission concept see Von Ballmoos and Knödlseder these proceedings) would open the possibility to Springer

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investigate the origin of the primary emission mechanism in AGN, presumably responsible of the high energy cut-off, with important consequences for the scientific objectives discussed in this paper. Acknowledgements This work was partially funded by a MIUR grant (Cofin 03-02-23) and by ASI. AC thanks Gabriele Ghisellini for useful discussions, Filippo Frontera for the kind invitation and Peter Von Ballmoos for organizing an interesting and stimulating workshop.

References 1. Worsley, M.A., Fabian, A.C., Bauer, F.E., Alexander, D.M., Hasinger, G., Mateos, S., Brunner, H., Brandt, W.N., Schneider, D.P.: The unresolved hard X-ray background: the missing source population implied by the Chandra and XMM-Newton deep fields. MNRAS 357, 1281 (2005) 2. Hickox, R.C., Markevitch, M.: Absolute measurement of the unresolved X-ray background in the 0.5–8 keV band with Chandra ApJ in press (astro-ph/0512542) (2006) 3. Risaliti, G., Maiolino, R., Salvati, M.: The distribution of absorbing column densities among Seyfert 2 galaxies. ApJ 522, 157 (1999) 4. Matt, G.: Broad band spectral properties of AGNs and quasars, observations and theory Nuclear Physics B – Proceedings Supplements 132, 97 (2004) 5. Comastri, A.: In multiwavelength AGN surveys; proceedings of the Guillermo Haro conference held December 8–12, 2003. In: Cozumel, Mexico. Mujica, R., Maiolino, R. (eds.), World Scientific Publishing Company, Singapore, p. 323 (2004a) 6. Comastri, A.: Compton-thick AGN: The dark side of the X-Ray background in supermassive black holes in the distant universe. Barger, A.J. (eds.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 2004, p. 245 (2004b) 7. Pounds, K.A., Nandra, K., Stewart, G.C., George, I.M., Fabian, A.C.: X-ray reflection from cold matter in the nuclei of active galaxies. Nature 344, 132 (1990) 8. Perola, G.C., Matt, G., Cappi, M., Fiore, F., Guainazzi, M., Maraschi, L., Petrucci, P.O., Piro, L.: Compton reflection and iron fluorescence in BeppoSAX observations of Seyfert type 1 galaxies. A&A 389, 802 (2002) 9. Guainazzi, M., Matt, G., Perola, G.C.: X-ray, obscuration and obscured AGN in the local universe. A&A 444, 119 (2005) 10. Hasinger, G., Miyaji, T, Schmidt, M.: Luminosity-dependent evolution of soft X-ray selected AGN: New Chandra and XMM-Newton surveys. A&A 441, 417 (2005) 11. Gilli, R., Comastri, A., Hasinger, G. in preparation (2006) 12. Malizia, A., Bassani, L., Stephen, J.B., Di Cocco, G., Fiore, F., Dean, A.J. BeppoSAX Average Spectra of Seyfert Galaxies. ApJ 589, L17 (2003) 13. Matt, G. et al.: One more surprise from the circinus galaxy: BeppoSAX discovery of a transmission component in hard X-rays. A&A 341, L39 (1999) 14. Soldi, S., Beckmann, V., Bassani, L., Courvoisier, T.J.L., Landi, R., Malizia, A., Dean, A.J., de Rosa, A., Fabian, A.C., Walter R.: INTEGRAL observations of six AGN in the Galactic Plane. A&A 444, 431 (2005) 15. Giommi, P., Colafrancesco, S., Cavazzuti, E., Perri, M., Pittori, C.: Non-thermal backgrounds. A&A 455, 843 (2006) 16. Galbiati, E., Caccianiga, A., Maccacaro, T., Braito, V., Della Ceca, R., Severgnini, P., Brunner, H., Lehmann, I., Page, M.J.: XMM-Newton spectroscopy of an X-ray selected sample of RL AGNs. A&A 430, 927 (2005) 17. Reeves, J.N., Turner, M.J.L.: X-ray spectra of a large sample of quasars with ASCA MNRAS 316, 234 (2000) 18. Page, K.L., Reeves, J.N., O’Brien, P.T., Turner, M.J.L.: XMM-Newton spectroscopy of high-redshift quasars. MNRAS 364, 195 (2005) 19. Lopez, L.A., Brandt, W.N., Vignali, C., Schneider, D.P., Chartas, G., Garmire, G.P.: A Chandra snapshot survey of representative high redshift radio-loud quasars from the Parkes-MIT-NRAO sample, AJ in press astro-ph/0601037 (2006) 20. Gruber, D.E.: The hard x-ray background in: The X-ray background. Collected papers and reviews from a workshop held in Laredo, Spain, September, 1990. Barcons, X., Fabian, A.C. (eds.), Cambridge University Press, Cambridge; New York, NY. p. 44 (1992) Springer

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21. Revnivtsev, M., Gilfanov, M., Jahoda, K., Sunyaev, R.: Intensity of the cosmic X-ray background from HEAO1/A2 experiment. A&A 444, 381 (2005) 22. Ferrando, P. et al.: SIMBOL-X: a formation flying mission for hard X-ray astrophysics Optics for EUV, X-Ray, and Gamma-Ray Astronomy II. Citterio, O., O’Dell, S.L.(eds.), Proc. SPIE, 5900, 195 (2005) 23. Gilli, R., Comastri, A., Brunetti, G., Setti, G.: The contribution of AGN to the X-ray background: the effect of iron features New Astronomy 4, 45 (1999) 24. Watanabe, K., Hartmann, D.H., Leising, M.D., The, L.-S., Share, G.H., Kinzer, R.L.: The cosmic gamma ray background from supernovae in proceedings of the fourth compton symposium (eds.), Dermer, C. D., Strickman, M. S., Kurfess, J. D. Williamsburg, VA April 1997: AIP Conference Proceedings 410, 1223. (1997) 25. Kappadath, S.C. et al.: The preliminary cosmic diffuse γ -ray spectrum from 800 keV to 30 MeV measured with COMPTEL. A&AS 120, 619 (1996)

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Focusing supernova gamma rays Questions for a high sensitivity gamma-ray telescope M. D. Leising

Received: 16 January 2006 / Accepted: 26 May 2006 C Springer Science + Business Media B.V. 2006

Abstract Despite their great intrinsic interest and extensive use as tools in other areas of astronomy, fundamental questions remain as to the nature of supernovae of all types. The radioactivity produced by nuclear fusion reactions in the explosions provides several excellent diagnostics, observable through gamma-ray emission. This great potential is largely unrealized because the fluxes from events at common distances are very small. Instrument sensitivity is paramount, and gamma-ray optics offer an excellent possibility for greatly increasing collecting area, without a large increase in background rates, and reaching the required sensitivities. Here we outline some of the major open questions about supernovae and discuss how gamma-ray spectroscopy can address them, including instrument requirements for a future focusing gamma-ray telescope. Keywords Supernovae . Gamma-rays . Radioactivity

1. Introduction Supernovae have been known for thousands of years as bright new stars that appeared where none was visible before. In visible light they are intrinsically as bright as a small galaxy. Fairly homogeneous in their peak brightnesses and light curves, it has been known for a century that spectral properties of supernovae are quite inhomogenous. Over the past twenty-five years, it has become clear that two distinct and very different underlying mechanisms cause supernovae: the collapse and rebound of the cores of massive stars, and the thermonuclear runaway of electron degenerate, low mass, white dwarf stars. Most of our understanding of supernovae has come from visible light observations. This emission originates from the photospheric surface (early in the evolution) so information about the initial conditions and primary energy

Supported by NASA and CESR. M. D. Leising Department of Physics & Astronomy, Clemson University e-mail: [email protected] Springer

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input is often hidden. Later, emission is from a dilute nebula, which is often far from local thermodynamic equilibrium, so detailed quantitative information is often difficult to derive. The nuclear fusion reactions that are fundamental to both types of supernovae result in, besides important energy input and new stable nuclei, radioactive nuclei that serve as clear tracers of the nuclear processing that occurs. In fact, radioactivity dominates the luminous display of the ejected material after the first few weeks. Some of the radioactive decays result in gamma-rays from the de-excitation of the daughter nuclei. These penetrating photons can be used to count the radioactive nuclei produced, measure the ejecta kinematics, and locate the radioactive nuclei within the ejecta [3]. The observational situation depends on the radioactive lifetimes: short-lived isotopes can be observed in new supernovae, intermediate lifetimes in nearby (i.e., galactic and in the local group of galaxies) supernova remnants, and long-lived nuclei in the collective, unresolved emission of the Milky Way. Our emphasis here is mostly on thermonuclear supernovae, because that is where the impact of a gamma-ray lens on our understanding of supernovae is likely to be greatest.

2. Thermonuclear supernovae Spectroscopically classified as supernovae of Type Ia (i.e., lacking hydrogen lines but with a characteristic prominent silicon line) these are the classical thermonuclear runaway and complete disruption of a white dwarf star. When the nuclear burning becomes exothermic the temperature increases, but because the star is supported by degeneracy pressure, no structural adjustment ensues, and the burning accelerates. The nuclear flame propagates in an unknown manner through the star, burns much of it to iron-peak nuclei, and destroys the white dwarf. How this compact star comes to this situation is unclear. It is presumably bound in a binary system, with a donor star that is either another white dwarf or a normal star. Favored models include a carbon-oxygen white dwarf that accretes matter until it reaches about 1.4 M , when the nuclear instability occurs near its center. More than 1 M of the star is burned, with about 0.6 M of radioactive 56 Ni produced. Just how much and where depends on how the nuclear flame propagates. Complete detonations (supersonic burning fronts) are ruled out by observations but whether and how a subsonic flame transitions to a detonation (known as “delayed detonation”) is unknown. Double white dwarf merger models, and lower mass white dwarfs whose explosion is triggered by a helium burning detonation in accreted surface layers, are also possible models, at least for some of the observed Type Ia supernovae. Thermonuclear supernovae are the sources of most of the iron peak elements in nature. They occur in the Milky Way galaxy at the rate of one every few centuries. They are used extensively to measure vast distances with dramatic implications for the apparent acceleration of the expansion of the universe, caused by some otherwise undetected “dark energy” [9]. Almost standard candles, their absolute magnitudes are deduced from the width in time of their visible light curves, assuming there is a one to one mapping of these properties [15]. Whether there is truly one physical parameter of the explosion that determines both is not known. Even if there is, whether the same relationship should hold exactly to redshifts approaching unity, when, for example, the metallicity of the systems was much lower than in the nearby events for which this relationship is calibrated, is also not clear [5]. Complete confidence in the accuracy of using supernovae of Type Ia to measure such distances awaits better understanding of the explosions themselves, which is where gamma-ray line studies of nearby SNe Ia will prove to be so useful. Springer

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Fig. 1 The escaping gamma-ray spectrum of delayed detonation model DD202c [6] at 25 days post-explosion, as calculated by [13] At this time lines of both 56 Ni (158, 749, 812 keV) and 56 Co (847, 1238, 2599, 511 . . . keV) are prominent, as is the compton scattered continuum

The prodigious production of radioactivity is what makes these objects excellent gammaray astronomy targets. The decay chain 56

Ni (6d) −→

56

Co (77d) −→

56

Fe

produces most of the power for the optical display through the deposition (scattering and absorption) of the gamma-ray photons. The 56 Ni decays while the ejecta are still mostly thick to gamma-rays, so the escaping luminosity of its 158 and 812 keV lines (among others) is very sensitive to where within the ejected material the 56 Ni is produced. Later, after the 56 Ni has decayed away, the 56 Co lines are prominent, and eventually nearly all escape. With gamma-ray measurements we can in principle unfold the distribution of radioactive 56 Ni in mass and in velocity space. In most models some 56 Ni is ejected at speeds up to 10,000 km s−1 ; it extends up to 15,000 km s−1 in some, so energy resolution better than 1% is essential. Where the radioactivity is produced is a direct diagnostic of the burning conditions and flame propagation. Deriving this requires of order 1000 photons detected in a few lines (see, e.g., Figure 1 for the prominent ones) at a few times. With peak line fluxes of ∼10−5 cm−2 s−1 for even near SNe Ia, it is clear that the effective area of the telescope will have to be at least hundreds of cm2 even for zero background (which is unrealistic in this energy range.) A huge improvement in sensitivity over previous and current missions is clearly required. To illustrate the requirements for real progress with a gamma-ray spectrometer, we consider current models. Different models can be distinguished by their differing 56 Ni distributions in mass, which can be measured in the gamma-ray light curves (flux vs. time), or by their 56 Ni distribution in velocity, measured by the Doppler profiles of the lines. A narrowfield gamma-ray focuser, unless it was completely dedicated to these particular observations, will not revisit enough supernovae enough times for the former objective, so it will have to excel at the latter, and do high-precision, moderate resolution spectroscopy. For example, two mildly different models, a standard deflagration (model W7 of [14]) and a delayed detonation (see Figure 1) are shown at 25 days in Figure 2. A line flux sensitivity of roughly 3 × 10−6 cm−2 s−1 (3σ for lines of width 25 keV) is required to clearly distinguish these two, admittedly similar, models. At this time, each of these lines would be measured at ∼ 10σ significance. The discrimination is actually better achieved near 80 days, when the 847 keV line flux is four times higher. Such sensitivities are frequently discussed for near-future instruments (e.g., for MAX; see Barriere et al. this volume) but for integration times of 106 seconds, and this is a very nearby event. Of interest for lenses is the energy bandpass required. Early on, line centroids can be shifted by 4–5% of their energies to the blue. They move back Springer

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Fig. 2 The gamma-ray spectrum near 800 keV for a delayed detonation model (solid line) and a deflagration model (dashed line) at 25 days at distance 10 Mpc, in units of photons cm−2 s−1 MeV−1 . The two lower energy lines are from 56 Ni, the higher one from 56 Co. The spectrum will have to be measured with high precision to distinguish these two models, especially if the distance is not well known

Fig. 3 The cumulative distribution of nearby SNe of Type Ia discovered in the past 10 years versus distance. The smooth line shows the number expected if 150 per year are homogeneously distributed within 100 Mpc. The sample is by no means complete, but suggests that one per year closer than 20 Mpc is very likely, even if only considering those discovered optically

to the rest energies at roughly 1% every 10–12 days. The expected line widths are typically 3–5% FWHM. Million second integrations present two problems: the spectra can change significantly over such times, and the long observations severely limit the number of objects a telescope can observe. In any case, one will want to observed each supernova at least a few times in its evolution. The most information will be obtained from the nearest, most precisely measured objects, but as SNe Ia do show variety, it will be necessary to observe at least several. Therefore, the required sensitivity is that needed to make very significant detections of supernovae that are likely to occur at the rate of a few per year. To see what fluxes are to be expected at this rate, we consider the recent supernova record. Simply taking confirmed SNe Ia in the ten years ending 1 July 2005, and taking distances of their host galaxies from Tully’s (1988) Nearby Galaxies Catalog, gives the cumulative distribution of SNe Ia vs distance shown in Figure 3. Clearly this sample still suffers from incompleteness (even the brightest SN display a zone of avoidance along the galactic plane, see Figure 4) but at least one SN Ia per year closer than 20 Mpc seems assured. At distance of 20 Mpc, most SN Ia models reach line fluxes of at least 7 × 10−6 cm−2 s−1 . In order to discriminate among them, or to constrain the distribution of 56 Ni within the ejecta in a single observation, the lines must be measured with significance near 25σ . Thus the instrument must have a 3σ sensitivity to broad lines near 1 × 10−6 cm−2 s−1 , to insure real Springer

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Fig. 4 The distribution on the sky, in galactic coordinates, of recent supernovae. Most searches focus on individual galaxies, and avoid the galactic plane

progress. Ideally, this would be for integration times of a few days or less. An instrument such as this would make very detailed measurements of several thermonuclear supernovae in a few year mission, clarifying the nature of the progenitor systems and the nuclear flame propagation.

3. Core collapse supernovae After massive stars have exhausted all central exothermic nuclear fuels, their cores exceed the mass that can be supported by electron degeneracy pressure and collapse. After reaching nearly nuclear density, the huge gravitational binding energy (a few 1053 ergs) is released and mostly radiated as neutrinos. A fraction of this energy is coupled to the more slowly infalling mantle of the star, which is shocked, heated, and ejected. How this coupling occurs, or the explosion mechanism, is uncertain at present. Peak temperatures reach that of nuclear statistical equilibrium in the innermost ejecta, and decrease moving outward. The radioactive 56 Ni is produced in the inner few tenths of a M ejected, and more falls back into the compact remnant object. This decay chain again powers the later optical display. The ejecta kinetic energy is typically 1–2 × 1051 ergs. These events produce most of the natural abundances of the elements oxygen through calcium, and probably many heavy elements as well. Their optical spectra include absorption lines of the stellar envelope material – whatever has not been lost in stellar winds – including, sometimes, hydrogen (known as Type II supernovae), helium (Type Ib), or neither (Type Ic.) These events occur at the rate of a few per century in the Milky Way. The major questions that remain about core collapse supernovae are how the large binding energy is transferred to the star, and how important are dynamical complications, such as mixing and jets. Material near the ejection cutoff radius, and that carried outward by instabilities and jets, are highly radioactive. Thus gamma-ray lines can help clarify these questions. In general, the large ejecta masses make line fluxes low because of attenuation, so opportunities will be rare. A great deal of what we know about core collapse supernovae derives from Supernova 1987A. It is one of the most remarkable and best observed objects in modern astronomy. Springer

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Table 1 Isotopes possibly detectable in galactic SN and remnants and local group SNe

Isotope

Half-life

line energy (keV)

7 Be

53 d 2.6 y 0.7 My 44 d 1.5 My 5.3 y 0.1 My

478 1275 1809 1099, 1292 59 1173, 1332 87

22 Na 26 Al 59 Fe 60 Fe 60 Co 126 Sn

Among many firsts were observations of live radioactive isotopes freshly synthesized in the explosion, which provide detailed diagnostics of the nuclear burning conditions and explosion dynamics. These included 56 Co (synthesized as 56 Ni) detected directly in γ -ray lines [12] and indirectly as the power source for the intermediate time optical light curve e.g. Bouchet et al. [1]; 57 Co (made as 57 Ni) detected directly in γ -ray lines [10], inferred from infrared spectra [16] and from the visible light curve see however Clayton et al. [4]; and 44 Ti, which possibly powers the nebula at late times [2, 11]. This was a very rare event, which we can not expect to repeat any time soon, but some of the same studies can be done on other core collapse supernovae. The 56 Ni chain will be difficult to observe. Scaling from SN 1987A, even allowing that some supernovae will have lower mass envelopes at explosion, we can hope to detect the 56 Co gamma-ray lines to only 2–3 Mpc distance for line sensitivities near 10−6 cm−2 s−1 . The 57 Co line fluxes are much lower still, so we must wait for a local group supernova. Some supernovae might exceed these estimates. Strong jets might carry core 56 Ni to outer region, perhaps enhancing 56 Co line fluxes by up to a factor of five [7]. The longer-lived isotope 44 Ti (63 y) is produced in the innermost ejected material, even interior on average to the ejected 56 Ni. It is the source of 44 Ca in nature, after the intermediate 44 Sc decay, and is produced in the alpha-rich freezeout of nuclear statistical equilibrium. Because the initial temperature is so high, of order 1010 K, the temperature of freezeout (∼3 × 109 K) is reached at lower density than for slightly exterior regions, when a large number of free alpha particles are present to alter the equilibrium abundances. It has been detected in the supernova remnant Cas A in our galaxy [8], in an unexpectedly large quantity. A gamma-ray lens, if it includes a band at 68, 78, or 1157 keV, could determine the mass of this isotope there to 1–2%. SN 1987A again offers an interesting prospect; the fluxes in these lines could be 3 × 10−6 cm−2 s−1 or more. So this isotope’s abundance could be determined to 10% or better. The Doppler line profiles in both of these, and possibly other supernova remnants, might show the presence of jets as higher than average speed 44 Ti. In nearby core-collapse supernovae and remnants, a number of other isotopes are possibly detectable. Some of these are listed in Table 1. The last entry is an example of one of several possible r-process isotopes (made from the rapid addition of neutrons to heavy seed nuclei.) Fluxes from these are likely to be quite low, however, the discovery of a very nearby object, or significant enhancements by jets, could make a detection possible.

4. Summary It is apparent that gamma-ray line observations of supernovae can contribute greatly to answering fundamental questions about their nature. Instrument sensitivity is by far the most Springer

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important attribute for making real progress; a sensitivity to broad lines reaching or exceeding 10−6 cm−2 s−1 is essential. A focusing gamma-ray telescope, even with only a few narrow bands, offers a strong possibility, but if it is to achieve a number of supernova objectives, among many other interesting sources, this sensitivity will probably have to be achieved in integration times of a few 105 seconds or less – a huge challenge at present.

References 1. Bouchet, P., Danziger, I.J., Lucy, L.B.: Bolometric light curve of SN 1987A – Results from day 616 to 1316 after outburst. AJ 102, 1135–1146 (1991) 2. Chugai, N.N., Chevalier, R.A., Kirshner, R.P., Challis, P.M.: Hubble space telescope spectrum of SN 1987A at an age of 8 years: radioactive luminescence of cool gas. ApJ 483, 925 (1997) 3. Clayton, D.D., Colgate, S.A., Fishman, G.J.: Gamma-ray lines from young supernova remnants. ApJ 155, 75 (1969) 4. Clayton, D.D., Leising, M.D., The, L.-S., Johnson, W.N., Kurfess, J.D.: The Co-57 abundance in SN 1987A. ApJ 399, L141–L144 (1992) 5. Dominguez, I., Hoflich, P., Straniero, O., Wheeler, C.: Evolution of type Ia supernovae on cosmological time scales. Memorie della Societa Astronomica Italiana 71, 449–460 (2000) 6. Hoeflich, P., Wheeler, J.C., Khokhlov, A.: Hard X-rays and gamma rays from type IA supernovae. ApJ 492, 228 (1998) 7. Hungerford, A.L., Fryer, C.L., Rockefeller, G.: Gamma rays from single-lobe supernova explosions. ApJ 635, 487–501 (2005) 8. Iyudin, A.F., Diehl, R., Bloemen, H., Hermsen, W., Lichti, G.G., Morris, D., Ryan, J., Schönfelder, V., Steinle, H., Varendorff, M., de Vries, C., Winkler, C.: COMPTEL observations of Ti-44 gamma-ray line emission from CAS A. A&A 284, L1–L4 (1994) 9. Knop, R.A., Aldering, G., Amanullah, R., Astier, P., Blanc, G., Burns, M.S., Conley, A., Deustua, S.E., Doi, M., Ellis, R., Fabbro, S., Folatelli, G., Fruchter, A.S., Garavini, G., Garmond, S., Garton, K., Gibbons, R., Goldhaber, G., Goobar, A., Groom, D.E., Hardin, D. Hook, I., Howell, D.A., Kim, A.G., Lee, B.C. Lidman, C., Mendez, J., Nobili, S., Nugent, P.E., Pain, R., Panagia, N., Pennypacker, C.R., Perlmutter, S., Quimby, R., Raux, J., Regnault, N., Ruiz-Lapuente, P., Sainton, G., Schaefer, B., Schahmaneche, K., Smith, E., Spadafora, A.L., Stanishev, V., Sullivan, M., Walton, N.A., Wang, L., Wood-Vasey, W.M., Yasuda, N.: New Constraints on M , , and w from an independent set of 11 high-redshift supernovae observed with the hubble space telescope. ApJ 598, 102–137 (2003) 10. Kurfess, J.D., Johnson, W.N., Kinzer, R.L., Kroeger, R.A., Strickman, M.S., Grove, J.E., Leising, M.D., Clayton, D.D., Grabelsky, D.A., Purcell, W.R., Ulmer, M.P., Cameron, R.A., Jung, G.V.: Oriented scintillation spectrometer experiment observations of Co-57 in SN 1987A. ApJ 399, L137–L140 (1992) 11. Lundqvist, P., Kozma, C., Sollerman, J., Fransson, C.: ISO/SWS observations of SN 1987A. II. A refined upper limit on the mass of 44Ti in the ejecta of SN 1987A. A&A 374, 629–637 (2001) 12. Matz, S.M., Share, G.H., Leising, M.D., Chupp, E.L., Vestrand, W.T.: Gamma-ray line emission from SN1987A. Nature 331, 416–418 (1988) 13. Milne, P.A., Hungerford, A.L., Fryer, C.L., Evans, T.M., Urbatsch, T.J., Boggs, S.E., Isern, J., Bravo, E., Hirschmann, A., Kumagai, S., Pinto, P.A., The, L.-S.: Unified one-dimensional simulations of gamma-ray line emission from type Ia supernovae. ApJ 613, 1101–1119 (2004) 14. Nomoto, K., Thielemann, F.-K., Yokoi, K.: Accreting white dwarf models of Type I supernovae. III – Carbon deflagration supernovae. ApJ 286, 644–658 (1984) 15. Phillips, M.M.: The absolute magnitudes of Type IA supernovae. ApJ 413, L105–L108 (1993) 16. Varani, G.F., Meikle, W.P.S., Spyromilio, J., Allen, D.A.: Direct observation of radioactive cobalt decay in supernova 1987A. MNRAS 245, 570 (1990)

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Exp Astron (2005) 20:57–64 DOI 10.1007/s10686-006-9036-3

Nucleosynthesis in nova explosions: Prospects for its observation with focusing telescopes M. Hernanz · J. José

Received: 19 December 2005 / Accepted: 3 March 2006 C Springer Science + Business Media B.V. 2006

Abstract Nova explosions are caused by the explosive burning of hydrogen in the envelope of accreting white dwarfs. During the thermonuclear runaway some radioactive isotopes are synthesized, which emit γ -rays when they decay. The γ -ray signatures of a nova explosion still remain undetected, because even the best instruments like SPI onboard INTEGRAL are not sensitive enough for the dim and broad lines emitted by novae at their typical distances. A very different situation is expected with a focusing telescope, like MAX. Prospects for detectability with a future γ -ray lens telescope are presented, with a special emphasis on the important information that γ -rays would provide about the explosion mechanism and the underlying white dwarf star. Keywords Gamma-ray astronomy . Gamma-ray lines . Nucleosynthesis . Novae . Cataclysmic variables

1. Introduction Novae are one example of so-called variable stars that shine in the sky. The name nova comes from nova stella, referring to the sudden appearance of a new star, followed by its fast or relatively fast fading. It was thought during many centuries that it was really a new star, before understanding that in fact it was an already existing star that brightened considerably by some reason. Nowadays we know that a classical nova is an explosion on top of a white dwarf star in a close binary system, which leads to an increase in luminosity by 7 or more orders of magnitude, and to mass ejection to the interstellar medium of about 10−5 − 10−4 Mstar , with M. Hernanz () Institut d’Estudis Espacials de Catalunya (IEEC/ICE-CSIC), Campus UAB, Facultat de Ciències, Torre C5 – parell – 2a planta 08193 Bellaterra (Barcelona), Spain e-mail: [email protected] J. José IEEC and Departament de F´ısica i Enginyeria Nuclear (UPC), Sor Eulalia d’Anzizu s/n, B5 08034 Barcelona, Spain Springer

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Mstar ∼M (M is the mass of the sun, i.e. 2 × 1033 g), at typical velocities of hundreds to thousands of km/s. Novae reach intrinsic luminosities which are ∼104 −105 L . Before understanding what a classical nova really is, it is important to be aware that white dwarfs are stars which have spent all their nuclear fuel and have as only destiny cooling down (when they evolve as isolated stars), at the expenses of their internal thermal energy (associated to the ions), with the electrons forming a degenerate Fermi gas which sustains the star’s gravity, keeping it at extremely large densities with extremely small sizes (typically a solar mass within an Earth-sized sphere, i.e. radius about 1000 km; the correponding surface gravities are very large −108 –109 cm.s−2 – and also the central densities – between 106 and 109 g.cm−3 ). But the final fate of a white dwarf can be quite different when it belongs to a close binary system, where it interacts with its companion star. Then, accretion of matter from its neighbor star can lead to a wealth of spectacular phenomena; in particular, accreting white dwarfs can explode as supernovae (thermonuclear, also called type Ia) or as classical novae. Thermonuclear supernova explosions affect the whole star and are triggered by degenerate carbon burning (see Leising’s contribution in this same volume). Classical novae explosions are powered by degenerate hydrogen burning on top of the white dwarf; since only the white dwarf’s envelope is affected, the star recovers its previous state after the explosion (some months-years later), and the phenomenon is recurrent, with a period of about 104 –105 years. The companion star of the exploding white dwarf is a low-mass main sequence star (i.e. a star like the sun but with lower mass) and the binary system is called a cataclysmic variable. The nova rate in our galaxy, the Milky Way, is hard to determine, since optical observations are hampered by dust extinction. Two approaches have been used to estimate the global galactic nova rate: either the local observed nova rate is extrapolated (see for instance [25], who obtained 35 ± 11 yr−1 ), or a comparison with the nova counts in other nearby galaxies is made (see [26] for a review of both methods). It is worth mentioning that visual extinction reduces the number of discovered galatic novae to about 5, at most, per year.

2. Main observational properties of novae The visual light curves (temporal evolution of optical luminosity) of novae display a steep maximum, followed by a continuous decrease of luminosity. The steepness of the light curve (“speed class” of the nova) determines how fast the nova declines in luminosity after the outburst. The fastest novae decrease in 2 magnitudes in less than 10 days (the magnitude is a logarithmic measure of the luminosity, such that an increase in 5 magnitudes means a decrease by a factor of 100 in luminosity); slower novae can need more than 100 days for a similar luminosity variation. An important step forward in the comprehension of the nova phenomenon was made thanks to the advent of space observatories in the ultraviolet (UV). It was discovered that simultaneous to the decrease in visual luminosity there was an increase in the ultraviolet emission, so that the global “bolometric” luminosity was constant during some weeks-months after the outburst. (e.g. Nova Ser 1970 [7], Nova Cyg 1978 [30] or Nova Aql 1982 [28]). The interpretation of such an increase, observed in many novae thanks mainly to the International Ultraviolet Explorer (IUE) satellite, is that the energy distribution shifts towards higher frequencies (energies), since deeper and thus hotter regions of the expanding envelope are successively seen; that’s because the photosphere (the visible atmosphere, emitting approximately as a blackbody) recedes as expansion proceeds. Another important piece of information comes from infrared observations (when the nova forms dust), which show an Springer

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increase in infrared (IR) luminosity when the UV one diminishes; this is interpreted as the resulting re-radiation by dust grains of the UV energy they have absorbed. In addition to light curves, spectra in different energy bands give information about velocities and chemical composition (atomic) of the ejecta. An important property of many novae is their enhancements in several atoms, mainly C, N and O, but also Ne in several cases. For instance, Nova QU Vul 1984 showed an abundance of neon 100 times solar and a global metallicity 23 times solar. Another spectacular case was Nova V1370 Aql 1982, with metallicity Z = 0.86 = 45Z and Ne mass fraction about 300 times solar (see [9] for a compilation of nova abundances deduced from optical and UV observations). The physical interpretation of these enhancements relies on some process of mixing between the accreted material (assumed to be roughly solar, since it corresponds to the envelope of a “normal” companion star) with the underlying white dwarf core. At this point it is crucial to understand that the chemical composition of the underlying white dwarf, and specially that of its most external layers, is dictated by its previous stellar evolution, which mainly depends on its progenitor’s mass. For masses between ∼9 M to 10 − 12 M , non degenerate carbon burning produces an ONe white dwarf, with mass larger than ∼1.1 M [6, 8, 24]. Lower initial masses lead to CO white dwarfs. So, novae occurring on top of ONe white dwarfs can show some neon in their ejecta, whereas this is not the case for novae on CO white dwarfs. As we will see in Section 3, the chemical composition of the white dwarf is not only important to interpret the observations, but also to understand the explosion mechanism itself.

3. Why a nova explodes: The thermonuclear runaway scenario As mentioned in Section 1, a white dwarf which accretes H-rich matter from a companion star in a binary system can be “rejuvenated” and experience an outburst (instead of cooling down to invisibility as when it is isolated). The reason is the following: when matter is accreted on top of the white dwarf, it is strongly compressed (because the gravity at the surface of white dwarfs is extremely large – see above), until reaching temperatures large enough to enable fusion of hydrogen nuclei, i.e. thermonuclear hydrogen burning. Since large densities are reached, there is electron degeneracy, meaning that matter can not respond as an ideal gas (it can not expand much) to the injection of energy by hydrogen thermonuclear burning. As a consequence of this degenerate nuclear burning, a thermonuclear runaway ensues, with an increase of temperature “without control”. Convection–in addition to usual radiation in star’s envelopes- is needed to transport heat outside the burning shell. Convective transport plays a very important role in the final success of the explosion, since it transports some radioactive nuclei (β + -unstable) produced during hydrogen burning through the CNO cycle (see Figure 1 and [29]) to the outer envelope, where they are prevented from destruction by proton captures, thus being able to decay and release energy. This later injection of energy in the outer less dense zones provoques large envelope expansion–such that there is ejection of mass- and large increase in luminosity, the two basic properties of a nova explosion.

4. Nucleosynthesis of radioactive nuclei Hydrogen thermonuclear burning starts with the proton-proton chains [2], but once temperature is larger than ∼2 × 107 K, burning through the CNO cycle (see Figure 1) is dominant, provided that there is some carbon available. In novae, some initial carbon is in general assumed, since some mixing between solar accreted matter and the underlying core is adopted Springer

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Fig. 1 Scheme of the carbon-nitrogen-oxygen (CNO) cycle of hydrogen burning, which operates out of equilibrium in nova outbursts. The lifetimes of the β + -unstable nuclei, which act as bottlenecks of the cycle, are displayed

(however, the exact mechanism through which this mixing occurs is still not well understood; see a recent multidimensional attempt to model it in [1]). As can be seen in Figure 1, a succession of proton captures (p, γ ) and β + -decays occurs, and the cycle is closed by (p, α) reactions, where a proton is captured and an α particle is released. But in novae the CNO cycle is out of equilibrium (it is “not closed”), because the timescales of some β + -decays are longer than the evolutionary lifetime; then the corresponding nuclei act as a kind of “bottleneck” of the cycle. As mentioned above, the energy release associated to those β + -decays is the final responsible for the atmospheric expansion, luminosity increase and mass ejection, since the nuclei (mainly 14,15 O,17 F, see Figure 1) have been transported to the outer envelope by convection, being thus preserved from destruction in the hotter shells at the envelope’s bottom. The main radioactive nuclei synthesized in novae that are relevant for the γ -ray emission are: 13 N and 18 F (positron emitters), 7 Be, 22 Na and 26 Al (see Table 1). The first two are produced during the CNO cycle; theoretical models indicate that they are both produced in novae on CO and on ONe white dwarfs [15]. On the contrary, 22 Na and 26 Al are only produced in ONe novae; the reason is that there is the need of some seed nuclei for their synthesis through the so-called “Ne-Na” and “Mg-Al” cycles (mainly 20 Ne and 24,25 Mg for 22 Na and 26 Al, respectively; see for instance [17]). Finally, 7 Be synthesis is larger in CO novae, because the presence of a larger fraction of 12 C (as compared with ONe novae) makes the rise to temperatures around 108 K, where photodisintegration of 8 B − 8 B(γ , p)7 Be-prevents 7 Be destruction, faster [12,15]. Table 1 Radioactivities in nova ejecta

Isotope 13 N

Lifetime 862 s

Type of emission

Main disintegration process

Nova type

511 keV line &

β + -decay

CO & ONe

continuum 158 min

511 keV line &

β + -decay

CO & ONe

7 Be

77 days

continuum 478 keV line

e− -capture

CO

22 Na

3.75 years

1275 & 511 keV lines

β + -decay

ONe

26 Al

106 years

1809 & 511 keV lines

β + -decay

ONe

18 F

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It is worth mentioning at this point that the depth of the white dwarf outer core at which mixing with accreted matter occurs is unknown (or alternatively, how much mass of the external layers above the ONe core of the progenitor star is lost during thermal pulses in the prior asymptotic giant branch (AGB) phase). Therefore, since there is an outer zone with some carbon (and oxygen) on top of ONe degenerate cores, it is possible that some novae would erode this “CO buffer” instead of the ONe core itself. Then the properties of the explosion would be a bit different and a nova hosted by an ONe white dwarf could also synthesize some 7 Be [18], and would not display any neon. Since neon is observed in many novae, mixing with the core should occur in some ONe novae, but perhaps in not all of them. Also, since the size in mass of the CO buffer decreases as white dwarf mass increases, mixing with the core is favored in novae on massive white dwarfs.

5. Gamma-rays from novae The role of novae as potential γ -ray emitters was noticed long ago [ 3, 4, 19]. In addition to the very short-lived isotopes responsible of the nova explosion, other longer-lived nuclei are synthesized which are relevant for the γ -ray emission of individual novae, as well as for the radioactivity of the Galaxy (see Table 1). As mentioned in Section 4, the short-lived nuclei 13 N and 18 F are produced in similar quantities in all nova types, whereas 7 Be is mainly produced in CO novae and 22 Na and 26 Al are synthesized only in ONe novae. The role played by the radioactive nuclei ejected by novae depends on their lifetimes. The short-lived nuclei 13 N and 18 F produce an intense burst of γ -ray emission, with duration of some hours, which is emitted at peak temperature epoch, well before the nova visual maximum (see [11,13] for details), i.e. before the nova is discovered optically. This emission is related to positron annihilation, which consists of a line at 511 keV and a continuum at energies between 20 and 511 keV, related to the positronium continuum plus the comptonization of the photons emitted in the line (see Figure 2, where the spectral evolution of a CO and an ONe nova at different epochs after peak temperature is shown). The emission related to medium-lived nuclei, 7 Be and 22 Na, appears later and is different in CO and ONe novae, because of their different nucleosynthesis: CO novae display a line at 478 keV related to 7 Be decay, whereas ONe novae show a line at 1275 keV related to 22 Na decay. The long-lived isotope 26 Al is also produced by novae. The Galactic γ -ray emission observed at 1809 keV ([21] with the HEAO 3 satellite and [5] with the CGRO/COMPTEL) corresponds to the decay of 26 Al. Its distribution seems to trace a young population of massive stars and the contribution of novae is not the dominant one (see [16, 23]). However, the recent detection of 60 Fe (traditionally only attributed to core collapse supernovae) in the galactic center with the RHESSI and INTEGRAL satellites [10, 27] has shown that an extra source of 26 Al is needed to explain the low 60 Fe/26 Al ratio observed (with respect to the ratio expected if only core collapse supernovae contributed to galactic 60 Fe and 26 Al). So, there is room for Wolf-Rayet stars, AGB stars and novae to contribute to the global galactic content of 26 Al [22]. But, the contribution of Wolf-Rayet stars to 60 Fe [20] also has to be taken into account to do proper comparisons between observations and theory.

6. Discussion In summary, classical novae explosions produce γ -rays, being the signature of CO and ONe novae different. The detectability distances for the lines at 478 and 1275 keV with the Springer

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Fig. 2 Early temporal evolution of the gamma-ray spectra of a CO (dotted) and an ONe (solid) nova, at a distance of 1 kpc

INTEGRAL/SPI instrument range between 0.2 and 0.5 kpc [14]; the width of the lines (∼7 keV for the 478 keV line and ∼20 keV for the 1275 keV line), is not negligible and largely degrades the sensitivity of the SPI instrument (because it has germanium detectors, with very good energetic resolution). The continuum and the 511 keV line are the most intense emissions, but their appearence before visual maximum and their very short duration requires “a posteriori” analyses, with large field-of-view instruments monitoring the whole sky at the appropriate energies (some hundred keVs). With future instruments of these characteristics, novae would be detectable more easily in γ -rays than visually, because of the lack of extinction. In order to improve the detectability prospects for classical novae (and the same occurs for supernovae, see Leising’s contribution in this same volume), an important step forward in sensitivity for broad and moderately broad lines (in novae, E/E∼ 1.5%) is required. The best possibility by now is a focusing γ -ray lens, since it allows for a combination of large detection area with a small detector volume, a necessary condition to increase significantly the signal to noise ratio (see various contributions in this volume). With a sensitivity of 5 × 10−7 phot.cm−2 .s−1 for narrow lines, i.e. ∼1.5 × 10−6 phot.cm−2. s−1 for the 20 keV broad 1275 keV 22 Na line, this line could be detected up to 4 kpc, with at least one ONe nova per year. To detect virtually all (ONe) novae, the sensitivity for the 1.5 % broad line at 1275 keV should be around 3 × 10−7 phot.cm−2 .s−1 (i.e. 10−7 phot.cm−2 .s−1 for a narrow line at the same energy). The detection of novae in γ -rays would give crucial insights on the nova theory: amount of 7 Be (and of its daughter nucleus 7 Li, with a still not well known galactic origin) and of 22 Na, classification of novae as CO or ONe (and relationship with white dwarf mass), temperature attained in the burning shells (which strongly affects the nucleosynthetic output of novae), distribution and rate of novae in the Galaxy, dynamics and effectiveness of convection in the envelope (which strongly affects the prompt emission related with electron-positron Springer

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annihilation). Therefore, a push in the technology involved in γ -ray instrumentation is essential for the study of explosive phenomena such as novae and supernovae.

Acknowledgements This work has been supported by the spanish MEC grants AYA2004-06290-C02-01 and -02 and by the catalan DURSI.

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

11. 12. 13.

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

25.

Alexakis, A. et al.: On heavy element enrichment in classical novae. Astrophys. J. 602, 931–937 (2004) Clayton, D.D.: Principles of stellar evolution and nucleosynthesis. Mc.Graw-Hill (1968) Clayton, D.D.: 7 Li gamma-ray lines from novae. Astrophys. J. 244, L97–L98 (1981) Clayton, D.D., Hoyle, F.: Gamma-ray lines from novae. Astrophys. J. 187, L101–L103 (1974) Diehl, R., et al.: COMPTEL observations of Galactic 26 Al emission. Astron. & Astrophys. 298, 445–460 (1995) Dom´ınguez, I., Tornambé, A., Isern, J.: On the formation of O-Ne white dwarfs in metal-rich close binary systems. Astrophys. J. 419, 268–275 (1993) Gallagher, G.S., Code, A.D.: Ultraviolet photometry from the orbiting astronomical observatory. X.Nova FH SER 197. Astrophys. J. 189, 303–314 (1974) Gil-Pons, P., Garc´ıa-Berro, E., José, J., Hernanz, M., Truran, J.W.: The frequency of occurrence of novae hosting an ONe white dwarf. Astron. & Astrophys. 407, 1021–1028 (2003) Gehrz, R., Truran, J.W., Williams, R.E., Starrfield, S.E.: Nucleosynthesis in classical novae and its contribution to the interstellar medium. Pub. Astron. Soc. Pacific 110, 3–26 (1998) Harris, M.J., Knödlseder, J., Jean, P., Cisana, E., Diehl, R., Lichti, G.G., Roques, J.-P., Schanne, S., Weidenspointner, G.: Detection of gamma-ray lines from interstellar 60 Fe by the high resolution spectrometer SPI. Astron. & Astrophys. 433, L49–L52 (2005) Gómez-Gomar, J., Hernanz, M., José, J., Isern, J.: Gamma-ray emission from individual classical novae. Month. Not. R.A.S. 296, 913–920 (1998) Hernanz, M., José, J., Coc, A., Isern, J.: On the synthesis of 7 Li and 7 Be in novae. Astrophys. J. 465, L27–L30 (1996) Hernanz, M., José, J., Coc, A., Gómez-Gomar, J., Isern, J., Gamma-ray emission fom novae related to positron annihilation: constraints on its observability posed by new experimental nuclear data. Astrophys. J. 526, L97–L100 (1999) Hernanz, M., José, J.: γ -rays from classical novae: expectations from present and future missions. New Astron. Rev. 48, 35–39 (2004) José, J., Hernanz, M.: Nucleosynthesis in classical novae: CO versus ONe white dwarfs. Astrophys. J. 494, 680–690 (1998) José, J., Hernanz, M., Coc, A.: New results on 26 Al production in classical novae. Astrophys. J. 479, L55–L58 (1997) José, J., Coc, A., Hernanz, M.: Nuclear uncertainties in the NeNa-MgAl cycles and production of 22 Na and 26 Al during nova outburts. Astrophys. J. 520, 347–360 (1999) José, J., Hernanz, M., Garc´ıa-Berro, E., Gil-Pons, P.: The impact of the chemical stratification of white dwarfs on the classification of classical novae. Astrophys. J. 597, L41–L44 (2003) Leising, M.D., Clayton, D.D.: Positron annihilation gamma-rays from novae. Astrophys. J. 323, 159–169 (1987) Limongi, M., Chieffi, A.: New Astron. Rev. in press (2006) Mahoney, W.A., Ling, J.C., Wheaton, W.A., Jacobson, A.S.: HEAO 3 discovery of 26 Al in the interstellar medium. Astrophys. J. 286, 578–585 (1984) Prantzos, N.: Radioactive 26Al and 60Fe in the Milky Way: Implications of the RHESSI detection of 60Fe. Astron. & Astrophys. 420, 1033–1037 (2004) Prantzos, N., Diehl, R.: Radioactive 26 Al in the galaxy: observations versus theory. Phys. Rep. 267, 1–69 (1996) Ritossa, C., Garc´ıa-Berro, E., Iben, I.: On the evolution of stars that form electron-degenerate cores processed by carbon burning. II. Isotope abundances and thermal pulses in a 10 M model with an ONe core and applications to long-period variables, classical novae, and accretion-induced collapse. Astrophys. J. 460, 489–505 (1996) Shafter, A.W.: On the nova rate in the galaxy. Astrophys. J. 487, 226–236 (1997) Springer

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26. Shafter, A.W. (2002).: The Galactic nova rate, in Classical Nova Explosions, AIP CP 637, New York. p. 462–471 (2002) 27. Smith, D.M.: The Reuven Ramaty High Energy Solar Spectroscopic Imager Observation of the 1809 keV Line from Galactic 26Al. Astrophys. J. 589, L55–L58 (2003) 28. Snijders, M.A.J., Batt, T.J., Roche, P.F., Seaton, M.J., Morton, D.C., Spoelstra, T.A.T., Blades, J.C.: Nova Aquilae 1982. Month. Not. R.A.S. 228, 329–376 (1987) 29. Starrfield, S.: in Classical novae, eds. M.F. Bode & A.M Evans, Wiley. Chichester p. 39–60 (1989) 30. Stickland, D.J., Penn, C.J., Seaton, M.J., Snijders, M.A.J., Storey, P.J.: Nova Cygni 1978. I – The nebular phase. Month. Not. R.A.S. 197, 107–138 (1981)

Springer


Puzzles and potential for gamma-ray line observations of solar flare ion acceleration David M. Smith

Received: 14 November 2005 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract The best tool for understanding ion acceleration in solar flares is gamma-ray line emission from nuclear de-excitation, positron annihilation, and neutron capture. These techniques have not yet come close to reaching their potential due to limited counting statistics in the lines. Instruments with focusing optics and large effective areas promise real breakthroughs in understanding high-energy solar processes. I discuss what can be learned from the various lines and the instrumental requirements for future focusing observations. Keywords Solar flares . Gamma-rays . Particle acceleration . Nuclear astrophysics

1. Introduction The Sun is our nearest astrophysical laboratory. Its photosphere and interior give us our clearest picture of “ordinary” stellar processes, but, in addition, the remarkable particle acceleration in its corona gives us a close-up look at processes that may occur not only in other active stars (some of them stunningly more violent than our own) but also in exotic environments like the magnetospheres of pulsars and the accretion disks around black holes. Solar flares outshine the rest of the Sun at many wavelengths outside the visible: radio, x-ray, and the extreme ultraviolet. We are fairly certain that they take place due to a violent reconfiguration of the coronal magnetic fields, but the details of the process are not understood. Many models exist, and many of them may correctly explain some of the variety of flares observed. An astonishing fraction of the magnetic energy released – on the order of half [2,3] – goes directly into the acceleration of electrons and ions to high energies. These nonthermal distributions of particles can reach energies of hundreds of MeV for the electrons and several GeV for the ions, energies normally associated with cosmic rays. The acceleration processes “Mama always told me not to look into the sights of the Sun; oh, but mama, that’s where the fun is. . .” [1] D. M. Smith Physics Department and Santa Cruz Institute for Particle Physics, University of California, Santa Cruz Santa Cruz, CA 95064, USA e-mail: [email protected] Springer

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are both rapidly acting and sustained: ions are accelerated to tens of MeV in seconds and to GeV energies in a time on the order of a minute, yet the latter process (which may occur much further from the surface than the flare loops) can persist for hours. Flare electrons can be studied by the bremsstrahlung x-rays they emit when interacting either with chromospheric plasma (in flare footpoints) or in coronal loops that have filled with hot, dense plasma in the middle and later stages of a flare. The electrons and x-rays are copious, so instruments of modest size can produce excellent spectra and images of the thermal bremsstrahlung (< ∼10 keV), nonthermal bremsstrahlung (> ∼25 keV), and the transition energies where they overlap. Satellites such as the Solar Maximum Mission (SMM), Yohkoh, and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) have made major advances with this technique; Sui, Holman and Dennis [4] provide an excellent example of the state of this art. Accelerated ions, however, tend to produce fewer photons. Those at low energies (< ∼1 MeV per ion) produce little emission at all. Protons and alpha particles of several MeV can excite nuclei in the solar atmosphere to produce characteristic de-excitation lines (Figure 1), and heavier accelerated ions of comparable energy can themselves be excited into these states. At even higher energies (tens of MeV), spallation reactions occur that produce free neutrons, positrons from radioactive decay of the products, and further characteristic nuclear decay lines. The neutrons produce the narrow line at 2.223 MeV when captured by protons after thermalization, and the positrons produce annihilation photons at 511 keV or below when they annihilate with an electron after slowing down. Understanding the composition and energy spectrum of the accelerated ions at the solar surface not only constrains the acceleration process, but makes for interesting comparisons with the compositions of solar energetic particles (SEPs) in interplanetary space [6] and of cosmic rays. The many gamma-ray lines from many species should carry more information than the smooth continuum of the electron bremsstrahlung. In practice, however, we know less about ion acceleration than about the electrons due to the small number of flares that have shown gamma-ray lines and the small flux of line photons emitted in each case. Furthermore, the

Fig. 1 De-excitation lines observed with RHESSI from the X4.8 flare of 23 July, 2002. Redshifts are required by the Gaussian fits (heavy curves versus unshifted thin curves), but the statistics are insufficient to make out the details of the shapes. From Smith et al. [5] Springer

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lines are more difficult to detect than bremsstrahlung at keV energies due to the instrumental challenges in stopping such high energy radiation and reading out the energy to sufficient precision. Theoretical modeling and sophisticated analyses of gamma-ray data from SMM and other missions have run ahead of the quality of the available data in many cases. As this paper is intended to look forward rather than review the literature, only a few citations, to recent results, are included; interested readers are encouraged to explore the references in Mandzhavidze and Ramaty [7], Ramaty and Mandzhavidze [8], and the other papers cited here. 2. Specific diagnostics 2.1. Accelerated particle spectrum; accelerated and ambient abundances The spectrum of the accelerated ions is usually deduced from line ratios, either among nuclear de-excitation lines or between them and the spallation-induced positron-annihilation and neutron-capture lines. The de-excitation lines typically have a sharp threshold for excitation, varying from about 2.5 MeV for the 1.64 MeV line of 20 Ne to about 8 MeV for the 6.13 MeV line of 16 O [9]. The positron-annihilation and neutron-capture lines originate primarily from the interactions of ions of tens of MeV per nucleon, although the former can also have a component due to pion decay, which requires ion energies of hundreds of MeV. The use of these ratios is complicated by several factors. The de-excitation lines can be stimulated by alpha particles as well as protons, and the alphainduced lines have a lower threshold in energy per nucleon [9]. Thus the alpha/proton ratio and any spectral differences between the accelerated alphas and protons [10] will affect the line ratios. The abundances of the target nuclei in the solar atmosphere can also vary with height and with location on the solar surface; unless these abundances can be measured or deduced, they make up another variable interfering with determination of the accelerated spectrum from ratios. Some lines, such as the 4.4 MeV line from excited 12 C, can be created either by simple excitation of the stable counterpart nucleus or, in the case of a very energetic proton/alpha, by spallation of a heavier nucleus (in this case oxygen). This complicates the relation between accelerated particle spectrum and abundances in generating the line. The solution to these problems lies partly in making intelligent guesses about missing information, but also in using the Doppler profiles of the de-excitation lines to separately constrain the alpha/proton ratio and other parameters (see below). The neutron-capture line at 2.2 MeV will fade in time as neutrons are captured not only by protons but by 3 He, which has a higher cross section. The decay time of the line emission therefore constrains the atmospheric abundance of this isotope, which is astrophysically important but extremely difficult to measure [7, 11, and references therein]. A concise but rich summary of the various lines and their applications to accelerated ion spectra and abundances, with many useful references, is given by Mandzhavidze and Ramaty [7]. A particularly in-depth example of their use in a very large flare is given by Murphy et al. [12]. This study included abundance variations with time, which probably suggest abundance variations with position. A true imaging gamma-ray telescope with angular resolution on the order of 5–10

could test this. 2.2. Angular distribution of accelerated particles The nuclear excited states produced by collisions between accelerated and ambient particles have such short lifetimes that the decay gamma-ray is emitted with a Doppler shift due to the Springer

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Fig. 2 Simulated line shapes for the de-excitation line of 20 Ne due to accelerated protons (dashed line) and alphas (dot-dashed line), and their sum for an alpha/proton ratio of 0.5 (solid line). The rest energy is shown by the vertical line. These shapes were calculated for a spectral index of −3.75 for the particles, a flare heliocentric angle of 30 deg, and an incident particle distribution isotropic in the downward hemisphere. Models calculated by Ronald Murphy [5]

recoil from the original collision. Thus, the line profiles can be compared to calculations for different angular distributions of incident particles with respect to the local normal (pancake, isotropic, and beamed distributions, for example, or distributions derived from modeling collisions in the loop). Accelerated alpha particles produce greater recoil, and can thus give a broad, red “tail” to the line shape (see Figure 2); fitting this tail can constrain the alpha/proton ratio independently of line fluxes and ratios. Accelerated nuclei heavier than He also produce de-excitation lines, but these tend to be so broadened that they run together into a quasicontinuum. The narrow lines (Figure 1) are sufficiently few in number that they are not expected to overlap in most cases (for a list of expected lines and reactions, see Kozlovsky, Murphy and Ramaty [9]). Line redshifts and widths have been studied using data from SMM and RHESSI [5, 13]. The former study showed the expected loss of redshift in moving from disk center to the limb when averaging over many flares, while the latter found that an individual flare can have high redshifts even near the limb, suggesting a particular tilt to the loops containing the ions. More recently, asymmetric, theoretically-calculated shapes like that shown in Figure 2 have been used to fit high-resolution INTEGRAL data [14]; a similar analysis of RHESSI data is in progress.

2.3. Density, temperature, and convection of the solar atmosphere Recent high-resolution RHESSI spectra (e.g., Figure 3) of the positron annihilation line in flares [15, 16] show surprisingly broad and variable Doppler widths. Since the positrons mostly thermalize before annihilating, this is a direct probe of the temperature of the annihilating region. The implied temperatures are on the order of 105 K, a transitional temperature Springer

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Fig. 3 Count spectra of the solar 511 keV annihilation line from two intervals in the flare of 28 October 2003. During the later part of the flare, when the emission was weaker, the line was much narrower (bottom data). From Share et al. [16]

found in only a negligible layer in the quiet solar atmosphere. To stop the positrons, quite a bit of plasma must be maintained at this temperature during a flare despite extremely effective cooling. The ratio between the 511 keV annihilation line and the three-photon annihilation continuum below it due to decay of ortho-positronium gives an added constraint on the density of the region, since collisions disrupt the long-lived ortho-positronium at high densities, so that more annihilations occur either via free positrons or para-positronium. This new tool is revealing a part of the flare environment that has eluded all other observational techniques. Another way of studying the solar atmosphere using gamma-ray lines was proposed by Ramaty and Mandzhavidze [8], using the lines at 847 and 1238 keV from 56 Co produced in the flare. This isotope, with a half-life of 78.8 days, should be produced during spallation reactions and be visible as a hot spot that moves with the solar rotation while decaying, perhaps diffusing outward and being convected to deeper layers of the Sun. The rate of fading of this radioactive tracer is a unique tool to study the rate at which material is exchanged between the chromosphere and the deeper Sun. The lines have never been observed, being on the edge of sensitivity of existing instruments. The RHESSI data from after the series of large flares of October/November 2003 are currently being searched. The flux predictions are shown in (Figure 4). 2.4. Location of the acceleration sites by imaging RHESSI made the first arcsecond images of MeV gamma-rays from solar flares (indeed, of any source in space), resulting in a second major surprise. The positions of the 2.2 MeV neutron-capture hot spots were found to be significantly shifted from the sites of electron bremsstrahlung. In one case, the ion interactions seemed to be taking place at the footpoint of a larger loop [17]. In another case (Figure 5), they are shifted to footpoints further along an arcade [18]. When sampled over more flares and perhaps at higher resolution, these observations have the potential to reveal differences between ion and electron acceleration and help us identify the mechanisms of both. Springer

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Fig. 4 Approximate predicted flux versus time for the 847 keV line of 56 Co during and after the series of major X-flares in October–November 2003. The horizontal bars show the periods when the active region is visible on the near side of the Sun. These very rough estimates are based on scaling the predictions of Ramaty and Mandzhavidze [8] to the x-ray luminosity of these flares Fig. 5 Overlay of the 50, 70, and 90% contours of 35-arcsecond resolution gamma-ray images from RHESSI on a contemporaneous TRACE EUV image. The flare is the X17 event of 28 October 2003, and the energy bands are the 2.2 MeV neutron capture line (dark contours) and electron bremsstrahlung at 200–300 keV (lighter contours). The primary sites of ion and electron acceleration are, surprisingly, not cospatial; both footpoints are shifted in roughly the same direction. From Hurford et al. [18]

3. Role of MAX and other focusing missions 3.1. Observational capabilities Ideally, of course, we would like to study every line at once with extremely high sensitivity. Barring that, the highest priority should be simultaneous high sensitivity and high energy Springer

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resolution in the 511 keV line and at least one of the de-excitation lines. Most of the lineshape science can then be done with unprecedented precision. A traditional, non-focusing spectrometer could then obtain sufficient statistics to derive fluxes (if not shapes) for the other lines in a large flare, for purposes of deriving the spectrum of the accelerated particles (which would be difficult with only two lines). The neutron-capture line, being the brightest in the flare, will be detected with good statistics in many flares even without focusing, sometimes at levels that allow studies of the decay time. An advance of at least a factor of four beyond the statistics shown in Figure 1 is necessary to resolve the widths, redshifts, and relative amplitudes of the proton and alpha components shown in Figure 2. Improvements beyond that would allow the data to be split up into many time intervals, showing changes during the flare that can be compared to activity at other wavelengths. The 23 July 2002 flare shown in Figure 1 was of GOES class X4.81 , which would be typically among the dozen or so largest of a given solar maximum. Its line fluxes (around 20 photons/cm2 per line) therefore provide a reasonable benchmark as the best flare a new mission can be confident of seeing. Typical line widths are 3–10 keV at 511 keV and 4–10 keV at 847 keV (proton and alpha components, respectively). The de-excitation lines of lighter nuclei are much broader: about 50–100 keV for the C and O lines between 4 and 7 MeV. The planned energy bands for MAX (511 keV and 847 keV) match the criteria for optimal bands for solar studies on two conditions. First, the instrumental resolution must be high enough to resolve the solar widths of both lines: ∼2 keV FWHM, i.e. a well-designed germanium detector plane. Second, the width of each band must include the full line in the broadest solar cases, meaning a total width of at least 30 keV centered around each band. A significant additional advantage will accrue if the 511 keV band can be extended downwards as far as 450, 400, or even 350 keV: this allows increasingly effective inclusion of the orthopositronium continuum and the nuclear lines from alpha/He interactions. The latter are particularly effective probes of both the accelerated alpha fraction and the angular distribution of the accelerated ions [19]. The effective area of RHESSI from 511-847 keV is fairly constant at around 26 cm2 . With a collecting area averaging about 500 cm2 over the two bands [20] and a likely photopeak efficiency in the detector plane on the order of 30–50%, MAX would have almost an order of magnitude more effective area. For the long-lived 847 keV line due to radioactive decay rather than de-excitation, the predicted fluxes of 1 − 10 × 10−5 ph/cm2 /s (see Figure 4) after major flares can be compared to the MAX 3σ narrow-line sensitivity of ∼10−6 ph/cm2 /s [20]. This is an opportunity to make an absolutely new measurement with, for once, a significance of more than 3σ . 3.2. Operational considerations Revolutionary solar observations could be made even without a mission dedicated to flare science. A focusing gamma-ray telescope such as MAX should be designed so that solar pointing is possible. This is not difficult with regard to the instrument, since even tens of layers of mylar thermal blanketing do not attenuate gamma-rays significantly. Spacecraft design considerations, however, often require that only a limited range of pointing angles with respect to the Sun be possible (for example, to simplify thermal design or to avoid having

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to articulate solar panels). Astrophysical spacecraft often choose to leave a region near the Sun inaccessible for these reasons. In most cases, however, this exclusion zone could just as easily be chosen, during the space-craft design phase, to be in the anti-Sunward direction instead. For non-solar science, that should be no worse than a solar-pointing exclusion. Most of the largest flares come from active regions that produce more than one, usually at intervals of one to a few days (see, e.g., the events of June 1991 and October/November 2003). A practical and possibly even optimal pointing strategy for a non-solar mission is to wait until the first of these giant flares occurs, then point to the active region responsible for the next week or so until it goes behind the Sun. This will require the ability to decide, command, and repoint in a period of one or two days. Dedicating a few weeks per year to this mode (5–10% of the mission schedule) is likely to capture a significant fraction (perhaps even a majority) of the largest flares during that year. The requirement on the field of view is approximately 1.5–3 arcmin in radius, based on images of the largest flares seen with RHESSI (e.g. Figure 5). Pointing would have to be updated continuously in a way not necessary for cosmic operations to track both the motion of the Sun on the sky and the motion of the active region on the Sun. The latter can be tracked with ground-based solar telescopes or space-based instruments at other wavelengths. 3.3. Focusing at the neutron capture line? Imaging at 2.2 MeV would require both an energy band and an instrumental strategy not yet contemplated for a proposed mission. The Laue lens system for MAX is a concentrator, not a true imager. In the most straightforward adaptation, subsets of tuned Laue crystals could all be optimized to a very narrow energy band (the line is naturally very narrow), but focused separately on different elements of an array of focal-plane detectors covering different parts of the field of view. A grid of 10 × 10 20-arcsec pixels, for example (each pixel consisting of a subset of Laue crystals focusing to its own detector), would cover the largest flares (Figure 5) with an angular resolution somewhat better than RHESSI’s. This technique is not nearly as effective as a true telescope, since each lens segment serves only one pixel of the image, not all of it. In sensitivity, it is equivalent to a small single-pixel instrument doing a long raster scan, except that such a scan would not be possible during the minutes or tens of minutes of the flare. A simple extension of RHESSI’s technique (rotating modulation collimator [RMC] imaging, with no lens) to a larger instrument might prove to be preferable for this application. In a large flare, the 2.2 MeV line is often strongly source dominated even without focusing, compared to either the instrumental background or the flare continuum. Thus, the only purpose for focusing is that the effective area of the collecting lens might be cheaper than adding the same collecting area using more detectors instead; background reduction is no longer a major advantage. A hybrid configuration might be considered, where RMC grids sit in front of the Laue lens, which focuses the temporally modulated gamma-rays onto a small detector. Imaging would be accomplished by the grids, concentration by the (possibly corotating) lens - assuming a large lens is less expensive than a large detector array.

References 1. Springsteen, B.: Blinded By The Light, lyrics, Greetings From Asbury Park, N.J. (1973) 2. Lin, R.P., Hudson, H.S.: Non-thermal processes in large solar flares. Sol. Phys. 50, 153–178 (1976) Springer

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3. Ramaty, R., Mandzhavidze, N., Kozlovsky, B., Murphy, R.J.: Solar atmospheric abundances and energy content in flare accelerated ions from gamma-ray spectroscopy, ApJ 455, L193–196 (1995) 4. Sui, L., Holman, G.D., Dennis, B.R.: Determination of low-energy cutoffs and total energy of nonthermal electrons in a solar flare on 2002 April 15, ApJ 626, 1102–1109 (2005) 5. Smith, D.M., Share, G.H., Murphy, R.J., Schwartz, R.A., Shih, A.Y., Lin, R.P.: High-resolution spectroscopy of gamma-ray lines from the X-class solar flare of 2002 July 23, ApJ 595, L81–L84 (2003) 6. Lin, R.P.: Relationship of solar flare accelerated particles to solar energetic particles (SEPs) observed in the interplanetary medium, AIP Conf. Proc. #781, 246–251 (AIP: Melville, New York) (2005) 7. Mandzhavidze, N., Ramaty, R.: Particle acceleration and abundances from gamma-ray line spectroscopy, Astron. Soc. Pac. Conf. Series. #206, 64–70, (ASP: San Francisco) (2000) 8. Ramaty, R., Mandzhavidze, N.: Gamma-Rays from solar flares Proc. IAU Symp. #195, 123–132 (ASP: San Francisco) (2000) 9. Kozlovsky, B., Murphy, R.M., Ramaty, R.: Nuclear Deexcitation Gamma-Ray Lines from Accelerated Particle Interactions, ApJS 241, 523–541 (2002) 10. Toner, M.P., MacKinnon, A.L.: Do fast protons and alpha particles have the same energy distributions in solar flares?, Sol. Phys. 223, 155–168 (2004) 11. Murphy, R.J., Share, G.H., Hua, X.-M., Lin, R.P., Smith, D.M., Schwartz, R,A.: Physical implications of RHESSI neutron-capture line measurements. ApJ 595, L93–L96 (2003) 12. Murphy, R.J., Share, G.H., Grove, J.E., Johnson, W.N., Kinzer, R.L., Kurfess, J.D., Strickman, M.S.: Accelerated particle composition and energetics and ambient abundances from gamma-ray spectroscopy of the 1991 June 4 solar flare, ApJ 490, 883–900 (1997) 13. Share, G.H., Murphy, R.J., Kiener, J, de Séréville, N.: Directionality of solar flare-accelerated protons and α-particles from γ -ray line measurements. ApJ 573, 464–470 (2002) 14. Kiener, J., Gros, M., Tatischeff, V., Weidenspointner, G.: Properties of the energetic particle distributions during the October 28, 2003 solar flare from INTEGRAL/SPI observations, A&A in press (2005) 15. Share, G.H. et al.: High-resolution observation of the solar positron-electron annihilation line, ApJ 595, L85–L88 (2003) 16. Share, G.H., Murphy, R.J., Smith, D.M., Schwartz, R.A., Lin, R.P.: RHESSI e + −e− Annihilation radiation observations: implications for conditions in the flaring solar chromosphere, ApJ 615, L169– L172 (2004) 17. Hurford, G.J., Schwartz, R.A., Krucker, S., Lin, R.P., Smith, D.M., Vilmer, N.: First gamma-ray images of a solar flare, ApJ 595, L77–80 (2003) 18. Hurford, G.J., Krucker, S., Lin, R.P., Schwartz, R.A., Share, G.H., Smith, D.M.: Gamma-ray imaging of the october/november 2003 solar flares, in preparation (2006) 19. Share, G.H., Murphy, R.J., Smith, D.M., Lin, R.P., Dennis, B.R., Schwartz, R.A.: Directionality of flareaccelerated alpha-particles at the sun. ApJ 595, L89–L92 (2003) 20. Barriere, N.: Exp. Astron. 20, DOI: 10.1007/s10686-006-9058-x (2006)

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Exp Astron (2005) 20:75–83 DOI 10.1007/s10686-006-9057-y ORIGINAL ARTICLE

The INTEGRAL – HESS/MAGIC connection: A new class of cosmic high energy accelerators from keV to TeV P. Ubertini∗

Received: 12 April 2006 / Accepted: 27 June 2006 C Springer Science + Business Media B.V. 2006

Abstract The recent completion and operation of the High Energy Stereoscopic System [1], an array of ground based imaging Cherenkov telescopes, has provided a survey with unprecedented sensitivity of the inner part of the Galaxy and revealed a new population of very high energy gamma-rays sources emitting at E > 100 GeV. Most of them were reported to have no known radio or X-ray counterpart and hypothesised to be representative of a new class of dark nucleonic cosmic sources. In fact, very high energy gamma-rays with energies E >1011 eV are the best proof of non-thermal processes in the universe and provide a direct in-site view of matter-radiation interaction at energies by far greater than producible in ground accelerators. At lower energy INTEGRAL has regularly observed the entire galactic plane during the first 1000 day in orbit providing a survey in the 20–100 keV range resulted in a soft gamma-ray sky populated with more than 200 sources, most of them being galactic binaries, either Black Hole Candidates (BHC) or Neutron Stars (NS) [5]. Very recently, the INTEGRAL new source IGR J18135-1751 has been identified as the soft gamma-ray counterpart of HESS J1813-178 [18] and AXJ1838.0-0655 as the X/gamma-ray counterpart of HESS J1837-069 [14]. Detection of non-thermal radio, X and gamma-ray emission from these TeV sources is very important to discriminate between various emitting scenarios and, in turn, to fully understand their nature. The implications of these new findings in the high energy Galactic population will be addressed.

Keywords Gamma-ray sources . High energy emission processes

∗ On

behalf of the IBIS Survey Team.

P. Ubertini Istituto di Astrofisica Spaziale e Fisica Cosmica (IASF), Roma, Italy e-mail: [email protected] Springer

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1. Introduction HESS (High Energy Stereoscopic System), a ground-based Cerenkov array telescopes has been operated since a few years and in 2004 has performed the first Galactic plane scan with a sensitivity of a few percent of the Crab at energies above 100 GeV, resulting in the discovery of eight sources, most of which without any counterpart at different energies [1, 2]. Particular attention was devoted to HESS J1813-178, not identified with any known X/gamma ray emitter and hypothesised to be a dark particle accelerator. Independently, and at the same time, INTEGRAL discovered a new soft gamma-ray source, namely IGR J18135-1751, identified as the counterpart of HESS J1813-178. This high energy emitter, whose nature was still mysterious at the time of the discovery was then associated with the supernova remnant (SNR) G12.82 0.02 [6, 10, 18]. Even if a chance coincidence cannot be completely ruled out in view of the 2 arcmin INTEGRAL error box and the possible angular extension in the high energy, the overall characteristics of this star forming region [7] comprising SNR G12.82 0.02 are consistent with supernova/plerion origin. More recently, the MAGIC (Major Atmospheric Gamma Imaging Cerenkov telescope) collaboration has reported a positive observations of HESS J1813–178, resulting in a gamma-ray flux consistent with the previous HESS detection and showing a hard power law with α = 2.1 in the range from 0.4–10 TeV [3]. The detection of a substantial number of very high energy Galactic sources emitting a large fraction of energy in the GeV to TeV range has opened a new space window for astrophysical studies related to cosmic particle acceleration. Different types of Galactic sources are known to be cosmic particle accelerators and potential sources of high energy gamma rays: isolated pulsars/pulsar wind nebulae (PWN), Supernova remnants, star forming regions, binary systems with a collapsed object like a microquasar or a pulsar etc. The HESS detection of several TeV emitters without any counterpart at different energy has made the detection of X and gamma-ray emission from these sources a key issue to disentangle the mechanisms active in the different emitting regions and, in turn, to understand the source nature. The IBIS gamma-ray imager on board INTEGRAL is a powerful tool to search for their counterpart above 20 keV in view of the arcmin Point Source Location Accuracy associated to ∼ mCrab sensitivity for exposure >1 Ms [17]. 2. HESS J1837-069 = AXJ1838.0-0655: The first IBIS/HESS new source AXJ1838.0-0655 is located in the Scutum arm region and has been detected as a new INTEGRAL source by Bird [5] and Molkov [15] and it is detected by IBIS up to 300 keV with a high statistical significance, exceeding 15σ . The best positional location is R.A. (2000) = 18 h 38 m 01.7 s and Dec = −06◦ 54 14.4

with an error radius uncertainty of ≤3 [14]. The IBIS data provide a good fit with a simple power law with a resulting χν2 /do f = 0.3/5 with a photon index = 1.66 ± 0.23 (90% c.l) and a 20–300 keV flux of 9 × 10−11 erg cm−2 s−1 [14]. HESS J1837-069 is one of the 10 very high energy sources located in the central part of the Galaxy plane, detected in the TeV range with a statistical significance of 7–8 σ . It is located at R.A. (2000)= 18 h 37 m 42.7 s and Dec (2000) = −06 55 39 (error box of about 1–2 ) [1] and the estimated flux, above 200 GeV, is 9 × 10−12 photons cm−2 s−1 . The authors suggest AXJ1838.0-0655 to be the candidate for HESS J1837-069, in view of the spatial coincidence (see Figure 2). AXJ1838.0-0655 was discovered by the Einstein satellite in X-rays and named 1E1835.30658 [11] then observed by ASCA at higher energy during the Galactic plane survey [4] with a positional uncertainty of 1 in radius, basically coincident with the position of the Springer

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Fig. 1 Left panel: from Malizia et al. [14]. The IBIS/ISGRI 20–300 keV significance map showing the location of AX J1838.0-0655 as well as the position and extension of HESS J1837-069 (white circle) and the Einstein position (black cross). The position and uncertainty of the ASCA source is basically coincident with the central, brightest IBIS pixel. Right panel: from Aharonian et al. [1]. The emission region of HESS J1837-069 overlapped to the ASCA error box of AXJ1838.0-0655. As can be seen even if the two sources are positionally coincident the TeV emission is suggestive of an extended object

Fig. 2 The large IBIS sky region map containing AXJ1838.0-0655

original discovery. It was found to be bright in the 0.7–10 keV band at a flux level of 1.1 × 10−11 erg cm−2 s−1 and a hard ( = 0.8) and absorbed (N H = 4 × 1022 cm−2 ) power law shape. The summary of the observed positions for the different component, from soft X-ray to TeV range, is shown in Figure 1 (see [14] for details). From the angular distribution it looks evident that the Einstein, ASCA and IBIS sources are the same emitting source which is also likely to be active at TeV energies. Finally [14] report the presence of a strong radio source, TXS1835-069-CUL1835-06, associated in Simbad with a candidate supernova remnant, SNR025.3-00.1 [9], positioned at the side of the IBIS error box, though not compatible Springer

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with ASCA/Einstein X-ray position. The X/gamma-ray data indicate a point source nature for this object, while the high energy results are more in line with an extended emission, (see Figure 1) suggestive of a non-thermal radiation mechanism pointing to a SNR and/or a PWN [1]

3. HESS J1813-178 and IGR J18135-1751: Same emitting region/mechanism? IGR J18135-1751 was one of the newly discovered source during the compilation of the second IBIS/ISGRI survey catalogue [5]. It was immediately clear that the soft gamma-ray excess was positionally coincident with the very high energy source named HESS J1813-178, one of the 8 unknown sources found in the HESS survey of the inner region of the Galactic plane. The source position was found at R.A. (2000) = 18 h 13 m 37.9 s and Dec (2000) = −17◦ 50 34

and has a positional uncertainty of 1–2 arcmin. The source was reported to be slightly extended, about 3 arcmin and had a statistical significance of about 9σ . Even if the source was reported to be quite bright 12 × 10−12 photons cm−2 s−1 above 200 GeV, it was impossible to find an evident counterpart. An archival search for soft X-ray data resulted in a possible counterpart in the ASCA archive data: AGPS273.4-17.8 at R.A. (2000) = 18 h 13 m 35.8 s and Dec (2000) = −17◦ 49 43.35

with an associated uncertainty of 1 . In the X-ray band the source is fairly bright showing a 2–10 keV flux (corrected for absorption) of 1.8 × 10−11 erg cm−2 s−1 [18]. In Figure 3 is shown the IBIS/ISGRI 20–40 keV map with the location of IGR J181351751. The authors report the relative significance contours to be 6 (for the external one), 8, 10, 20 and 40 σ , that are compatible with a point source. The extension of HESS J1813-178 as well as the position of AGPS273.4-17.8 are both contained within the internal IBIS/ISGRI contour. Also it is shown the location and the extension of W33 and the 4 nearest radio pulsars, namely PSR J1814-1744, PSR J1812-1733, PSR J1815-1738 and PSR J1811-1736. The combined IBIS-ASCA spectrum, obtained adding the two data set without the need of any normalisation, confirm that HESS J1813-178 has a point like X-ray counterpart with a power law emission from 2 to 100 keV and an associated radio counterpart. The data set is strongly suggesting that it is a non-thermal source, possibly accelerating electrons and positrons which radiate through synchrotron and inverse Compton mechanism. Brogan et al. [6] have provided a possible interpretation of the HESS/ASCA spectrum by fitting the broadband emission assuming that all the flux originates from the shell of SNR G12.8 (see Figure 5 and Brogan et al. [6], for a detailed description). The two proposed models (corresponding to two different Nh absorption values) are shown by the red and blue lines that provide the best fit to the data. The models include X-ray emission from synchrotron radiation (solid lines) and Inverse Compton processes (dashed lines), assuming a filling factor of 15% for the magnetic field in the IC emitting region. More recently the MAGIC experiment has observed HESS J1813-178, resulting in the detection of a differential gammaray flux consistent with a hard-slope power law, described as dNγ /(dAdtdE) = (3.3 ± 0.5) × 10−12 (E/TeV)−2.1±0.2 cm−2 s−1 TeV−1 [3]. The image of the MAGIC field containing the high energy excess is shown in Figure 4. The authors quote the systematic error to be 35% in the flux level determination and 0.2 for the spectral index. Within errors, the flux was found steady in the timescales of weeks as well as in the year-long time span between the MAGIC and HESS pointings. They report a multiwavelength emission associated to HESS J1813-178, is shown in Figure 6, including the MAGIC data at high energies. The authors compare the hadronic and leptonic emission models with the high-energy gammaray data (see [3, 16] for details). The main conclusions are that for hadronic models the Springer

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Fig. 3 From Ubertini et al. [18]. The IBIS/ISGRI 20–40 keV significance map showing the location of IGR J18135- 1751 and relative significance contours; the source spatial profile is compatible with the detector response to a point source. The extension of HESS J1813-178 as well as the position of AGPS273.4-17.8 are both contained within the internal IBIS/ISGRI contour. Also shown is the location (and extension) of W33, of the 4 nearest radio pulsars (PSR J1814-1744,PSR J1812-1733, PSR J1815-1738 and PSR J1811-1736) and of the ROSAT source 1WGA J1813.7-1755 (white small diamond). The ASCA-SIS image is shown as an insert on the top right side of the figure: contour levels provide marginal evidence of extended emission. In the picture is also present GX13+1 and the transient source SAX J1818.6-1703 that are field sources not contaminating in any way IGR J18135-1751, in view of the large angular distance between the objects (see text for details). The coordinates are displayed in Galactic system [18]

observed high energy luminosity (2.5 × 1034 erg s−1 at a distance of 4 kpc) implies a matter density of ∼6 cm−3 assuming gamma-ray are generated in the whole Supernova remnant, an acceleration efficiency for the hadrons of ∼3% and a Supernova power of 1051 ergs with a target mass for relativistic particles of about 2 Solar masses (within or close to the SNR) to justify the observed luminosity. For leptonic models, they assume relativistic electrons distribution of dNe /(dV dE) = Ae (E/GeV)−αe exp (−E/E max,e ) GeV−1 cm−3 and obtain good fits with value of αe ∼ 2.0–2.1 E max,e ∼ 20–30 TeV, assuming the cosmic microwave background as target photons. The best fit to the radio synchrotron emission is α ∼ 2.0 and require a magnetic field of 10 µG with a filling fraction of about 20% [3]. This model is not very different from the blu one in Brogan et al (see Figure 5), even if a lower filling factor E max,e is assumed.

4. Implication of the synchrotron – inverse compton scenario The detection of soft gamma-ray photons from sources emitting in the TeV range is important to understand the emission mechanisms and the particle acceleration processes present in the SNR environment. In addition, the consistency with a power law of X-Ray spectra, spanning from few keV to few hundred of keV, and the lack of X/gamma variability is Springer

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Fig. 4 From Albert et al. [3]. Sky map of gamma-ray candidate events (background-subtracted) in the direction of HESS J1813-178 for an energy threshold of about 1 TeV. Overlaid are contours of 90 cm VLA radio (black) and ASCA X-ray data (green) from Brogan et al. [6]. The two white stars denote the tracking positions W1, W2 in the wobble mode (see [3] for details)

Fig. 5 From Brogan et al. [6]. Fits to the broadband emission of HESS/ASCA source assuming that all the flux originates from the shell of SNR G12.8 0.0. The diagonal black lines indicate both the uncertainty in the HESS flux measurements, and the fact that no spectral information has yet been published for the TeV emission. The two models indicated by the red and blue lines show the range of parameter space that best fit the data: the red model uses the spectral index from the best fit ASCA Nh of 10.8 × 1022 cm−2 (black X-ray spectrum), while the blue model uses the spectral index implied by the 1σ lower limit to Nh of 8.9 × 1022 cm−2 (green X-ray spectrum). Both models include contributions from synchrotron (solid lines) and IC (dashed lines) mechanisms. The authors have assumed that the filling factor of the magnetic field in the IC emitting region is 15% Springer

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Fig. 6 From Albert et al. [3]. Leptonic and hadronic models for the J1813-178 data. Details are given in Albert et al. [3]. Radio data are from the VLA, Bonn, Parkes, and Nobeyama observatories [6]; X-ray and hard X-ray data are from ASCA [6] and INTEGRAL [18]

compatible with a SNR or a Pulsar Wind Nebula, the latter not yet evident from observational view point. As an example, HESS J1813-1751 has a very young remnant, of the order of 300 to 3000 year, assuming a density medium of ∼1 cm−3 . The IBIS detection of soft gamma-ray photons up to ∼100 keV [19] in the Synchrotron – Inverse Compton Scenario force the lifetime of the emitting electrons to be quite short if compared to the one of the radiating electrons in the GHz frequency [12, 8, 9]. In fact, the lifetime for the high energy electrons is t1/2 ∼ 224 × (B/10 µG)−3/2 y. This model also imply the radio and X/soft gamma-ray synchrotron emission to be spatially coincident and X-ray emission that sharply drops behind the shock. Because of this effect, the X-Ray photons will be confined close to the electrons acceleration region while the same electron population would eventually drift having a diffusion speed of a fraction of the light one. The detection of a substantial flux of soft gamma-rays from the HESS J1813-1751 region is supportive of the red fit model proposed by Sy [6], implying a lower ratio of peak emission frequencies Rν = ν pI C /ν p if compared with the blue one, not capable to fit the IBIS data and, in turn, not compatible with the single source scenario. Unfortunately, the red model is unable to fit the HESS data, the physical reason being the synchrotron losses, in the presence of a quite strong magnetic field predicted by the model, constraining the density of the electrons necessary to radiate via Inverse Compton interaction with the CMB radiation. The picture improves considering that a substantially higher UV light flux could be supplied by W33, a close HII region. An energy density of ∼3 eV cm−3 could be easily provided, a factor ∼10 higher than the density of ∼0.26 eV cm−3 of the CMB photons [1] (for a detailed analysis of the IC model see [19]).

5. Conclusions It is clear that both the hadronic and leptonic models so far proposed fails to easily explain the whole observational picture if the radio, X/soft gamma-rays and TeV high energy photons are produced in the same SNR region by a single physical process. In fact, to finally confirm the above hypothesis it is necessary to have instruments capable to provide spatially resolved spectroscopy with a fraction of arcsec. While in the X-ray range this seems to be possible with long CHANDRA exposures it is not with the present generation of gamma ray instruments Springer

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Fig. 7 The lap in sensitivity expected from new generation gamma ray observatorysuch as MAX+ or the newly prosed Gamma Ray Imager (GRI) based on Laue Lens complemented at lower energy by a large CZD detrector (in the figure is shown the SMAX sensitivity, this conference)

in the best case providing arcmin angular resolution [13, 17]. This will be achievable with a new generation of Gamma Ray Imagers providing at the same time a factor of 10 better sensitivity, as discussed in the present conference, as shown in Figure 7. On a shorter time frame it could be possible to improve the lack of our knowledge in the blank region in between the soft gamma ray range covered by INTEGRAL and the very high energy one by HESS and MAGIC. In fact, the imminent launch of the Italian AGILE gamma-ray satellite, covering the 30 MeV–50 GeV range with a good sensitivity over a wide field of view, and GLAST in perspective, will be a powerful tool to finally disentangle the nature of the high energy sky. Acknowledgements The author acknowledge this research has been granted by the Italian Space Agency via contract n. I/R/046/04 ASI/IASF.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Aharonian, F. et al.: Science 307, 1938 (2005) Aharonian, F. et al.: ApJ 636, 777 (2006) Albert, J. et al.: ApJ 637, L41 (2006), Bamba, A. et al.: ApJ 589, 253 (2003) Bird, A.J.: ApJ 636, 765 (2006) Brogan, C. et al.: ApJ 629, L105 (2005) Churchwell, E.: A&A Rev. 2, 79 (1990) Condon, J.J. et al.: AJ 115, 1693 (1998) Dulk, P., Slee, O.: AJPh 25, 429 (1972) Helfand, D.J., Becker, R.H., White, R.L.: astro-ph/0505392 (2005) Hertz, P., Grindlay, J.: AJ 96, (1998) Lazendic, J.S. et al.: ApJ 602, L271 (2004) Lebrun, et al.: A&A 411, L141 (2003) Springer

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Malizia, A.: ApJ 630, L157 (2006) Molkov, S. et al.: Astr. Lett. 30, 534 (2004) Torres, D.F. et al.: Phys. Rept. 382, 303 (2003) Ubertini, P. et al.: A&A 411, L131 (2003) Ubertini, P. et al.: ApJ 629, L109 (2005a) Ubertini, P. et al.: Proceedings–Conference “A Life with Stars” Amsterdam 22–26/August–Elsevier. (2005b)

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Exp Astron (2005) 20:85–92 DOI 10.1007/s10686-006-9033-6

Replicated nickel optics for the hard-x-ray region Brian D. Ramsey

Received: 11 January 2006 / Accepted: 24 February 2006 C Springer Science + Business Media, B.V. 2006

Abstract Replicated nickel optics has been used extensively in x-ray astronomy, most notably for the XMM/Newton mission. The combination of relative ease of fabrication and the inherent stability of full-shell optics, make them an attractive approach for mediumresolution, high-throughput applications. MSFC has been developing these optics for use in the hard-x-ray region. Efforts at improving their angular resolution, particularly for the very-thin-wall shells required to meet the weight budgets of future missions, are described together with the prospects for future significant improvements. Keywords Replicated . X-ray astronomy . x-ray optics Background X rays can undergo total external reflection from smooth surfaces at very shallow graze angles. The critical angle in degrees, below which this takes place, is given by θ ∼ 0.93 √ λ (ρ), where λ is the wavelength of the incident x ray (nm) and ρ is the density of the reflecting medium (g/cm3 ). Thus at 6 keV, for example, a nickel surface will reflect x rays up to an angle of approximately 12 degree. This phenomenon can be used to realize an x-ray telescope. A single parabolic section, limiting graze angles to 12 degree for a parallel input beam, would focus x rays to ∼6 keV. This optic, however, would have serious off-axis image distortions, and in 1951 a combination of parabolic and hyperbolic sections was proposed that overcame this limitation. This configuration, known as a Wolter-1 geometry after its proposer (Wolter, 1952), has been widely adopted for x-ray astronomy. Typically, several such reflector pairs would be concentrically nested to build up collection area. The power of focusing optics goes beyond the capability to produce more detailed source images. Signals from cosmic sources are extremely faint and are observed against a large background flux that is dependent on the detector area and the amount of sky being viewed. B. D. Ramsey () NASA/Marshall Space Flight Center, Huntsville, Alabama, USA e-mail: [email protected] Springer

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By concentrating source flux from a small area of the sky onto a tiny detector area, an x-ray telescope enables an enormous increase in signal to noise ratio, and thus in sensitivity. By way of an example, the currently operating Chandra x-ray observatory has the same collecting area as the first x-ray satellite, UHURU, but has nearly 5 orders of magnitude more sensitivity by virtue of its focusing optics. Because of this resulting sensitivity enhancement, x-ray optics has revolutionized the field of soft-x-ray astronomy. The situation at higher energies, above 10 keV where x-ray optics have not been employed, is quite different though. The hard-x-ray region is very important for study as in this energy regime sources transit from thermal to non-thermal emission mechanisms. In addition, nuclear lines appear and obscured objects become visible. Despite this significance, this energy region remains relatively unexplored at high sensitivities and fine angular scales. The remedy is obvious – grazing optics needs to be extended to higher energies. To do this we must accept the very small graze angles that this entails and develop techniques for efficiently fabricating large numbers of light-weight optics that can be heavily nested to build up useful collecting areas.

Electroformed nickel replication Process The mirror fabrication process that we are developing is electroformed nickel replication (ENR). In this, nickel mirror shells are electroformed onto a figured and superpolished aluminum mandrel from which they are later released by differential thermal contraction. This process, pioneered in Italy for x-ray mirror fabrication, has been used for soft-x-ray astronomy in such missions as XMM-Newton,1 which featured 3 mirror modules with 68 electroformed nickel shells each. The attraction of the ENR process is that the resulting full shells are inherently stable and thus can give good angular resolution. At MSFC we utilize this process and have made additional developments in high-strength nickel alloys, which permit very thin shells to be fabricated, and in plating bath stress control to achieve good figure accuracy. Application: The HERO program HERO, for High Energy Replicated Optics is a balloon program designed to demonstrate MSFC-developed hard-x-ray optics while simultaneously performing new science. The project utilizes all-in-house fabricated optics plus supporting x-ray detectors, gondola and pointing system. The optical design philosophy for HERO is to utilize a large number of shallow-grazeangle, iridium-coated full-shell mirrors, and to obtain significant collecting area by nesting many thin shells. To reduce costs, appropriate for a balloon program, we utilize long shells (which reduces the number of mandrels) and make each a conical approximation to a true Wolter-1 configuration. For mandrel fabrication, we use inexpensive grinding and simple in-house fabricated polishing machines, and for shell production use a multipart plater so that multiple shells can be electroformed simultaneously. Figure 1, below, shows a HERO mandrel being polished and a series of thin nickel shells ready for iridium coating.

1

http://www.sci.esa.int/science-e/www/object/index.cfm?fobjectid = 31318. Springer

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Fig. 1 A HERO mandrel being polished and shells awaiting iridium coating

A proving flight of a HERO payload took place in 2001, when the first focused hard-x-ray images of galactic sources were obtained with just 6 replicated shells of focal length 3 m (Ramsey et al., 2002). Since that time, the payload has been re-built and now features around 100 6-m-focal-length shells giving mCrab-level sensitivity in just a 3-h observation. Table 1 gives the optics configuration for HERO and Figure 2 shows the payload in New Mexico awaiting launch. Table 1 HERO current optics configuration Number of modules Number of shells per module Inner, outer shell diameters Shell thickness Shell length Focal length Angular resolution (module) Field of view Effective area (total)

8 12 50, 94 mm 0.25 mm 300 mm 6m 20–25 arcsec 9 arcmin @ 40 keV 80 cm2 (40 keV) 40 cm2 (60 keV)

Quality-control tests on individual HERO shells show that they typically fall into the 13– 15 arcsec resolution range (Ramsey et al., 2003). When mounted in a 12-shell flight module this degrades to 20–25 arcsec for the overall module half-power diameter, due to distortions around the spider. A new alignment technique is being developed in which the shells are held at their intersection and then lowered into the spider grooves without touching. The intervening space, between the spider groove wall and the mirror shell, is then taken up by epoxy. By floating the shells in position we hope to avoid distortions occurring when the spider contacts the shell wall and deflects it locally. The current plan is to re-assemble all 8 flight modules using this technique before a Fall 2006 scheduled flight. Application: The constellation-X program Constellation-X is the planned successor to the Chandra mission and is currently planned for launch in the 2015–2020 timeframe. It will feature a very large area of soft-x-ray telescopes, primarily for spectroscopy, and also hard-x-ray telescopes (HXT) with ∼1500 cm2 effective area at 40 keV. To meet the HXT baseline requirement, approximately 12 mirror modules Springer

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will be necessary (assuming 10 m focal length) with each module housing ∼80–90 nested mirror shells. Currently, different technologies are being assessed for the HXT optics. MSFC is collaborating with the Smithsonian Astrophysical Observatory and the Observatory of Brera, Italy, in the development of a prototype unit using ENR technology (see Figure 3). For this, MSFC will produce 2 shells, one 150 mm diameter to be coated with iridium, and one 230 mm in diameter, to be coated with multilayers. Both will be just 100 micron thick to meet the stringent Constellation-X weight budget. The Observatory at Brera will produce two additional multilayer-coated shells and the 4-shell prototype will assembled at Brera and tested in Germany in late 2006.

Fig. 2 The HERO payload in Fort Sumner, New Mexico.

Fig. 3 Con-X prototype 4-shell module

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Table 2 Typical mirror shell error budget

Surface error type Delta-delta radius Average radius P Average radius H Average axial sag Axial slope (mid freq) Roundness Circumferential slope (mid freq) P-H tilt P-H decenter Total ∗ Measurement

Image RMS diameter sensitivity

Allocation per shell

Image RMS diameter arcsec

5.4 arcsec/micron rms 0.04 arcsec/micron 0.11 arcsec/micron 12.5 arcsec/micron 8 arcsec/arcsec rms 0.15 arcsec/micron rms 8.3·10−3 arcsec/arsec rms 2 arcsec/arcsec 3.4·10−2 arcsec/micron

0.4 micron rms 2 micron 2 micron 0.3 micron 0.8 arcsec 3 micron rms 6 arcsec rms 0.5 arsec∗ 0.5 micron

2.2 0.08 0.22 3.5 8.0 0.5 0.05 1.0 0.02 9.0

limit

Further ENR developments Typical mirror shells fabricated to date at MSFC have half-power-diameters (HPD) in the 13–15 arcsec range so it is natural to ask if this can be significantly improved upon. To answer this, we have developed a budget showing the contributions of various sources of error to the overall mirror performance (ignoring mounting errors). The total, derived by taking the square root of the summed squares of each individual component, is given as an overall RMS diameter. This can be converted to a half power diameter, assuming a Gaussian flux distribution, by multiplying by 1.35. The error budget is shown in Table 2. The allocation per shell for each error type is obtained from measurements of typical shells. It is evident from this table that two components, namely the average axial sag and the axial slope are the dominant contributors. The average axial figure sag represents the departure of the mandrel figure from the perfect Wolter-1 shape. In our case it represents the limit of the conical approximation that we use in all our mandrels to facilitate fabrication; this requires just two straight cuts rather than a hyperbolic/parabolic figuring. Thus this component can be controlled as necessary simply by figuring the mandrel. The major component in the error table is the mid-frequency axial slope. This error is a measure of the mm- to cm-scale variations in the axial figure of the replicated shell. These variations may be present in the mandrel and carried over through replication, or may come about during electroforming of the shell. Figure 4 (left) shows axial figure profiles for a mandrel and for the shell replicated from it. While the mandrel has small figure variations, at the 100-nm level, there are relatively large variations, micron-level, in the resulting shell figure. We identify two contributors to these figure variations. The first is simply due to changes in the mandrel shape with temperature. The mandrel is fabricated at room temperature while the plating bath is at ∼45 ◦ C. Small variations in thermal expansion coefficient at different points in the mandrel can lead to changes in shape as the mandrel is heated. These differences can come about if, for example, the mandrel is made of a solid piece of aluminum but has not been thermally conditioned (cycling from high temperatures down to cryogenic levels) sufficiently to relieve residual stresses before final machining. They can also come about if the mandrel is hollow and the end caps are made from the same aluminum but which has been processed in a different manner to the cylindrical body. This latter effect is shown in Figure Springer

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1500

0.8 mandrel shell mirror

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Fig. 4 Typical axial figure profile of a mandrel and the resulting shell (left) and the effect of temperature on a mandrel figure (right)

4 (right), where a mandrel is measured at two temperatures showing a distinct change in shape. The second contributor to axial figure variations, and the most difficult to eliminate is stress imparted during electroforming; this can have a significant effect on very-thin-walled shells. Note that there are also stresses imparted by applied coatings, particularly multilayers, and these stresses (∼5·106 Pa) are an order of magnitude larger than typical controlled plating bath stresses, but as the coating thicknesses are very tiny, relative to the shell thickness, their effects are quite small. Tests at MSFC have shown that 1-micron-thick multilayers (100 bilayers), deposited on 100-micron-thick shells, have no measurable effect on the overall shell figure. To control the plating bath stress we first adjust the chemistry of the bath so that the bath stress is relatively insensitive to the plating current density. Then, using computer models of the plating bath, we fine tune the layout of shields and the bath electrodes to generate as uniform an electric field as possible along the full plated length of the mandrel. A uniform field ensures that there are no departures in plating current density that would in turn affect the stress of the plated nickel. The plating stress level necessary to distort the figure of electroformed shells is very small, about 5·105 Pa, and difficult to measure. We have, instead, optimized the plating current density by using stress measurements to get us close and then plating a series of shells each at a slightly different current value. These were then measured to give the inside shell profile and thus determine, through predictive software, which conditions gave the mirror shell with the best performance. To test this we have utilized a solid, thermally-conditioned mandrel, and plated a shell using the optimum plating conditions found above. To enable testing, but avoid spider-mountinduced errors, the shell was held at its intersection by gluing it to a support plate as shown in Figure 5 (left). The result of the x-ray test, shown in Figure 5 (right), is a half-power diameter of 11.5 arcsec at 40 keV. We can now ask, what are the factors contributing to this measured resolution ? The first of these is gravity sag. Under 1 g, the optic, supported at each end, droops slightly. Using a finite element analysis program, we estimate the (small) effect of this sag and remove it from the measured resolution. This leaves us with 11 ± 0.5 arcsec. Next, we can remove the inherent mandrel figure. The conical mandrel used to electroform this shell has a predicted performance (derived from mandrel metrology) of 8.3 arcsec at this energy. This must be Springer

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Fig. 5 Test shell mounted at its intersection (left) and the resulting x-ray point-spread distribution (right)

subtracted in quadrature from the 11 arcsec to leave us with the inherent axial figure errors imparted by the electroforming process. This is 7 arcsec. We can now turn this around and ask, if we used a top-quality Wolter-1-figure mandrel what is the best (zero-g) shell that we could expect. The best mandrels available have figure accuracies of 4 arcsec (the Con-X program procured 0.5-m-diameter mandrels from Zeiss with this specification). Applying our best electroformed-shell axial-figure quality to this, in quadrature, we could expect to fabricate mirror shells having a half-power-diameter of around 8.5 arcsec. It will be extremely challenging to improve electroformed optics much beyond this. The production of very thin shells necessitates an extremely low adherence of the plated deposit to the mandrel, otherwise large figure-distorting stresses will be imparted on the shell during separation, and this in turn necessitates a small amount of tensile stress in the plating bath to prevent the deposit from detaching from the mandrel surface during electroforming. Thus it can be expected that stress-induced figure distortions will always be present. One way to attempt to mitigate these effects is to stretch the shell material on the mandrel, to force it to more accurately conform, while simultaneously applying heat to anneal out residual stresses. We have investigated this effect with test samples and have found that both nickel and nickel/cobalt shell material can be strain hardened and take a permanent set at quite low temperatures. In practice this means simply heating the mandrel after electroforming the shell and before the shell is released. The mandrel, of course must maintain its figure at the elevated temperature. Figure 6 shows early results of this process on a small-diameter mandrel. In this figure a profile of the mandrel is shown together with the internal profile of a plated and released pure nickel shell, together with the profile of a nickel shell that was heated to 75 ◦ C on the mandrel for 48 hr before release. It is evident from this figure that slightly stretching the shell, above its microyield point where parts-per-million permanent set takes place, has forced it to conform better to the mandrel’s shape. We are investigating this thermal setting phenomenon to derive optimum temperatures and strains to apply for both pure nickel and nickel/cobalt alloys. In parallel with this we are fabricating a high-stability 23-cm-diameter mandrel on which we hope to demonstrate sub-8-arcsec HPD shells using this stretching technique in the near future. Conclusion MSFC has an ongoing development program in electroformed-nickel replication for hardx-ray optics. Over 150 shells have been fabricated for the HERO balloon program and Springer

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Fig. 6 Comparison of “stretched” and “unstretched” shells (see text)

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for Constellation-X technology development. While ‘routine’ shells have 13–15 arcsec half-power diameters (HPD), optics at the 11 arcsec level have been demonstrated and ∼8–9 arscec-level optics should be possible with good stress control and stable high-quality mandrels. Techniques for improvements beyond this, by thermal setting/stretching, are currently under investigation.

References Ramsey, B.D., Alexander, C.D., Apple, J.A., Benson, C.M., Dietz, K.L., Elsner, R.F., Engelhaupt, D., Ghosh, K.K., Kolodziejczak, J.J., O’Dell, S.L., Speegle, C.O., Swartz, D.A., Weisskopf, M.C.: First images from HERO: A hard-x-ray focusing telescope. Astrophys. J. 568, 432–435 (2002) Ramsey, B.D., Elsner, R.F., Engelhaupt, D., Gubarev, M., Kolodziejczak, J.J., O’Dell, S.L., Speegle, C.O., Weisskopf, M.C.: The Development of Hard-X-ray Optics at MSFC. SPIE 5168, 129–135 (2003) Wolter, H.: Spiegelsysteme streifenden einfalls als abbildende optiken fur Rontgenstrahlen. Physik. Ann. 10, 94–114 (1952)

Springer


Small d-spacing WC/SiC multilayers for future hard X-ray telescope designs Carsten P. Jensen · Kristin K. Madsen · Finn E. Christensen

Received: 15 November 2005 / Accepted: 29 December 2005 C Springer Science + Business Media, B.V. 2006

Abstract Multilayer coatings for reflecting hard X-rays up to 80 keV, like W/Si and Pt/C, have been studied for several years. To go to higher energies, in the range of 100 keV to 250 keV, one needs coatings with smaller d-spacings than can currently be made with these material combinations, and a lower interfacial roughness. With the new material combinations of WC/SiC the interface roughness can be reduced down to between 0.23 nm and 0.25 nm enabling bi-layer thicknesses down to 1.0 nm to reflect efficiently. The production of thinner period coatings thus enables the possibility for focusing optic designs with reasonable focal lengths and throughput up to 250 keV. Keywords Hard X-ray telescopes . Multilayer . WC/SiC

1. Introduction Over the last 20 years several very successful satellites have been flown with focusing optic for soft X-rays up to 10 keV, among these are Chandra, ROSAT, and XMM. These satellites have been using a conical approximation to a Wolter I design with total external reflection from Ir or Au, which prove inefficient above 10 keV at the graze angles that were used. By going to depth graded multilayers in a conical approximation to a Wolter I design the regime of focusing X-ray is extended to energies above 10 keV, and two balloon payloads employing multilayers have been flown to prove the concept. In 2004 the International Focusing Optics Collaboration (InFOCuS) (Ogasaka et al., 2003) flew a single replicated mirror optic with a diameter of 400 mm, deposited with Pt/C multilayers and optimized for 20 keV to 40 keV. In 2005 the High Energy Focusing Telescope (HEFT) (Harrison et al., 2000) flew three slumped glass optics each 240 mm in diameter, deposited with W/Si and optimized for 20 keV to 69 keV. Several satellite missions whose main goal is the energy band above 10 keV and below 100 keV are currently planned, and all intend to use multilayers such as NASA’s NuSTAR (Koglin

C. P. Jensen () · K. K. Madsen · F. E. Christensen Danish National Space Center, Copenhagen, Denmark e-mail: [email protected] Springer

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et al., 2004) and Constallation-X (White and Tananbaum, 2003), ESA’s XEUS (Parmar et al., 2003) and Japans NeXT (Furuzawa et al., 2003). Among proposed missions extending above 100 keV there is the High-Resolution Spectroscopic Imaging (HSI) mission (Harrison et al., 2003). The Danish National Space Center, DNSC, has for a long time been involved in the development of multilayers for hard X-ray optics, and besides having delivered all the coatings for the three HEFT optics, DNSC will also be coating the optics for NuSTAR, and are producing test coatings for XEUS and various other future high energy missions. Part of the development of multilayer coatings is the discovery and testing of new material combinations. Thus far W/Si has reigned supreme in the 20 keV to 69 keV range because of its relative low interfacial roughness and excellent stability over time, however, W has an absorption edge at 69 keV. The interface roughness of W/Si influence the limit by how small a dspacing it has been possible to produce, which influences the radius and energy of a telescope design. In this paper we will present results of a new type of multilayer coating, WC/SiC, which is both smoother than W/Si and allows for very small d-spacings. We will discuss the possibilities these properties open up in telescope design, and present a straw man design covering the energy band from 100 keV and up to 250 keV.

2. Multilayer designs Several types of thickness depth profiles are in use for multilayers; constant d-spacing, linear grading and power-law graded are among a few, each of which has their own particular area of application. In the case of a narrow band response or for multilayer coating development, the constant d-spacing thickness profile is preferred. Such a profile is described by its bilayer thickness, d = dspacer + dabsorber , the absorber thickness fraction, = dabsorber /d, and the number of bi-layers, N . For space application, a power-law graded thickness profile of the multilayer is preferred, as the gradual grading of the layers shifts the position of the first Bragg peak in such a way that a broad-band response is possible, which is needed for many astrophysical objects. The power-law thickness profile used by HEFT and to be used by NuSTAR is defined by Mao et al. (1999a), di =

a , (b + i)c

i = 1, . . . , N .

Here a, b and c are design constants, i the bi-layer number where N is next to the substrate, and thus the thickest bi-layer, dmax , is at the top of the stack and the thinnest, dmin , at the bottom. 3. Scattering theory Attenuation of the specular reflectivity as defined by Fresnels equations (Born and Wolf), where the incidence angle is equal to the exit angle, is caused by interfacial roughness/interdiffusion, σ , which is the overall width of the interfacial density profile. This can be divided into two main categories; inter-diffusion, which is the mixing of the two materials at the interface, and real roughness. The former causes absorption at the interface, while the latter is a sharp but jagged interface that causes the specular reflectivity to be reemitted at other Springer

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Fig. 1 A 2-dimentional scattering map of a sample with a constant d-spacing W/Si coating. The scatter angle, θscat , is the exit angle, θexit , minus the incidence angle, θinci , of the X-ray on the sample. The horizontal streak at θscat = 0 is the specular reflectivity and the angled streaks the transverse scans. The vertical shading strips are filter changes

angles than the incidence (Holý). At the Fresnel specular condition, these two roughnesses are indistinguishable. However, at non-specular angles it becomes possible to separate the two. There are several models describing the scattering off rough surfaces valid at different wavelength regimes. For X-rays two of the more well known are the Born Approximation and the Distorted Wave Born Approximation (DWBA) (Sinha et al., 1988). The Born Approximation is a kinematical theory and valid for graze angles much larger than the critical, and breaks down at small graze angles. Here the DWBA scalar theory works well, and treats the roughness as a perturbation of the reflectivity of an ideal surface. If the real roughness is perfectly replicated by each layer, correlated, the non-specular reflectivity will be concentrated into high intensity streaks intersecting the Bragg peaks as seen in Figure 1. If the roughness, on the other hand, is not correlated at all from layer to layer the scattered intensity will be redistributed into a uniform halo. Real stacks are a combination of both correlated, σcorr , and uncorrelated, σucorr , roughness but for W/Si there is a clear preference for correlated roughness (Madsen et al., 2004). This is also true for the other material combinations discussed in this paper W/SiC, WC/Si, and WC/SiC, and we have thus assumed the uncorrelated component to be negligible in all our modeling calculations, σucorr = 0. On this basis we define the interfacial roughness to be a combination of correlated jagged 2 1/2 roughness, σcorr , and a diffuse component, σd , such that, σtot = (σd2 + σcorr ) . Assuming that a surface is self-affine, the surface can be described in the DWBA theory by a height-height correlation function (Sinha et al., 1988) 2/ h

2 [−(|R|/ξ ) h(r − R)h(r ) = σtot e

]

.

Here the fractal exponent h is connected to the fractal dimension D = 3 − h, 0 < h < 1, and describes the jaggedness of the surface, so that h → 0 means increasing jaggedness while h = 1 is a Gaussian distribution. The correlation length ξ is the in-plane correlation length Springer

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and is assumed to be equal for all layers. In the event that there is an uncorrelated component to the roughness, each layer is described by its own correlation length and additionally a depth dependent correlation length.

4. X-ray measurements If nothing else is mentioned, the X-ray measurements are made using an in house rotating anode, which operates at 8 keV (Cu K α ). The 40 keV measurements presented were made at beam line BM5 at the European Synchrotron Radiation Facility, ESRF, in Grenoble, France. To extract the non-specular information we have performed two types of scans, specular and transverse. To illustrate these two types of scans Figure 1 shows a 2-dimensional map of a constant d-spacing coated multilayer. The horizontal intensity streak at the scatter angle, α(scat) = 0 is the specular reflection with the higher intensity peaks on the streak corresponding to the Bragg peaks. The slated lines intersecting the Bragg peaks are the transverse scans. In the specular scan the incidence angle on the sample, αinci , is equal to the exit angle from the sample, αexit , so when the sample is rotated α the detector is rotated 2α. From this reflectivity curve we can derive the overall parameters, bi-layer thickness, d, absorber fraction, , and the total combined specular roughness/inter-diffusion σ spec . The transverse scans are made through a Bragg peak in the specular scan where the incidence angle αinci = αBragg . In the transverse scan the detector is held fixed at 2 × αBragg with respect to the direct beam, while the incidence angle on the sample is scanned from αinci = 0 to αinci = 2 × αBragg . The shapes of the wings adjacent to the peak are then used to fit the parameters, h, ξ , σd and σcorr . In an ideal world the roughness from the transverse scan, σtot , should be equal to the roughness/inter-diffusion derived from the specular scan, σspec .

5. Coating procedure All the coatings are made using the coating facility at DNSC. The coating chamber was, when the coatings for this work were made, equipped with two DC magnetron sputter cathodes. The cathodes are sputtering outwards and the samples are mounted facing inwards on a rotating ring. When all other parameters are set constant during a coating, like Ar pressure and applied power to the cathodes, the thickness of the coated layers are determined by the speed by which the substrate is rotated past the cathode. A full description of the coating facility is given in Jensen et al. (2003). The materials used for sputtering in this paper are W, WC, Si, and SiC and the purity of the materials are respectively 99.95%, 99.5%, 99.999%, and 99.5%. To make Si and SiC conducting they are both doped with B, Si with 32 ppm and SiC with 6900 ppm. All the coatings are made on commercial available Si wafers that have a surface roughness of 0.25 nm. After coating the samples are wrapped in a piece of lens paper and placed in a standard laboratory conditions.

6. WC/SiC coatings For years W/Si multilayer coatings have been heavily studied as coating for astrophysics missions. It is a good baseline material combination because it can coat relatively smooth multilayers and it maintains stability over time. It is very important to have a low interface Springer

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Table 1 Roughness parameters calculated for four different multilayers with approximate the same constant d-spacing and gamma. The roughness is calculated from both reflectivity scans and from 2 + σ 2 )1/2 transverse scans from the same samples. σtot = (σcorr d Reflectivity scan d-spacing (nm)

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roughness of the multilayer coating since that increases the reflectivity of the coating and decreases the scatter. In Table 1 are shown results from four constant d-spacing multilayer coated with W/Si, W/SiC, WC/Si, and WC/SiC. They are all 10 bi-layer coatings with d-spacings around 9.5 nm and gamma around 0.37. The roughness is calculated from the specular scans, and the diffuse and sharp interfacial roughness from the transverse scans. It can be seen from the reflectivity scans, that the specular roughness, σspec , of WC/SiC is much lower than for W/Si and that there is good agreement between the roughness calculated from the specular scan, σspec , and the total roughness calculated from the transverse scan, σtot . From the transverse scan there is an explanation for the decrease of the roughness. When introducing C in one of the layers we see an increasing diffusion, σd , compared to W/Si, probable caused by diffusion of C. When C is in both materials the diffusion decreases below that for W/Si. Now the C atoms can not defuse anywhere and the spaces between the W atoms is filled out with C so the Si atoms have a harder time to diffuse anywhere. The correlated roughness, σcorr , decreases when C is introduced in either W or Si and the fractal exponent parameter, h, also decreases. So the surface gets more jagged, but its height gets smaller than the height of the smoother more Gaussian surfaces. For the correlated roughness there is not a big effect to add C to both materials compared with adding it to just one of them. For all four coatings the correlation length, ξ , are the same since all the substrates are the same standard Si wafers. We have made the same experiment on 3 mm thick float glass and here the correlation length was 900 nm independent of the multilayer material combination, indicating that the correlation length are dictated by the substrate. In order to have a good reflecting depth graded multilayer, it is important that all layers in the coating have a low roughness. The roughness as a function of the d-spacing is plotted in Figure 2 for some 30 bi-layer constant d-spacing WC/SiC coatings. It can be seen that the roughness calculated from the specular scans, σspec , are independent of the d-spacing and are between 0.23 nm and 0.25 nm. This is in good agreement with the roughness calculated from the transverse scans, σtot , except for the very thin coatings. The correlated roughness, σcorr , are independent of the d-spacing and in the range between 0.10 nm and 0.15 nm. From Figure 2 the diffusion seems to go up for coatings below 1.5 nm. When the d-spacing is about 1.0 nm the single layers are in the order of 0.5 nm and the assumption that the uncorrelated component of the roughness can be negligible is probably not correct. Unfortunately the transverse measurements of the very thin coatings so far have been background limited and a more precise analysis has not been possible. The increases in diffuse roughness for multilayer with a d-spacing below 1.5 nm are not a real effect and are also not seen in the roughness calculated from the specular scans. Springer

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In Figure 3 are shown the reflectivity and transverse scans for a 1.68 nm thick 30 bi-layer WC/SiC coating measured with both 8 keV and 40 keV. To compare the measurements they are plotted in reciprocal space with reflectivity as function of q. Except for a measuring ˚ −1 for the 40 keV data, there is a really good agreement between artifact at around 0.1 ( A) the 8 keV and 40 keV reflectivity data and the fitted curve. The fit for both the specular scan and the transverse scan were first made using the 8 keV data. Using the same parameters and only changing the energy to 40 keV the fit to the specular scan done at 40 keV was perfect. To fit the transverse scans one has to use an equipment function, which is different for the two experiments. Even though we took that into account there is a small difference in the fit to the transverse scan when using the same parameters found at 8 keV and changing the energy to 40 keV. The correlated roughness was the same for the 8 keV and the 40 keV data, Springer

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but the diffuse roughness was a little lower at 40 keV than at 8 keV. In the plot only the fitted curves to the 8 keV data are shown in order to make the plot a little easier to look at. Another important property of a multilayer is the stability over time. In Figure 4 are shown two different WC/SiC constant d-spacing multilayers measured with nine month gap in between. Both coatings, 0.8 nm d-spacing and 3.6 nm d-spacing, shows no degradation over the nine months. The transverse measurements made on WC/SiC with different d-spacings presented in this paper are all made nine month after the coatings were done.

7. Optical constants for SiC and WC To analyze the X-ray measurements of the multilayers and to model the properties at higher energies one needs to know the optical constants of the materials. It has been shown (Windt et al., 2003) that there is better agreement between theory and experiments when using measured optical constants instead of theoretical calculated for high energies. The telescope designs discussed in next section are up to 250 keV so this section will discuss the optical constants used in this paper for WC and SiC. The measured optical constants for SiC (Windt et al., 2003) are from 35 keV to180 keV and the values are by them extended to 200 keV. Figure 5 shows the measured optical constants, n and k, plotted as function of energy. At high energy both curves are very close to be flat and the figure shows the extension that is used in this paper for energy up to 250 keV. For WC there are no measured optical constants and only calculated values up to 100 keV. For W we also have the calculated values up to 100 keV and measured values up to 180 keV. Figure 6 shows a good agreement between the calculated and measured optical constants for W in the range of 35 keV and up to 100 keV, with only a small shift in k and some disagreement around the W-absorption edge at 69 keV. When comparing the calculated optical constants for W and WC it is seen that for both n and k the difference is a shift caused by the smaller mass density of WC. With this in mind the optical constants for WC up to 250 keV used in this paper are designed by shifting the measured optical constants for W with the same amount as between the calculated optical constants for W and WC and then extrapolating the shifted curve for W to 250 keV. Springer

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Fig. 6 (a, b) The thin black lines are measured optical constants, n and k, for W (Windt, 1998). The thin and thick gray lines are calculated optical constants for W and WC (Windt, 1998). The thick black lines are an extension from 100 keV and up to 250 keV for WC following the trend from the measured values (thin black line) of W. Inserted in (b), are the measured values for W and the extended values for WC multiplied by 10

8. Optimizations for a high energy telescope Telescopes using a Wolter I design employing W/Si multilayers have thus far been constrained by the smallest d-spacing it has been possible to coat, which is currently at 2.0 nm. This has placed limits on the largest radius one can reflect a given energy, and the highest possible energy that can be reflected at a fixed radius. Figure 7 illustrates the dependence of the minimum bi-layer thickness, dmin , as a function of the energy for two fixed grazing incidence angles. The energy and dmin are calculated using the refraction-corrected first order Bragg law (Mao et al., 1999b). It can be seen that since the minimum bi-layer thickness can be decreased using WC/SiC the maximum energy it is possible to reflect at the given angle increases. This in turn means that by using WC/SiC coatings one can go to larger radii at a Springer

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6

dmin (nm)

5 4 3 2 1 0 100

150

200

250

Energy (keV) Fig. 7 The minimum d-spacing necessary for reflection of a maximum energy. The numbers are calculated using refraction-corrected first order Bragg law. The black line is for a graze angle of 1.27 mrad, which with a focal length of 50 m corresponds to a radius of 0.25 m, and the gray line is for a graze angle of 1.82 mrad corresponding to a radius of 0.36 m

fixed maximum energy than has been previously possible for a W/Si coated telescope, and thus in effect increase the effective area. The optimization procedure we have employed is based on Peter Mao’s Figure of Merit, FOM, optimization code (Mao et al., 1999a), and has been run on the parallel processing machines of CACR, Caltech’s Center for Advanced Computer Research. For the chosen energy range the minimum and maximum d-spacing can be determined using refractioncorrected Bragg’s law for the first order peak, and from these the constants of the power-law profile, a and b, are uniquely determined. For a power-law profile, as described above, keeping the minimum and maximum d-spacing fixed one optimizes over the number of bilayers, N, the power-law index, c, and the WC element thickness fraction, = dwc /d. The optimization runs over increasing N, and for each N finds the optimal combination of and c. Where the FOM tops the recipe is considered optimal. We have decided to optimize for an annulus, using WC/SiC as our multilayer. We have optimized for an annulus at graze angles, α = 1.27 mrad to α = 1.82 mrad, which for a focal length of 50 m corresponds to a radius of R = 0.25 m to R = 0.36 m. The energy range is 100 keV to 250 keV and the smallest bi-layer thickness we have used is 1.3 nm as can be seen in Table 2. The length of the two mirror sections in the Wolter I design are both 0.40 m and the mirror thickness is 0.2 mm. Table 2 shows the optimized design of the annulus broken down into 4 groups. Each group contains on average of 27 mirror shells, which are coated with the same recipe. The optimization has been stopped at 1000 bi-layers to keep the total thickness of the multilayer below 2.5 µm and the numbers of layers within a range so that the coating can be done in a day. The FOM is a very flat function for such a high number of bi-layers and it is possible to decrease the numbers of bi-layers to 1000 without severely affecting the reflection. As discussed above, the optical constants of WC are currently unknown above 100 keV. To estimate the sensitivity of the design to a change in optical constants, we have calculated the optimized design for three different sets of optical constants: our estimated extrapolation and a small variation to each side. A “plus” variation with a small increase in n and a small decrease in k, and a “minus” variation with a small decrease in n and a small increase in k. Figure 8 shows the effective areas of the three designs, and illustrates the urgent need Springer

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Exp Astron (2005) 20:93–103 Table 2 Optimization results for an annulus of 0.25 m to 0.36 m coated with WC/SiC

Group

Material

R-range (m)

Dmin (nm)

Dmax (nm)

N

c

1

WC/SiC

0.25 – 0.27

1.78

6.96

1000

0.277

2

WC/SiC

0.27 – 0.30

1.63

6.36

1000

0.301

3

WC/SiC

0.30 – 0.33

1.49

5.81

1000

0.335

4

WC/SiC

0.33 – 0.36

1.36

5.31

1000

0.371

1000

2

Total effective areal (cm )

N is the number of bi-layers in the stack and c the optimized power-law index.

100

10

1 100

120

140

160

180

200

220

240

Energy (keV) Fig. 8 The black line shows the total effective area for the annulus described in Table 2 using the extrapolated optical constants for WC and SiC. A small “positive” variation of the optical constants causes the reflectivity to drop and thus the effective area. A “negative” variation has the opposite effect

for measurements of the optical constants. The “minus” variation causes the effective area to drop dramatically, while the “plus” variation increases it. In the best case there is about 100 cm2 effective area at 200 keV, and in the worst only a few cm2 . This is a factor of almost a hundred, and makes it difficult to proceed beyond the point of conceptual designs.

9. Conclusions and what to do We have in this paper presented a new material combination, WC/SiC, which – because of the very low interface roughness compared to traditional coatings for hard X-ray telescopes – can coat multilayers with d-spacing below 1.0 nm, and with an interface roughness between 0.23 nm and 0.25 nm. By comparing WC/SiC with W/Si, W/SiC, and WC/Si we have understood the mechanism that makes WC/SiC coat much smoother than W/Si. The possibility to coat such thin bi-layer thickness gives the possibilities to make a telescope design, which will have a good throughput up to 250 keV and also have a reasonable effective area. To use WC/SiC as the material combination for future telescopes seems therefore very promising, but we also show that as there are no reliable optical constants for WC above 100 keV a large uncertainty exists. It is therefore very important to measure the optical constants up to several hundreds keV before a more realistic design using WC can be made. Springer

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Acknowledgements The authors would like to thank David Lumb from ESA and Eric Ziegler from ESRF for help and measuring time for the 40 keV data.

References Born, M., Wolf, E.: Principles of Optics, Cambridge, Seventh (expanded) Edition ed (1977) Furuzawa, A., Okajima, T., Ogasaka, Y., Tamura, K., Tawara, Y., Yamashita, K.: Proc. SPIE 4851, 708 (2003) Harrison, F.A., Boggs, S.E., Bolotnikov, A., Christensen, F.E., Cook, W.R., Craig, W.W., Hailey, C.J., JimenezGarate, M., Mao, P.H., Schindler, S.E., Windt, D.L.: Proc. SPIE 4012, 693 (2000) Harrison, F.A., Boggs, S.E., Christensen, F.E., Gehrels, N., Grindlay, J.E., Chen, C.M.H., Craig, W.W., Hailey, C.J., Pinto, P., Thorsett, S.E., Tueller, J., Windt, D., Woosley, S. E.: Proc. SPIE 4851, 345 (2003) Holý, T. B.: Phys. Rev. B 49, 10668 (1994) Jensen, C.P., Madsen, K.K., Chen, H.C., Christensen, F.E., Ziegler, E.: Proc. SPIE 4851, 724 (2003) Koglin, J.E., Chen, C.M.H., Chonko, J.C., Christensen, F.E., Craig, W.W., Decker, T.R., Hailey, C.J., Harrison, F.A., Jensen, C.P., Madsen, K.K., Pivovaroff, M.J., Stern, M., Windt, D.L., Ziegler, E.: Proc. SPIE 5488, 856 (2004) Madsen, K.K., Christensen, F.E., Jensen, C.P., Ziegler, E., Craig, W.W., Gunderson, K., Koglin, J.E., Pedersen, K.: Proc. SPIE 5168, 41 (2004) Mao, P.H., Harrison, F.A., Windt, D.L., Christensen, F.E.: Applied Optics 38, 4766 (1999a) Mao, P.H., Harrison, F.A., Windt, D.L., Christensen, F.E.: Applied Optics 38, 4766 (1999b) Ogasaka, Y., Tamura, K., Okajima, T., Tawara, Y., Yamashita, K., Furuzawa, A., Haga, K., Ichimaru, S., Takahashi, S., Fukuda, S., Kito, H., Goto, A., Kato, S., Satake, H., Nomoto, K., Hamada, N., Serlemitsos, P.J., Tueller, J., Soong, Y., Chan, K.W., Owens, S.M., Berendse, F.B., Krimm, H.A., Baumgartner, W., Barthelmy, S.D., Kunieda, H., Misaki, K., Shibata, R., Mori, H., Itoh, K., Namba, Y.: Proc. SPIE 4851, 619 (2003) Parmar, A.N., Hasinger, G., Arnaud, M., Barcons, X., Barret, D., Blanchard, A., Bböhringer, H., Cappi, M., Comastri, A., Courvoisier, T., Fabian, A.C., Georgantopoulos, I., Griffiths, R., Kawai, N., Koyama, K., Makishima, K., Malaguti, P., Mason, K. O., Motch, C., Mendez, M., Ohashi, T., Paerels, F., Piro, L., Schmitt, J., van der Klis, M., Ward, M.: Proc. SPIE 4851, 304 (2003) Sinha, S.K., Sirota, E.B., Garoff, S., Stanley, H.P.: Phys. Rev. B 38, 2297 (1988) Windt, D.L.: Comput. Phys. 12, 360 (1998) White, N.E., Tananbaum, H.: Proc. SPIE 4851, 293 (2003) Windt, D.L., Donguy, S., Hailey, C.J., Koglin, J., Honkimaki, V., Ziegler, E., Christensen, F.E., Harrison, F.A.: Proc. SPIE 5168, 35 (2004)

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Design aspects of grazing angle multilayer mirrors for soft γ -rays Ernst-Jan Buis · Marco Beijersbergen · Giuseppe Vacanti · Marcos Bavdaz · David Lumb


Abstract If sensitive enough, future missions for nuclear astrophysics will be a great help in understanding supernovae explosions. In contrast to coded-mask instruments, both crystal diffraction lenses and grazing angle mirrors offer a possibility to construct a sensitive instrument to detect γ -ray lines in supernovae. We report on possible implementations of grazing angle mirrors and simulations carried out to determine their performance. Keywords Nuclear astrophysics · Multilayers · Gamma-rays

1. Introduction An efficient way to increase the sensitivity in future space-born γ -ray observatories is to use focusing optics. While the coded mask technique, such as applied on the Integral mission, is background limited, focusing optics offers the combination of a large collecting area with a small detector area. While focusing optics already have been realized using Laue lenses (Von Ballmoos et al., 2004), we discuss in this paper the design of a grazing angle multilayer optics. Grazing angle optics already have been realized for X-ray observatories, such as XMM-Newton and Chandra. With the use of multilayer coatings the reflectivity of the optics can be extended to the (soft) γ -ray regime. In particular, two nuclear lines are of interest in this regime. Firstly, the 158 keV γ -ray line is important for the study of Ni decay in supernovae. Secondly, observation of the line at 511 keV due to positron-electron annihilation is of interest for many subjects in (nuclear) astrophysics. For instance, the 511 keV line is found in supernovae and AGNs. Moreover there is an enigmatic strong source for this line in the center of our galaxy. E.-J. Buis () · M. Beijersbergen · G. Vacanti Cosine Science and Computing BV, Niels Bohrweg 11, 2333 CA Leiden, The Netherlands e-mail: [email protected] M. Bavdaz · D. Lumb Office of Advanced Concepts and Science Payloads, ESA/ESTEC Postbus 299, 2200 AG Noordwijk, The Netherlands Springer

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In this paper, we show how a γ -ray telescope would look like and we present possible implementations for telescopes optimized for observing 158 keV and 511 keV respectively. We require an effective area of about 1 m2 to reach a sensitivity which is several orders better than Integral. The outline of this paper is as follows: the next section deals with the general design parameters of a γ -ray telescope. In Section 3 we review the scattering of γ -rays on multilayers and the implementation in our software. We also discuss the material selection for multilayer coatings. Then, in the following section we present a design procedure and illustrate the design with four explicit implementations.

2. Mirror design parameters and technology For the purpose of this paper we assume a hypothetical mission making use of the optics described here, would be devoted to a survey of point sources. Such a mission would not require any imaging capability, and the telescope optics can be reduced to that of a singlecone collimator. This means that γ -rays reaching the focal plane are only reflected once. This in contrast to X-ray optics, double reflection optics can be used for γ -rays to reduce the focal length and has been investigated in Buis et al. (2004). However, such a design requires a total mirror area of more than 5000 m2 , which is deemed to be unrealistic. A general layout of γ -ray optic telescope is depicted in Figure 1. At the energies of interest the reflection or diffraction angles are small, which results in a long focal length. Already at relatively soft γ -ray energies, the focal length is such that formation flying of two spacecraft is required: one for the mirror and one for the focal-plane detector and associated electronics. Here, we only discuss the mirror spacecraft. Focusing mirrors for X-rays are produced using various technologies. An overview of the technologies is found in Beijersbergen et al. (2004). In order to get the maximum sensitivity any mirror design should aim for (i) the smallest plate scale and (ii) the smallest mirror spacing in combination with a minimum mirror thickness. The smallest plate scale is obtained with the smallest focal length. A small mirror spacing yields a small spot size on the focal plane detector and the focal plane detector should be as small as possible to reduce the number of background counts. The mirror thickness should be small to avoid aperture blocking. Hence an important parameter in the design of a γ -ray mirror is the so-called ‘aperture utility’,

Fig. 1 Schematic layout of a single-cone collimator. Various design parameters are indicated and discussed in the text.

nested mirrors

focal plane detector focal length

R0 mirror spacing mirror thickness

R1 L

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which is the fraction of the aperture which is not blocked by mechanical structure of the nests and the thickness of the mirrors. The technology to produce the γ -ray mirrors is assumed to be identical as the assembly of the XEUS mirror spacecraft. The so-called stacked mirror-plates Bavdaz et al. (2004) for the XEUS optics implies a mirror thickness of about 0.2 mm and a spacing of about 0.8 mm. According to these values for the thickness and spacing, an aperture utility of the order of 60–70% is anticipated.1 3. X-ray and γ -ray scattering on multilayers Starting point of the reflectivity calculations is the determination of the indices of refraction. The index of refraction n r for a given material is determined using the atomic form factors f 1 and f 2 using n r = 1 − ik − δ = 1 − nr0 λ2 ( f 1 + i f 2 )/(2π ),

(1)

where k and δ are the optical constants, r0 is the classical electron radius, λ is the wavelength and n the atom number density. The form factors f 1 and f 2 are obtained from photon interaction cross-sections taken from the Evaluated Photon Data Library (EPDL) Perkins and Cullen (1994) by adding the coherent effects to f 1 and the incoherent effects to f 2 . Once the atomic form factors have been determined, the reflectivity Ro can be calculated using the well-known Fresnel reflection formula. Reflection off a uniform medium, here called single-layer reflection in contrast to multilayer reflection, can be very efficient, albeit at very small grazing angles (0.03 degree at 158 keV). The models for reflection off a medium, based on a complex index of refraction from the oscillator strength and the Fresnel laws of refraction and reflection, are not verified at higher energies as well as in the X-ray regime, but seem to work in principle up to a few hundred keV Windt et al. (2004). As in the X-ray regime the index of refraction is less than 1 in combination with absorption, resulting in total external reflection. Where singlelayer mirrors are limited to γ -rays with grazing angles below or close to the critical angle for that material, multilayer mirrors can reflect the photons at much larger grazing angles. Multilayers are a form of synthetic non-uniform crystals and consist of bilayers which consist of absorbers and spacers. Each bilayer in the coating has its individual thickness which contributes to the bandwidth in reflectivity. The choice of the absorber and spacer media in a multilayer depends in first order on the optical constants. The index of refraction of the absorber medium is required to differ as much from unity as possible, whereas the index of refraction of the spacer should be close to unity. The index of refraction consists of a real and imaginary part. The imaginary part contributes to the absorption of the γ -rays, which should be small, but not too small since in principle a large imaginary part makes the index of refraction be further from unity. The X-ray reflection off uniform coating and the tracing of γ -rays through geometrical models has been included in an X-ray tracing software package, called “MSIM”. Originally the MSIM package is developed for simulation of X-ray reflections in XMM-Newton Erd et al. (1999). We have extended the energy range to γ -rays for design studies on γ -ray (imaging) missions by introducing the atomic form factors from Perkins and Cullen (1994) and reflection off a multilayer coating in the software. 1

The exact number depends on the number of nests and hence on the final geometry of the mirror. Springer

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4. Design procedure and implementation 4.1. Parameter scan The design of mirrors for γ -ray collimator yields an optimization of the following variables: 1. 2. 3. 4. 5.

γ -ray energy; grazing angle and its bandwidth; absorber and spacer material; thickness of each bilayer; fractional thickness of the absorber in the bilayer.

For several materials and at different energies we have optimized the reflectivity and the number of layers to achieve this reflectivity following the method described in Kozhevnikov et al. (2001). Once the reflectivity is known, the spacecraft layout is straightforward. The layout of the conical mirrors is done as follows. The optic has an annular aperture and the grazing angles range between α0 and α1 , the aperture has an geometrical area of A = π f 2 [tan2 (2α1 ) − tan2 (2α0 )]

(2)

so that the effective collecting area is approximately Ae = U · R · A = U Rπ f 2 [tan2 (2α1 ) − tan2 (2α0 )]

(3)

where f is the focal length, U is the aperture utility and R the reflectivity. As mentioned in Section 1, we aim for a telescope with an effective area of at least Aeff = 1 m2 . From this requirement and the determination of the mean reflectivity between the angles α0 and α1 we calculate the focal length using Equation (3). In Figure 2 we show the focal length for various points in the design parameter space. According to Equation (3) the focal length is decreased when the reflectivity is large, i.e. when the number of layers layers ion the multilayer coating

Fig. 2 Scan of the design parameter space: showing the possible values for the focal length for a W-C and a Ni-C multilayer coating (left) and the relation between the number of layers in the coating and the focal length for the W-C coating. Springer

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Table 1 Four models and their design parameters

Model

Design energy [keV]

Material

Design angles [deg]

Fractional thickness

Number of layers

I II III IV

158 158 511 511

W, C Ni, C W, C Mo, C

0.13–0.15 0.02–0.15 0.01–0.07 0.02–0.03

0.42 0.47 0.45 0.48

541 4852 4798 1419

is large. In Figure 2 (right) this relation between the number of layers and the focal length becomes apparent. Note that in any case, the focal length would not be less than 150–200 m. We have scanned the parameter space for two different energies: 158 keV and 511 keV. A scan was carried out for W-C, Ni0.93 V0.07 -C and Mo-C coatings, where the grazing angles were varied between 0.02 and 0.2 degrees and the fractional thickness between 0.1 and 0.9. Notice that, in principle, many more absorber materials can be chosen at this stage, such as Pt, Ir etc. As a spacer material, we have taken carbon in all scans. However, carbon is in practice not the most ideal material to use in a multilayer coating, in view of the obtained surface roughness. Better coatings have been produced using a mixture of carbon and silicon (SiC) as a spacer material (Jensen). But, as we shall see later, the choice of spacer materials has less impact on the optical performance of the multilayer coating, so we expected similar results with SiC as spacer material. Out of the parameter scans we have chosen four points: two models for the 158 keV mirror and two configurations for the 511 keV lens. The choice for a particular point in the parameter is mainly driven by the state of the art in multilayer coating. In general, as discussed above, the number of layers should be as large as possible. Below we discuss the four models: two for each energy of which one configuration has considerable less layers in the coating than the other. In Table 1 we list the four configurations with their design parameters. For two models, the number of layers is at least one order of magnitude higher than what have been produced to date an can be regarded as ideal case scenario. Models I and IV have multilayer coating, which are (nearly) within reach of the present technology. Figures 3 and 4 show the intensity reflectivity of the four configurations. In addition, the layer thickness distribution is shown. The plots show the relation between the number layers and the reflectivity of the coating: a

Fig. 3 Reflectivity (left) and layers thickness distribution (right). Springer

1 0.9

model III: W/C;

0.8

Edesign = 511 keV

model IV: Mo/C; E design = 511 keV

0.7 0.6

layer thickness [nm]

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reflectivity

110 5 4.5

model III: W/C; Edesign= 511 keV

4 model IV: Mo/C; Edesign= 511 keV

3.5 3 2.5

0.5 0.4

2

0.3

1.5

0.2

1

0.1

0.5

0

0.05

0.1

0.15 0.2 grazing angle [deg]

1000

2000

3000

4000 5000 layer number

Fig. 4 Reflectivity (left) and layers thickness distribution (right).

n = 1 - ik - δ change δ in W

1.2

change k in W change δ in C change k in C

1.1

1

relative change in reflectivity

relative change in reflectivity

n = 1 - ik - δ

change δ of Ni.93V.07

1.2

.93

change δ of C change k of C

1.1

1

0.9

0.9

0.8

0.8 0.8

0.9

1 1.1 1.2 change in optical constant

change k of Ni V.07

0.8

0.9

1 1.1 1.2 change in optical constant

Fig. 5 Relative change in the reflectivity as function of the relative change in the optical constants for model I (left) and model II (right).

high angular bandwidth is reach with a large number of layers. Moreover, a high reflectivity is found at lower grazing angles. In Figure 5 the relative change in the reflectivity as function of the relative change in the index of refraction is shown for model I and model II. The reflectivity in both models is mostly sensitive to the optical constant δ of the absorber material. The reflectivity in model II is in addition sensitive to δ in the spacer material, mainly due to the larger number of layers in this model. The figure shows the robustness of the results presented in this paper against the uncertainty of the optical constant at larger energies. For model I and IV in particular, the choice of the spacer material is not that crucial. 4.2. Mirror spacecraft layout To determine the on and off-axis response, we have constructed geometrical models in the MSIM package according the design parameters as listed in Table 2. A geometrical view is shown in Figure 6. Because the mirror space is fixed, the lengths of all nest in the geometry Springer

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Table 2 Relevant parameters for various geometries for mirror spacecraft for a γ -ray observatory Model

Focal length [m]

Radii of annulus [m]

Number of nests

Mirror area [m2 ]

I II III IV

372.5 189.1 384.6 833.5

1.69–1.95 0.132–0.990 0.134–0.940 0.582–0.873

261 859 806 291

978 1633 3116 2438

Fig. 6 Three dimensional view of two mirror spacecraft models: model I for 158 keV (left) and model III for 511 keV (right). The geometry of model I is a ring structure with large radii of annulus. The optical axis of the system is perpendicular to the ring. For model III, the inner most nest has a much smaller radius than the outer most nest as in contrast to model I. Therefore the shape of this mirror system is much different than the shape from model I.

are different Moreover, the difference in length of the nests in the telescope is proportional to the difference in the radii of annulus2 : for model I the inner most nest is twice as long as the outer nest, while for model III the inner nest is about seven times longer. The total area mirror area is less than or in the order of 3000 m2 , which is the design value for the planned XEUS mission. 4.3. Effective area and vignetting The effective area curves for models I and II (158 keV) and for models III and IV (511 keV) are plotted in Figure 7. The effective area is close to the initial requirement of an effective area of 1 m2 . Note that the blocking of the mirror thickness is included, but the blocking due to the mechanical structure is not. This will reduce the effective area as shown in the figures by about 20%. The decrease of the effective area due to surface roughness is included in the calculations. The surface roughness is represented by a Debye-Waller factor and a target value for future ˚ Surface roughnesses as low a 2.3 A ˚ have already been missions should be around 2 A. achieved for WC/SiC coatings (Jensen). From the graphs it can be concluded that the bandwidth of the model is closely related to the number of layers. The design driver is therefore the number of layers in the coating. The vignetting curves show a quite large FOV for the optics spacecraft. However, in practice, 2

The radii of annulus are defined as the radii of the inner most and outer most mirror nest. Springer

2

2

off-axis eff. area [m ]

Exp Astron (2005) 20:105–113 on-axis eff. area [m ]

112

1.4

Edesign=158 keV Ni/C; σ = 0 Å

1.2

Ni/C; σ = 1 Å Ni/C; σ = 2 Å

1

W/C; σ = 0 Å

0.8

W/C; σ = 2 Å

W/C; σ = 1 Å

1.4

Ni/C; σ = 2 Å W/C; σ = 1 Å

0.4

0.2

0.2

300

400

500

W/C; σ = 0 Å W/C; σ = 2 Å

0.8

0.4

200

Ni/C; σ = 1 Å

1

0.6

100

Ni/C; σ = 0 Å

1.2

0.6

0

Edesign=158 keV

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 o incoming angle θ [ ]

600 700 Energy [keV]

(a)

(b)

Mo/C; σ = 2 Å W/C; σ = 0 Å

1.2

W/C; σ = 1 Å W/C; σ = 2 Å

2

Mo/C; σ = 1 Å

1.4

off-axis eff. area [m ]

Mo/C; σ = 0 Å

2

on-axis eff. area [m ]

Edesign=511 keV

1.4

Edesign=511 keV Mo/C; σ = 0 Å

1.2

Mo/C; σ = 1 Å Mo/C; σ = 2 Å

1

W/C; σ = 0 Å

0.8

0.8

W/C; σ = 2 Å

0.6

0.6

0.4

0.4

0.2

0.2

1

0

100

200

300

400

500

(c)

600 700 Energy [keV]

W/C; σ = 1 Å

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 o incoming angle θ [ ]

(d)

Fig. 7 Effective area (on-axis) as a function of the γ -ray energy (left) and the off-axis effective area at a fixed energy (right). Note that the incoming angle is the defined here as the angle of the gamma-ray w. r. t. the optical axis of the mirror system, and should not be confused with the grazing angle.

the FOV of the telescope will determine by the size of the focal plane detector: the optics suffers severe coma. To reconstruct the coma unpractical large focal plane detectors would be needed.

5. Summary and conclusions In this paper we have discussed the design of a multilayer coated γ -ray mirror for nuclear astrophysics. We have reviewed the reflectivity of γ -rays off multilayers. Using the reflectivity we have scanned a parameter space, consisting of the most relevant design parameters such as grazing angle and multilayer thickness distributions. For various materials we have constructed a geometrical model optimized to reflect 158 keV and 511 keV γ -rays. The initial requirement of a effective aperture of 1 m2 can be met and for γ -ray telescope optimized for the 158 keV line this is within the reach of current technologies. In comparison with the planned XEUS mission, the mirror area and the number of nests is not unrealistic. The main Springer

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challenge of a multilayer mirror is the number of layers in the coating. Preferably this number ˚ should be somewhere between 1000 and 5000, with a surface roughness of no more than 2 A.

References Buis, E.J. et al.: Proceedings of the SPIE 5488, 691–699 (2004) Beijersbergen, M., et al.: Proceedings of the SPIE 5488, 868–874 (2004) Bavdaz, M., et al.: Proceedings of the SPIE 5488, 829–836 (2004) Erd, C., et al.: in Mehringer D.M. (eds.), Astronomical Data Analysis Software and Systems VIII ASP Conference Series 172, 119–123 (1999) Jensen, C.: (2006), DOI: 10.1007/s10686-006-9022-9 Kozhevnikov, I.V., et al.: Nucl. Instr. Meth. A A 406, p. 424 (2001) Perkins, S.T., Cullen, D.E.: ‘ENDL type formats for the LLNL Evaluated Atomic Data Library, EADL, for the Evaluated Electron Data Library, EEDL, and for the Evaluated Photon Data Library, EPDL’ (1994) Von Ballmoos, P.V., et al.: New Astronomy Review 48, 243–249 (2004) Windt, D.L., et al.: Proceedings of the SPIE 5168, 35–40 (2004)

Springer

Exp Astron (2005) 20:115–120 DOI 10.1007/s10686-006-9032-7

Progress toward light weight high angular resolution multilayer coated optics M. P. Ulmer · M. E. Graham · S. Vaynman · J. Echt · M. Farber · S. Ehlert · S. Varlese


Abstract We have been working on 3 separate projects that together will give us the ability to make 1 arc second, light weight Wolter I optics that work above 40 keV. The three separate tasks are: (a) plasma spraying of metal-coated micro-balloons; (b) coating of the inside of Wolter I mirrors, (c) actuator designs for improving figure quality. We give a progress report on our work on all three areas. Keywords X- and gamma-ray Telescopes · X-ray · Gamma-ray 1. Introduction The community knows how to coat functional multilayers on surfaces to enhance the hard X-ray (10 keV) reflectivity, and the community knows how to make sub-arc second X-ray optics. There would be little difficulty in carrying out this approach if money were no object. For example, 10 m focal length Chandra-like mirrors (see Figure 1) could be made and over-coated with graded d-spacing multilayers (Jimenez-Garate et al., 2000; Ulmer et al., 2002). The difficulty comes in trying significantly to reduce the cost of the X-ray mission. This involves reducing the cost of fabrication of the optics as well as reducing the mass of the optic and the optical bench. The mass of the optical bench and satellite can be reduced both by reducing the mass of the X-ray optics and by keeping the requirement of the focal

M. P. Ulmer () Department of Physics and Astronomy, Northwestern University, 2131 Tech Drive, Evanston, IL 60208-2900 e-mail: [email protected] M. E. Graham · S. Vaynman · J. Echt Department of Materials Science, Northwestern University M. Farber · S. Ehlert Department of Physics and Astronomy, Northwestern University S. Varlese Ball Aerospace and Technologies Corp Springer

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Fig. 1 The largest AXAF (now Chandra) hyperboloid undergoing final inspection at Hughes Danbury Optical (now Goodrich).

length flexible so as to meet the rocket fairing constraints. We have been addressing these new requirements by a three pronged approach: (a) making light weight optics by improving the value of the mirror material stiffness to mass ratio; (b) depositing multilayers on the inside of electroformed mirrors that are too small to have direct deposition on the inside; (3) actuator designs to modify the shape of the mirror after fabrication. The last point is key to achieve 1

or better angular resolution, as inherent stress in replicated optics has prevented better than approximately 10

half power diameter image quality (see Ref. Aschenbach (2002)). This paper is mostly a summary of previously reported work that touched on technology to reduce weight, to improve figure quality, and to coat the inside of electroformed Ni shells. We also give a summary of new work done at the Argonne National Laboratory Advanced Photon Source (ANL/APS). 2. Light weight optics We are using plasma spraying (Ulmer et al., 2002, 2003; Citterio et al., 2002; Hudec et al., 2003) to make light weight X-ray mirrors. Hollow micro-spheres made of glass or ceramic are precoated with Ni prior to being sprayed onto the backside of the initial electroformed nickel layer that replicates the mandrel surface. Thus, a low density layer is produced that, with the inclusion of another layer of Ni on top of the plasma sprayed surface, increases the stiffness and strength of the resulting shell. This lamination process is the unique feature of our approach compared to other published approaches. We have made some encouraging progress, as shown in Figure 2. The image on the left shows a flat with negligible stress. Optical profiler measurements show that the deviation from flat of 1/3 (λ, 600 nm) and smoothness as good as the master which was of 5.5 nm on the 10–100 µm length scale. The top Ni layer as seen in the figure is 140 µm thick and the total thickness is 400 µm, which translates into an areal density of 2 kg/m2 . This sample was dipped in liquid nitrogen with no discernible degradation in figure quality. The next step is to work a scale up to 10 cm diameter cylinders, and we have NASA Small Business Technology TRansfer (STTR) funding to extend this work. The requirement is to be able to make mirrors that are lighter weight than those that can be made out of pure Ni. This means that for about a 10 cm diameter mirror the net (the inner and outer layers combined) width of Ni width should be less than 80 µm. Preventing print through from the sprayed particle impact on the thin Ni replication layer as well as dealing with the potential stresses set up by the heat of the plasma spray (hot enough to melt Ni or ∼1,400 C) can be challenging. To alleviate the print through, we use Springer

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Fig. 2 Left, a laminate of Ni and microspheres; right a pipe shaped laminate on top of a flat made from the same microspheres. The flat has been made by a scintering process, and then treated by us to make smooth surface seen in reflection.

small mass (∼20–90 µm diameter) beads which have minimal momentum when sprayed. To minimize the stress, we keep the mandrel temperature below 100C during spraying. The payoff is the possibility of making optics with better figure quality than has been done to date with light weight glass segmented optics (Zhang et al., 2005). The plasma-sprayed laminates made by us have had about one half the coefficient of thermal expansion of pure Ni, which helps in maintaining figure control when temperature fluctuations or gradients can exist. 3. Multilayers There are several groups (e.g. Hudec et al., 2005; Jimenez-Garate et al., 2000; Pareschi et al., 2005; Romaine et al., 2005; Ulmer et al., 2003; Zhang et al., 2005) that are fabricating mirrors for hard X-ray astronomy. Our group is the only one that uses CNx to coat and smooth the mandrel (see Ulmer et al. (2003) and references therein), but the multilayer coating process we developed has been copied by at least one other group (i.e. Pareschi et al., 2005). This process is to coat a mandrel with multilayer, electroform over these layers, and then remove the electroformed multilayers with layers intact on the inside of the mirror. We used Cu as release layer that can then be removed without harming the multilayers as we have shown in Ulmer et al. (2003), and we repeat the main results from that work here. We show that the layers’ performance matches the same model for both 10 keV and 30 keV, which demonstrated the layers are intact both near the surface and significantly below the surface. We rotated the mirror and were able to achieve the same performance which demonstrated the layers were uniform around the circumference of the mirror.

Fig. 3 The data are in bold white, the best fits in dashed purple. The same model for the multilayers was used in all cases; we accumulated the two 10 keV data sets from a 90 before and after a 90 degree rotation of the mirror about its optical axis. Springer

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Fig. 4 Left image of a Ti-L line at 0.45 keV source 20 m from the mirror out of focus by 71 mm; pixel size 16 µm, 1.

47/pixel, image frame 512 × 576. Right, a 7 keV composite image from the APS slightly out of focus; see text.

4. Characterization of figure distortion and possible remediation A major drawback to all the current replication processes of making X-ray mirrors is that the best a replication process has achieved is ∼10

(see Aschenbach, 2002).This is not good enough for certain applications such as solar physics where approximately a factor of 10 improvement in angular resolution is needed (i.e., 1

). The major reason for the limitation to the angular resolution of replicated optics is that distorting stresses are built up in the mirror walls during the replication process. The application of restoring forces by judiciously designed actuators, however, may make it possible to reach an angular resolution of 1

or better. Therefore, our group has embarked upon a proof-of-concept study which, in “phase 1,” was simply to acquire data to model the deformations in the mirror and to carry out preliminary designs for the application of actuators. We present a small portion of our previous work (Ulmer et al., 2004) here along with new work. We show images in Figure 4 which we made to demonstrate simply that: (a) it is valuable to make out-of-focus images so the X-ray mirror azimuthal response can be examined; and, (b) we probably can use the ANL/APS within a 1 hour drive of the Northwestern University campus for X-ray measurements before using the much more extensive facilities used to calibrate the Chandra and XMM-Newton X-ray telescopes. The left image in Figure 4 was taken at the Lockheed Martin Advanced Technology Center Lockheed Martin Solar and Astrophysics Laboratory (LMATC/LMSAL) facility in Palo Alto. The later image was taken at the APS on the UNI-Cat 33 BM-C beam line. As the LMATC/LMSAL results have discussed in detail before (see Ulmer et al., 2004), we only discuss the ANL/APS measurements in this paper. The ANL/APS beam line we used was UNI-CAT 33BM-C beam line. The energy range we used was 7 keV. As the absorption is significant in air over the path length of about 4 meters total, and the CCD/phosphor camera we used in not very efficient (less than 1%), we placed He filled tubes in the air path of the X-ray beam. The beam was just wide enough in the horizontal direction (11.2 cm) to hit both sides of the front face of the mirror simultaneously. In the vertical direction, the beam was 1 mm wide. The beam emulates a nearly parallel beam with a divergence in the horizontal direction equivalent to a point source at 50 m. To produce the right hand image shown in Figure 4, we purposely tried to put the mirror out of focus to produce an image similar to that we obtained at the LMATC/LMSAL facility. The mirror we used was apparently deformed such that the initial out-of-focus image became nearly focused as we rotated the mirror about its optical axis. We estimate that the deformity corresponds to a change in graze angle slope of about 1 in both parts of the Wolter 1 mirror. Springer

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Such a slope deviation could be caused by a net deviation in radius of about 60 µm in each of the parabolic and hyperbolic 20 cm long sections of the Wolter I mirror. The effect of this deformation was that after we rotated the mirror and were committed to making a full 360 degree rotation about the optical axis, we found that most (all but 6 of 36) of the mirror orientations were actually nearly in focus at the separation distance (210 cm) between the parabola/hyperbola intersection portion of the mirror and the CCD camera. A lesson learned for further work is to allocate enough time to be sure we can take a set of measurements at more than one separation distance such as was done at the LMATC/LMSAL facility (see Ulmer et al. (2004)). The one drawback to working at the ANL/APS and at 7 keV versus 0.45 keV is that for mirrors that are not exceptionally smooth (e.g., 8

N (x) = 144725 + 15706.9297x − 73.034996x 2 − 33.49237x 3 + 1.30278x 4 − 0.0081205x 5 D(x) = 144725 + 27781.8340x + 1779.3622x 2 + 39.6246x 3 + 0.323458x 4 + 0.0087508x 5 P(x) = 1.0 − 0.015928x + 0.00334056x 2 − 0.00309143x 3 + 0.00172450x 4 Q(x) = 0.0781342 − 0.0050871x + 0.0010301x 2 − 0.0000876611x 3 + 0.0000806711x 4

(29) Springer

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Exp Astron (2005) 20:151–170 Table 3 Extinction length in µm at 293 K and 500 keV for various elements

Copper Silicon Germanium Gold

111

200

220

222

311

331

333

400

78.82 395.6 169.1 37.6

85

109.1 342.6 139.7 46.4

133.8

127.6 521.8 212.1 51.2

178.5 612.1 249.7 63.5

230.6 708.2 288.5 75.7

159.1 408.8 166.8 58.9

39.5

52.8

Finally, in the intermediate regime and considering an unpolarized beam, Equation (10) for the integrated reflectivity is always valid by replacing Q with Q defined as follows (in Laue geometry) [10]: Q =

I0 (2A0 ) + | cos 2θi |I0 (2A0 | cos 2θi |) Q 2A0 (1 + cos2 2θi )

A0 =

A t0 = K cos θi text

(30)

Given the small incident angles of X and γ rays: Q ≈

I0 (2A0 ) I0 (2A0 ) dhkl Q≈ 2 2A0 2A0 text

≈ 3.4939

˚ I0 (2A0 ) dhkl ( A) |Fs |cm−1 2t0 (E(keV)Vc ( A ˚ 3 ))

(31)

These equations clearly show that the integrated reflectivity per unit of length decreases when the blocks’ thickness increases. Since the “mosaic” crystals are a conglomerate of such crystallites, one should keep their size t0 as small as possible. Unfortunately, the thickness of the crystallites depends on the growing process and this parameter appears difficult to control. The extinction length is therefore the transition thickness from “thin” to “thick” crystals. For a given material and diffraction plane, the extinction length is proportional to the energy. Thus, a crystal which is “thick” at low energy may become “thin” (and so better) at higher energy. The Table 3 gives the extinction length for some materials and diffracting planes at 500 keV and 293 K (Debye factor). A simple proportional factor applies for any other energy.

5. Macroscopic crystals: The Darwin model According to the previous section, the integrated power of a “perfect” crystal saturates after a few tenth of mm, due to the extinction effect. Nevertheless, the measurements performed on “real” macroscopic crystals (of thickness T0 ) can be explained neither by the kinematical nor by the dynamical model of a “perfect” crystal. Actually, the angular (or energy) acceptance can be relatively large (up to a few degrees), and the integrated reflectivity is much higher than expected from a perfect crystal with a thickness T0 text . Darwin (see [10, 13–15]) proposed that a macroscopic crystal is actually an agglomerate of small, perfect crystals. The angular orientation of these small crystals is randomly distributed (see Figure 3). Thus, the diffracted beams from the individual crystals blocks do not interfere and the extinction effect Springer

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Fig. 3 Scheme of a mosaic crystal

(mostly) cancels out. This mosaic model is defined through the angular distribution of the crystallites W (∆) (where ∆ is the orientation of the block) and their mean thickness (t0 ). Usually, the angular spread is projected on a given diffraction plane, and is assumed to be normally distributed: 2 1 − W ( ) = √ e 2η2 2πη

(32)

√ The mosaicity is then the FWHM of this distribution: m = 2 2 ln 2η. Another assumption of the mosaic model is that the mosaicity is much bigger than the angular reflectivity range of a single crystal. This assumption is usually valid for mosaicities above ≈ 10

. In this case, the reflectivity power of a layer of thickness t0 is given by R ≈ W (θ − θ B )Rm where θ is the incident angle of the beam, θ B is the Bragg angle corresponding to the beam energy and the mean orientation of the diffraction planes, Rm is from Equation (10). σ is then defined as the integrated reflectivity per unit of length: σ = W (θ − θb )Rm /t0 . In case of crystallites of negligible size (i.e. smaller than the extinction length, t0 text ), the crystal is “ideally imperfect”, corresponding to the optimum reflectivity that can be obtained according to the Darwin model. Otherwise, the extinction effect (see Section 4.1) should be taken into account. So, using the appropriate expression for Q, depending on the mean thickness t0 (Equation (6) or (30)), one obtains: cos θ B σ ≈ σ ≈

W (θ B − θ)Q,

if t0 text

W (θ B − θ)Q ,

otherwise

(33)

When propagating through the crystal, the beam can be absorbed (linear absorption µ) or diffracted (σ ). Additionally, assuming the crystal to be homogeneous, the diffraction probability is the same from the incident to the diffracted direction, or vice versa. So, defining P0 (T ), resp. P(T ), as the power (or intensity) of the beam in the incident, resp. diffracted, direction at the depth T , the following set of differential equations follows (in Laue geometry) [10]: µ + σ P0 dT + σ PdT cos θ µ + σ PdT + σ P0 dT dP = − cos θ P0 (T = 0) = P0 (0), P(T = 0) = 0 dP0 = −

(34a) (34b) (34c) Springer

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which leads to: T0 µ 1 P(T0 ) = sinh(σ T0 )e−( cos θ +σ )T0 = (1 − e−2σ T0 )e−µ cos θ P0 (0) 2

(35)

T0 µ 1 P0 (T0 ) = cosh(σ T0 )e−( cos θ +σ )T0 = (1 + e−2σ T0 )e−µ cos θ P0 (0) 2

(36)

Usually, the Bragg angle is small and so: P(T0 ) ≈ sinh(σ T0 )e−(µ+σ )T0 P0 (0) ≈

1 (1 − e−2σ T0 )e−µT0 2

(37)

Formula 37, along with Equation 33, is of constant use to estimate the diffraction efficiency of a mosaic crystal, and by extension, the efficiency of a Laue lens. There are usually two kinds of experiments performed in the laboratory to measure the reflectivity of a mosaic crystal: – The incident beam is monochromatic (θ B is constant) and we consider the variation of the reflectivity while changing the orientation (angle θ) of the crystal. This method, called a rocking curve, is adequate to precisely measure the reflectivity function, since the variation in θ doesn’t influence any other parameter. – The position of the crystal is fixed (θ is constant), and the variation of reflectivity with the energy of the beam (variation of θ B ) is measured. In this case, the diffracted spectrum peaks at the energy E 0 that satisfies the Bragg relation for the mean plane orientation (λ0 = 2dhkl sin θ0 ). Besides, there are also 2nd order variations on µ and Q. These variations can be neglected if the diffracted energy bandwidth is small compared to the mean energy (i.e

E E 0 ) and the two experiments are then almost equivalent. 5.1. Some properties of the diffraction curve In this section, the orientation of the crystallites is assumed to be normally distributed: W ( θ ) = 2

ln(2) 1 − ln(2) e π m

θ m/2

2

,

(38)

Then, considering Equation (37), it is useful to define the following dimensionless parameters: α=4

ln(2) dhkl T0 , 2 π text m

u=

θ m/2

(39)

With these reduced parameters, the reflectivity curve has the form (see also Figure 4): 1 P(T0 ) − ln(2)u 2 e−µT0 , = 1 − e−αe P0 (0) 2

(40)

As previously mentioned, in the case of measurements with a constant incident angle but a variable wavelength, the variation of Q and µ in the diffracted energy bandwidth can usually Springer

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1

α = 0,1 α=1 α=5

0.8

0.6

0.4

0.2

0 0

1

2

3

4

5

2∆θ/m

Fig. 4 Normalized reflectivity curves for different values of α

be neglected. With this assumption, the FWHM and maximum of the diffraction curve are given by:

u FWHM = 2

P(T0 ) P0 (0)

= max

− ln −

P(T0 ) P0 (0)

1 α

ln 12 1 + e−α ln(2) =

u=0

1 (1 − e−α )e−µT0 2

(41a) (41b)

From these equations, one can demonstrate that u FWHM > 2 (i.e θFWHM > m) whatever the value of α. In other words, the FWHM of the rocking curve is always greater than the mosaicity. Additionally, it tends to the normal angular distribution of the crystallites for α → 0. More precisely, the Taylor series expansion around α = 0 of the diffraction curve and its FWHM gives: +∞ P(T0 ) 1 e−k ln(2)u k = (−1)k−1 α P0 (0) 2 k=1 k! α 1 α ≈ 2 1+ 1+ 1− 8 ln(2) 16 ln(2) 8 ln(2) 2

u FWHM

(42)

(43)

It is also often desirable to calculate the total flux diffracted by a crystal, i.e the integration 0) of PP(T over θ (or λ). Unfortunately, this integration cannot be done analytically, but an 0 (T0 ) good approximation can be obtained by multiplying the FWHM of the diffraction curve with Springer

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its maximum amplitude. Mathematically, this means: Ru (α) = ≈ Rθ = ≈ ≈ Rλ = ≈

+∞

1 ln(2)u 2 1 − e−αe du −∞ 2 − ln − α1 ln 12 1 + e−α −α (1 − e ) ln(2) +∞ P(T0 ) d θ P 0 (T0 ) −∞ +∞ 1 m −µ − ln(2)u 2 e T0 1 − e−αe du 2 −∞ 2 m u ln(2) Ru (α) −µT0 R (α)e−µT0 = 2 QT0 e 2 π α +∞ P(T0 ) dλ ≈ 2dhkl Rθ −∞ P0 (T0 ) ln(2) Ru (α) −µT0 QT0 dhkl e dhklm Ru (α)e−µT0 = 4 , π α

(44)

where the upper indexes indicate the integration parameter (θ, λ or µ). Ru is dimensionless but this is not the case of Rθ and Rλ which are, respectively, the integrated flux considering a rocking curve or a continuum energy emission, and are consequently expressed in photons(/s). So, m should be expressed in arcseconds in Rθ if the incident flux is in photons/arcsec (we are only interested in the projection of the incident flux in the meridian plane). In Rλ , m should be expressed in radians (since it indirectly comes from the linearization of the Bragg ˚ if the incident, polychromatic flux is in (or converted to, using the relation) and dhkl in A 2 ˚ E 0 / hc factor) photons/ A. The validity of this approximation can be checked on Figure 5, where the numerical and approximated values of Ru (α) and Ru (α)/α are plotted. This approximation is also used and compared with a MC simulation of a broad band Laue lens in a accompanying article ([3], this volume). Alternatively, integrating the Taylor series of the diffraction curve (see Equation (42)) u − ln(2)u 2 gives the expansion of 0 21 (1 − e−αe ) dv :

u

Fα (u) = 0

=

1 4

1 − ln(2)u 2 dv 1 − e−αe 2

√ +∞ π erf( k ln(2)u) k α (−1)k−1 √ ln(2) k=1 kk!

(45)

From this equation, the Taylor series expansion of the integrated reflectivity (Ru (α) = 2Fα (∞)) follows: Ru (α) = Springer

1 2

+∞ π (−1)k−1 k α √ ln(2) k=1 kk!

(46a)

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2 Norm. integrated reflectivity Peak * Width α Peak * Width / α

Normalised integrated reflectivity

1.5

1

0.5

0 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

α

Fig. 5 Normalized integrated reflectivity (without absorption) of a mosaic crystal. Crosses represent the numerical integration, the dot line is the approximated analytical model

The above equations (see also Figure 5) demonstrate that Ru (α)/α decreases with α and Ru (α)/α ≈ 1 if α 1. This means that the integrated reflectivity, for a given thickness T0 , asymptotically increases with the mosaicity, approaching a constant value if m 2dthkl2 T0 . ext This condition is not always satisfied though. Especially, the parameters optimization can 2 t . often lead to values for which Tm0 ≈ dext hkl 6. Crystal optimization strategies To get an idea of the “best” parameters of a mosaic crystal, let now try to “optimize” the reflectivity of a single crystal. In the context of the Darwin model, two parameters can eventually be optimized to non trivial values: the mosaicity and the thickness. The size of the crystallites (t0 ) should be much smaller than the extinction length (see Section4.1), so that the extinction effect is negligible. This latter condition is assumed to be satisfied in the following sections. 6.1. Maximum peak reflectivity for a given mosaicity The mosaicity of a crystal is often set by “external” constraints (e.g the growing process or the energy resolution of the detector in case of a line observation). In that case, optimizing the peak reflectivity (see Equation (41)) leads to the following thickness:

peak Tmax

dhkl ln 1 + 4 ln(2) 2 π mtext = , dhkl 4 ln(2) π mt 2

(47)

ext

Springer

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Since ln(1 + x)/x is always between 0 and 1 for x > 0, the optimal thickness is always peak smaller than the mean free path 1/µ, whatever the mosaicity m. Moreover, Tmax increases 2dhkl with m and tends to 1/µ if m t 2 µ . ext Since the width of the diffracted peak increases with the crystal thickness, the optimal significance (taking into account the background noise in the diffracted bandwidth) could peak lead to a slightly different value of T0 (see below), smaller than Tmax . 6.2. Detection optimization for a broad band emission Here, we assume that both mosaicity and crystal thickness are free parameters. The optimization criterion is the detection significance in the energy bandwidth of the crystal. According to the approximation of Equation (44), the signal is proportional to: PS ∝ m f (α) g(α)e−µT ,

(48)

where: 1 (1 − e−α ) 2 ln 12 (1 + e−α ) g(α) = − ln − α f (α) =

Besides, the background level can be estimated by integrating its flux over the diffracted FWHM. Thus, the detection significance (background dominated and assuming Poisson statistics) is proportional to: n σ ∝ f (α) m g(α)e−µT

(49)

The maximization of n σ , w.r.t the mosaicity m and to the thickness T0 can be performed analytically and leads to: σ Tmax =

1 2µ

m σmax = 0.57414

dhkl 1 ∝ 2 2 E µtext

(50)

In that case, it is worth noticing that the optimal thickness only depends on the material and diffracted energy, being half the mean free path, but not on the diffracting plane. Moreover, using this optimal mosaicity as an input for the peak reflectivity maximization procedure peak σ of the precedent section gives Tmax ≈ 1.18485.Tmax , which confirms that the significance optimization leads to thinner crystals than the peak efficiency optimization. The optimization criterion is nevertheless quite flat around the optimum (in both cases) and, consequently, even significant departure from optimal parameters (especially concerning the thickness) only slightly affects the “quality” of the crystal. In practice, other constraints affect the optimal parameters. First, experiments showed that the mean crystallites’ size is correlated with the mosaicity: the mosaicity is due to the dislocation density inside the crystal. Hence, the smaller the mosaicity, the bigger the mean Springer

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thickness of the perfect crystal blocks. Second, the flatness of the optimum may lead to choose thinner crystal in order to save mass budget and/or increase the number of tiles.

7. Diffraction by an extended crystal Up to now, the radial extension of the crystal has been neglected. This is obviously not always valid in practice. Actually, if the source is at finite distance from the crystal, the incident angle, and hence the diffracted energy, depends on the impact radius. Since the mosaicity represents the angular width over which a crystal “line” reflects a monochromatic beam, the radial extension of the crystal is negligible only if the angular size of the crystal (as seen from the source) is small compared to the mosaicity. Given a radial crystal size of 1 cm and a mosaicity of 1 arcmin, this means a source distance greater than 34 m! This condition may be hard to achieve in laboratory experiments, unless a small slit is mounted in front of the crystal, which may then reduce too much the diffracted flux. Nevertheless, some crystal properties can be derived from experiments with an extended crystal and a source at finite distance. Consider the experimental setup represented in Figure 6: a crystal with a radial extension of 2 r is mounted at a distance D of a source S. The detector is placed at the symmetrical point S , or at any other place so that the diffracted flux is totally intercepted (but not the direct beam). Moreover the source is assumed to be isotropic, with an intensity I0 . Two different cases are discussed hereafter: a monochromatic or a continuum source. Besides, the angular distribution of the crystallites is assumed to be Gaussian. 7.1. Monochromatic source In that case, the incoming intensity, projected on the meridian plane is given by I0 in units of ph · s−1 · cm−1 . I0 is non-zero only for a given wavelength (λ0 ). If θm is the incident angle on the middle of the crystal, then the incident angle at the radius r (varying from − r to r ) is given by: θ = θm + θ , where θ ≈ r/D. Following the approach given in Section 5.1, let us define the reduced parameters:

um =

θ B − θm , m/2

ur =

θ r = , m/2 Dm /2

u r =

r , Dm /2

(51)

Fig. 6 Diffraction of an extended crystal and a source at finite distance Springer

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where θ B is the Bragg angle for the incident energy (λ0 ). With these notations and using the definition of Fα from Equation (45), the diffracted intensity is given by: Idiff = =

Dm 2

+ u r

− u r

1 − ln(2)(u r −u m )2 1 − e−αe du r e−µT0 I0 2

Dm (Fα ( u r − u m ) + Fα ( u r + u m ))e−µT0 I0 2

(52)

If the source is close enough and the crystal correctly oriented, then the crystal’s mosaicity is much smaller than its angular size and the reflectivity curve can be integrated over the full angular range. Mathematically, these conditions are: ⎧

r ⎪ ⎨ u r − u m 1 ⇔ − (θ B − θm ) D ⎪ ⎩ u r + u m 1 ⇔ r + (θ B − θm ) D

m 2 m 2

(53)

In that case, the diffracted intensity (in · ph s−1 ) is given by Idiff = D R θ I0 , where Rθ is from Equation (44). The diffraction efficiency is then: Mono =

Idiff D θ = R , 2I0 r 2 r

(54)

As expected, the diffraction efficiency increases with the source distance (the diffraction “volume” increases). 7.2. Polychromatic source In that case, the incoming, polychromatic intensity, projected on the meridian plane is given ˚ −1 . As usual, the energy bandwidth is assumed to be small so by I0 in units of ph s−1 cm−1 A that the crystal properties are almost constant. With this assumption, Equation (52) is still valid for a given wavelength, with I0 and u m depending on λ. Moreover if I0 is constant over the energy bandwidth, then integrating over λ leads to the total diffracted intensity (in ph · s−1 ): Idiff = 2 r Rλ I0 = 4 r dhkl Rθ I0 = (2 r )2

2dhkl Mono I0 D

(55)

where Rλ and Rθ are from Equation (44). The total diffracted intensity from a continuum emission is then independent of the source distance. One should nevertheless keep in mind that the energy bandwidth increases as the source comes closer to the crystal. Additionally and contrary to the monochromatic case, there is no obvious definition of a global efficiency in the polychromatic case, since the diffraction process transforms a continuum emission into a band-limited spectrum. Nevertheless, the mosaic energy spread (that is not due to the crystal angular size) is, according to the Bragg relation, λ ≈ 2dhkl m. So, defining the averaged efficiency as the diffracted intensity divided by the incident flux in Springer

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the mosaic bandwidth, one gets: poly =

Idiff Rθ 2 r = = Mono 2I0 r 2dhkl m m Dm

(56)

The conversion factor (2 r/Dm) corresponds to the angular size of the crystal in units of mosaicity (as expected. . . ). From the conditions expressed in Equation (53), it follows that the efficiency for a monochromatic beam is much lower than the “efficiency” for a polychromatic one, provided that the source is close to the crystal. This corresponds to the fact that only a small portion of the crystal diffracts in case of a line emission, whereas the whole volume is efficient when using a continuum source. The above expressions are useful to estimate the expected diffracted intensity for a continuum emission knowing the efficiency measured with a monochromatic source, or vice versa. 7.3. Beam divergence of the diffracted beam Finally consider the effect of the mosaic spread on the divergence of the beam. The mosaic spread of a crystal increases its energy bandwidth and, consequently, the astrophysical interest of a Laue lens. However the mosaicity also induces a divergence of the diffracted beam in the meridian plane. So, since the deviation angle is twice the Bragg angle, the divergence of the beam is twice the angular width of the diffraction curve as given by Equation 40. In other words, due to the “reflection” effect on the crystal planes, the divergence of the diffracted beam is roughly twice the mosaic spread of the crystal. To first order, the diffraction curve is proportional to the crystallites distribution (i.e. a Gaussian whose FWHM is the mosaicity m). Consequently, in case of an extended crystal and assuming a parallel incoming beam, the radial spot size is then roughly proportional to the convolution of the crystal footprint (2 r ) by a normal distribution, whose FWHM is 2Fdet m, Fdet being the distance from the lens to the detector. Mathematically, this means for the radial intensity on the detector plane: Idet (r ) ∝

1

r − r

r + r erf √ + erf √ , 2 2β 2β

(57)

√ where β = Fdet m/ 2 ln(2). When β 2 r (i.e if the detector is close to the crystal), Idet (r ) tends to a rectangular shape of width 2 r , i.e. the projected footprint of the crystal. On the contrary, if β 2 r , the radial distribution is close to a Gaussian with a FWHM of 2Fdet m. This effect of mosaic defocusing (as introduced by N. Lund in this conference) appears finally as the major limiting factor on the focal length and mosaicity.

8. Conclusion The precedent sections described the basics of X-ray diffraction and their application to Xray and gamma-ray focusing. Based on the Laue diffraction laws and the Darwin model of mosaic crystals, these theoretical developments demonstrated the interest of this technique for astrophysics. An accompanying article (Halloin, in this volume) describes more precisely the application of these concepts to Laue diffraction lenses, comparing experimental results and Monte-Carlo simulations based on the theory presented here. Springer

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From this model, the “best” crystal for a Laue lens appears as a trade-off between the different parameters: – The mosaicity enables the energy overlap from one ring to another but causes mosaic defocusing. – The crystallites’ mean size should be as small as possible but its effect is energy-dependent, hard to control in practice and correlated with the mosaicity. – The thickness of the crystal should be of the order of one half of the mean free path but the optimum is flat enough to allow significant deviation in benefit of, e.g., the mass budget. – The radial extension of the tiles would ideally be very small so that the footprint be limited by mosaic defocusing. In practice, the consequently high number of tiles to be grown and the technical challenge of their cut and etching will temper this wish. One should nevertheless notice that the mosaic model, although well studied, understood . . . and realized, may not be the “best” for our purpose. Especially, the equilibrium between the diffracted and direct beams as well as the relatively large beam divergence (due to the wings of the crystallites’ angular distribution) limit the efficiency of the crystals. Further improvements in crystal growth or “synthesis” may potentially overcome these issues (e.g. see the article of R.K. Smither on gradient crystals in this volume [16]). To conclude, one should note that a computer program exists that can calculate many of the important crystal diffraction parameters, without the need of knowing the complicated mathematics behind the calculations. This program, called XOP (and available on many websites such as [17]) is extensively used in the synchrotron community and could now also be useful to the astrophysics community.

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

Friedrich, P.K.W., Laue, M.: Annalen der Physik 41, 971 (1913) Laue, M.: Annalen der Physik 41, 989 (1913) Halloin, H.: Exp. Astron. 20, DOI 10.1007/s10686-006-9063-0 (2006) Gouy, M.: Ann. Phys. de Chimie 5, 241 (1916) Dardord, R.: J. Phys. Le Radium 3, 218 (1922) Fermi, E.: Nuovo Cimento 25, 63 (1923) Guinier, A.: Théorie et Technique de la Radiocristallographie. Dunod, Paris (1956) Halloin, H.: Ph.D. thesis, University Paul Sabatier, Toulouse (2003) Warren, B.E.: X-ray Diffraction. Addison-Wesley Publishing Company (1969) Zachariasen, W.H.: Theory of X-Ray Diffraction in Crystals. Dover Publications Inc., New York (1945) Zachariasen, W.H.: Acta Crystallogr. 16, 1139 (1963) Cromer, D.T., Waber, J.T.: International Tables for X-Ray Crystallography, vol. 4. Kynoch Press, Birmingham, pp. 71–147 (1974) Darwin, C.G.: Philos. Mag. 27, 315 (1914) Darwin, C.G.: Philos. Mag. 27, 675 (1914) Darwin, C.G.: Philos. Mag. 43, 800 (1922) Smither, R.K.: Exp. Astron. 20, DOI 10.1007/s10686-006-9019-9 (2006) Sanchez del Rio, M., Dejus, R.J.: Web page of the X-ray Oriented Programs (XOP), http://www.esrf.fr/computing/scientific/xop2.1/ (2003)

Springer


Laue diffraction lenses for astrophysics: From theory to experiments Hubert Halloin

Received: 13 June 2006 / Accepted: 19 July 2006 C Springer Science + Business Media B.V. 2006

Abstract Based on the laws of X-ray diffraction in crystals, Laue lenses offer a promising way to achieve the sensitivity and angular resolution leap required for the next generation of hard X-ray and gamma-ray telescopes. The present paper describes the instrumental responses of Laue diffraction lenses designed for nuclear astrophysics. Different possible geometries are discussed, as well as the corresponding spectral and imaging capabilities. These theoretical predictions are then compared with Monte-Carlo simulations and experimental results (ground and stratospheric observations from the CLAIRE project). Keywords Focusing optics . Gamma-ray astrophysics . Crystal diffraction PACS 95.55.Ka, 61.50.Ah, 61.10.−i, 41.50.+h

1. Introduction Due to the very short wavelength of X and gamma rays, focusing instruments in high energy astrophysics has long been considered as impossible. Present telescopes in gamma-rays make use of direct shadowing (e.g. coded aperture telescopes such as INTEGRAL/SPI) or incoherent scattering (e.g. Compton telescopes such as CGRO/Comptel). Nevertheless, only a few years after the discovery of coherent scattering in crystal lattices by Friedrich, Knipping and Laue in 1912 [1], Gouy suggested an instrument focusing X-rays [2]. Following this method, Dardord in 1922 [3] and Fermi in 1923 [4] seem to have been the first to obtain images by mean of X-ray focusing. Though commonly used in crystallography, the application of Laue diffraction to high energy astrophysics is much more recent. One can refer to the work of Lindquist and Weber in 1968 [5], Smither in 1982 [6] and Lund in 1992 [7]. Recently, the first observation of an astrophysical source (the Crab nebula) has been performed during a stratospheric flight (the CLAIRE project, see the article by P. von Ballmoos et al. [8] in this H. Halloin CESR, 9, avenue du Colonel Roche, 31028 Toulouse, France e-mail: [email protected] Present address: APC, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France Springer

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volume and [9, 10]). A spaceborne gamma-ray lens project, MAX, has also been proposed to the French Space Agency (see the corresponding article by N. Barriere [11] in this volume and [12, 13]). The theoretical basis of Laue diffraction lenses for astrophysics has already been given in another article in this volume ([14], hereafter cited as Paper 1). In the present article, the geometry and instrumental response of a Laue lens are more specifically studied. The expected instrumental response from X-ray diffraction theory is then compared with the results of ground and stratospheric observations.

2. Design of a gamma-ray lens As presented in Paper 1, it is possible to coherently deviate hard X-rays and gamma-rays in crystals, using the Bragg relation: 2d sin θ = nλ,

(1)

where d is the planar spacing of the crystal, θ the incident angle, λ the beam wavelength and n an integer. Moreover, the Darwin model of mosaic crystals predicts efficiencies that are suitable for astrophysical purposes. These properties can be used to design a Laue diffraction lens. Consider an X-ray beam impacting a crystal at Bragg angle θ B . After diffraction the beam direction is changed by 2θ B . With a ring of crystals, the diffracted beam can be focused on a single point. If appropriate d-spacing are used with different radii the same energy is diffracted from several rings. Alternatively, using the same diffracting plane at different radii allows the energy bandwidth of the lens to be increased. In this section, we will describe some properties and characteristics of a Laue lens. 2.1. Choosing the diffraction material The choice of the diffracting material is crucial in the design of a Laue lens. It is a trade-off between diffraction efficiency, absorption and practicability of crystal growth. As mentioned in Paper 1, Section 3.1, the atomic scattering factor tends to Z for small incident angles. So, as a first approximation, the diffraction efficiency of a crystal is linked to its electronic density (see Figure 1). A more precise analysis would nevertheless require consideration of the lattice geometry of the crystal (via the geometrical factor) and the absorption (which increases with Z and decreases with energy). For our purpose here, the electronic density is a reasonably good indicator of the “quality” of the material. Among the “best” materials, at present only a few ones can be grown with the appropriate quality and mosaicity. Some of these candidates are indicated in Figure 1. Carbon (actually HOPG: Highly Oriented Pyrolitic Graphite) and silicon are widely used and their growth process is now well controlled thanks to the development of the semi-conductor industry (especially for silicon). The diffraction efficiency of these crystals is nevertheless quite low above a few tens of keV. Copper is a good diffraction material. While copper crystals with mosaicities at the level of a few arcminutes are “commonly” grown, until recently it has been quite difficult to get homogeneous copper crystals with a mosaicity of the order of the arcminute, as required for a gamma-ray lens above about 100 keV. Recent improvements in the growth process of copper Springer

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80

173

Be N Ne Al S K Ti Mn Ni Ga Se Rb Zr Tc Pd In Te Cs Ce Pm Gd Ho Yb Ta Os Au Pb Ra Pa Pu Bk Li C F Mg P Ar Sc Cr Co Zn As Kr Y Mo Rh Cd Sb Xe La Nd Eu Dy Tm Hf Re Pt Tl Po Th Np Cm He B O Na Si Cl Ca V Fe Cu Ge Br Sr Nb Ru Ag Sn I Ba Pr Sm Tb Er Lu W Ir Hg Bi Rn Ac U Am

70

Electronic density [10

23

cm ]

Au

60 Ag

50 Cu

40

Ge

30 C

Si

20 10 0 0

10

20

30

40

50 60 Atomic number

70

80

90

100

Fig. 1 Electronic densities of pure materials. Materials that have been considered for Laue lenses are indicated

crystals achieve mosaicities of 1 arcmin or less (see the article of P. Courtois et al. [15], in this volume). Germanium (actually Ge1−x Six ) crystals were used to build the first gamma-ray lens for astrophysics (the CLAIRE project, see [8] in this volume). Due to the amount crystals that had to be produced (≈1000), a good knowledge of the GeSi growing process and crystals parameters relevant for gamma-ray lenses now exists (see the article of N.V. Abrosimov in this volume [16] and [17]). Silver and gold are also promising candidates (especially at high energy) and have the same crystal structure as copper and similar melting temperature, although no attempt has yet been made to grow mosaic silver or gold crystals for a Laue lens.

2.2. Geometry of a Laue diffraction lens Let us now consider a crystal, located at a radius r from the optical axis of the lens, and a source at a distance D (see Figure 2). E ∞ , θ∞ and F∞ are the energy, Bragg angle and focal distance for a source on axis, at infinity. Similarly, E, θ and F refer to a source at a distance D from the lens. In the hard X- and gamma-ray regimes, the Bragg angles are small and the linearization of the Bragg relation leads to: ˚ hc 100 keV 1A θ≈ ≈ 213.11 arcmin 2dhkl E dhkl E

(2) Springer

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Fig. 2 Scheme of a crystal diffraction on a Laue lens

Additionally, if D r , one has θ ≈ θ∞ +

r D

and so:

2dhkl r 1 1 + ≈ E E∞ hc D

100 keV dhkl 100 keV 10 m r ≈ + 0.16128 ˚ E E∞ 10 cm D 1A

(3)

This equation specifies that it is equivalent (w.r.t the crystal planes orientation) to focus a beam of energy E ∞ from infinity or one of energy E at distance D. This property is very useful when tuning a Laue lens in laboratory, where the distance of the X-ray source is limited. r In addition we have, F∞ ≈ 2θr∞ and F ≈ θ +θ and, consequently: ∞ r E ∞ dhkl hc ≈ 0.80644

F∞ ≈

E∞ 100 keV

r 10 cm

ddhkl ˚ 1A

m

(4)

and: 1 1 1 − ≈ F D F∞

(5)

The latter equation is very similar to the equation of thin lenses (but with an associated dependence of the beam energy). Equation (4) allows to define two kinds of Laue lenses: – lenses with a few keV energy bandpass and consequently a relatively “short” (few meters) focal length – those with a broad energy bandpass and therefore a long focal length (tens of meters). Monochromatic Laue lenses In order to focus a single energy (from infinity) with crystals at different radii on the same focal point, the product r · dhkl should be constant (from Springer

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√ −1 Equation (4)). So, r (∝ dhkl ) can take only discrete values (e.g. r ∝ h 2 + k 2 + l 2 for cubic lattices). From the Bragg relation, any angular deviation θ (either the mosaicity or source’s depointing) leads to an energy offset E ≈ 2dhchkl E 02 θ . Since, in this configuration, all the ring diffracts the same nominal energy, any depointing greater than (roughly) the mosaicity causes a noticeable change in the energy response of the lens. The diffraction efficiency −1 decreasing with dhkl , the contribution of the outer crystals rapidly becomes small and in practice the number of rings is limited. The demonstration lens built for the CLAIRE project had to be flown on a stratospheric balloon and was consequently of this kind due to the requirement of a short focal length. This lens had a external diameter of about 40 cm, 8 rings of germanium crystals ((111) to (440) planes), a nominal diffracted energy of 170 keV at infinity and a focal length of 2.7 m (see [8] in this volume and references therein). Broad band lenses In this case, the diffracted energy depends on the radius and the lens covers a wider energy bandpass. Actually, from one ring to another (with radii R and R + 2

r, r R), the diffracted energies differ by E ≈ dhkl E ∞ /(F∞ hc) r . On the other hand, the FWHM of the diffracted peak for a given ring is linked to the mosaicity m of the crystal: E ≈ 2mdhkl E 2 /(hc). Consequently, there is an energy overlap between two identical crystals at different radii only if r < 2F∞ m. Typically, the desired angular resolution of the lens leads to required mosaicities of the order of 1 arcmin, whereas, for the lens and detector to be on the same spacecraft, the focal length should not be greater than about 10 m. With these values (m = 1 arcmin and F∞ = 10 m), the smoothness of the energy response requires r 6 mm. In this case, concentric Laue rings would require small crystal tiles, with the accompanying difficulties in terms of cutting process and positioning. Nevertheless, following an idea proposed by Lund [7], the tiles can be mounted according to an Archimedes spiral, the crystal radius varying linearly with its azimuth angle. These geometry ensures a very smooth energy distribution and is foreseen for the HAXTEL project (see the article from F. Frontera in this volume [18] and [19]). For a longer focal length (∼100 m), requiring separated platforms, the mosaic energy spread is enough to realize a smooth energy response, even in case of concentric rings (which usually simplifies the lens design). The MAX mission (see the article from N. Barriere in this volume [11] and [13]) is of this kind.

3. Spectral and imaging response of a Laue lens A Laue diffraction lens is similar to a “classical” optical lens as far as the capability of concentrating an on-axis source is concerned. Nevertheless, the observation of an off-axis source induces aberrations, i.e. a modification of the diffracted spectrum, associated with a deformation of the point spread function (PSF). 3.1. On-axis point source In order to quantify the Laue lens response to a point source, consider a single ring of crystals. This ring is assumed to have a mean radius r , focusing an energy E ∞ from an on-axis point source at infinity, on a detector located at the focal distance (F∞ ). The size of the focal Springer

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spot is due to the superposition of the tiles footprints, convolved by the radial divergence of the beam (see Paper 1, Section 7.3). Whereas the size of the crystals footprints does not depend on the detector distance, the “mosaic defocusing” (as introduced by N. Lund in this conference) increases with the focal length. This effect also induces a decrease of the instrument sensitivity, since the background level scales with the detection area. If the detector is close to the lens, or the mosaicity small, only the projection of the footprints has to be considered. In this case, the focal spot intensity distribution, diffracted by a full ring, is well approximated considering that the intensity at radius r on the detector is proportional to the mean value of the intensity diffracted by a single crystal at the same radius from its center (assuming a perfect alignment of all tiles). Mathematically, if 2L × 2l is the size of the tiles (with L > l), then the radial intensity is proportional to: ⎧ if r ≤ l ⎪ ⎪1 ⎪ ⎪ 2 1 ⎪ ⎪ ⎪ if l < r ≤ L ⎨ 1 − π arccos r I (r ) = √ ⎪ l L 2 ⎪ ⎪1 − arccos + arccos if L < r ≤ l 2 + L 2 ⎪ ⎪ π r r ⎪ ⎪ √ ⎩ 0 if r > l 2 + L 2

(6)

When the divergence of the beam cannot be neglected, the same procedure using the radial intensity from Paper 1, Equation (57) leads to:

I (r ) =

⎧ ⎪ 2 ⎪ ⎪ ⎨π

π/2

Idet (r sin θ)dθ

if r ≤ d⊥

0

⎪ ⎪ 2 ⎪ ⎩π

π/2

arccos(d⊥ /r )

(7) Idet (r sin θ)dθ

if r > d⊥ ,

where d⊥ is half the size of the crystal, perpendicular to the radius. As a consequence of this equation, I (r ) ∝ Idet (r )/r if r d⊥ . The effect of the mosaic defocusing has a major impact on the sensitivity. The area of the focal spot doesn’t depend on the focal distance F∞ , provided that the beam divergence (due to the mosaicity) is small w.r.t. the crystals’ footprint, i.e. if F∞ rc /m, where rc is the 2 half the radial size of a crystal. Conversely, it scales as F∞ if F∞ rc /m. Consequently, considering a position sensitive detector, the background noise variability is independent of F∞ for short focal length and increases as F∞ otherwise. 2 2 The collecting area being proportional to F∞ , the lens sensitivity scales as F∞ for short focal lengths and increases “only” linearly if F∞ rc /m (i.e. like a coded aperture telescope). This property is the main limiting factor, along with the mass constraint, to the increase of the focal length (and hence the effective area). 3.2. Off-axis point source Calculating the off-axis response of a Laue ring (with no radial extension) shows that the focal spot is no longer a circle but a ring with an azimuthal dependence of the energy. This effect is due to the “mirror effect” on the diffracting planes and the equivalence between angle and energy via the Bragg relation. Actually, considering a point source at infinity with a small off-axis angle , the incident angle on the crystal located at the azimuth χ on the ring is ψ = cos(χ − φ), where φ is the azimuth of the source. Due to the reflection on the Springer

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crystal planes, the impact positions on the detector are located on a circle of radius F∞ , centered on the lens axis: x(χ) = F∞ cos(2χ − φ) (8) y(χ) = F∞ sin(2χ − φ) χ varying from 0 to 2π, the image on the detector is the superposition of 2 circles with the same radii and centers. In addition, the energy diffracted by the crystal at azimuth χ is shifted from the nominal “on-axis” energy E by: E ≈ − 2dhchkl E 2 cos(χ − φ). Finally, if the position on the impact circle is parametrized by α = 2χ − φ(α ∈ [0 : 4π ]), then:

E(α) ≈ −

2dhkl 2 E cos((α − φ)/2), hc

α ∈ [0 : 4π]

(9)

This formula demonstrates that for the same impact position (i.e. for α ∈ [0 : 2π] and α + 2π ), two energies are diffracted: E · (1 ± 2dhchkl E cos(α − φ)/2)). Moreover, for α = φ + π[2π ] the beam divergence is tangential to the impact circle, whereas its direction is along the radius for α = φ[2π]. Consequently, the impacts density and spread depends on the position on the impact circle. Actually, the maximum impact density is at the “geometrical” position (i.e at the intersection of the detector plane and the line of sight). According to Paper 1, Equation (57) and simplifying the rectangular footprint by a Gaussian distribution, the beam divergence induces a spatial dispersion whose FWHM is roughly given by (2 rc )2 + (2F∞ m)2 . So, two point sources (with one on-axis) can be separated by the lens provided that the diameter of the impact circle (from the off-axis source) is greater than the diameter of the “on-axis” spot size. This means 2F∞ (2 rc )2 + (2m F∞ )2 . The angular resolution of the lens is then approximately: min ≈

( rc /F∞ )2 + m 2

(10)

Consequently, the angular resolution of a Laue lens improves with the focal length, but is roughly equal to the mosaicity as soon as F∞ rc /m. The energy response to an off-axis point source can be considered as a convolution product: the response for a perfect pointing convolved by the “off-axis” broadening, whose width is roughly E ≈ 2 2dhchkl E 2 , as explained above. Thus, in case of a broad band Laue lens (i.e. with a long focal length), the energy response is only slightly affected, whereas the PSF is quite sensitive to the off-axis angle. On the contrary, the energy response of a narrow line lens (i.e. with a short focal length) is strongly dependent on , but not the impacts distribution. 3.3. Monte-Carlo simulations The instrumental response (spectral and imaging) has been simulated using a Monte-Carlo software, specifically developed for Laue lenses simulations. Two lens configurations have been simulated: – a broad band (0.2–2 MeV) lens with a focal length of 150 m – a narrow band (3 keV @170 keV) lens with a focal length of 2.77 m Springer

178 Table 1 Parameters of the broad band Laue lens used for Monte-Carlo simulations

Exp Astron (2005) 20:171–184

Parameter

Value

Focal length Number of crystals Crystals size Crystal material (radius range)

150 m 92488 2 × 2 cm2 Ge111 (0.31–0.39 m) Au111 (0.41–0.97 m) Cu111 (0.99–4.45 m) 30

2131 kg

Mosaicity Crystals mass

The broad band Laue lens is made of concentric rings of germanium, copper and gold crystals. The rings radii vary from 0.3 m to 4.45 m, corresponding to an energy range from 200 keV to 2 MeV. In order to limit the mass cost and foreseeing a deployable mechanism, the outer crystals are mounted on petals, as shown in Figure 3. In this case, diffraction orders from 1 to 3 have been considered. Additional information about the simulation is listed in Table 1. Comparisons are also made with a MC simulation of a narrow band Laue lens. For this simulation, the design of the CLAIRE lens has been used. It consists of 8 Ge rings, focusing the same energy at infinity (170 keV) with a focal length of 2.763 m (see Table 2). The simulations have been performed for an on-axis source and for an off-axis angle of 3 arcminutes. The simulation results are illustrated on Figure 4 (broad band lens) and Figure 5 (narrow band lens). The simulated spectra are plotted in the upper part of the figures, above

Fig. 3 Implantation of crystals for the MC simulation of a broad band Laue lens. From inner to outer rings: Ge111 , Au111 and Cu111 Springer

Exp Astron (2005) 20:171–184 Table 2 Parameters of the narrow band Laue lens used for Monte-Carlo simulations

179

Parameter

Value

Focal length Number of crystals Crystals size

2.763 m 659 1 × 1 cm2 (except rings 5 and 7) 1 × 0.7 cm2 (rings 5 and 7) 61.7, 100.8, 118.2, 142.6, 156.18, 174.64, 188.15, 201.67 70 to 110

(depends on the ring) 111, 220, 311, 400 331, 422, 333, 440 2.1 kg

Rings radii in mm Mosaicity Diffracting planes Crystals mass

the density plot of the impacts on the detector, for the perfect pointing (right) and the off-axis source (left). Additionally, the spectral response of the broad band lens to an on-axis source has also been estimated using the analytical approximation of the total intensity diffracted by a crystal, as given in Paper 1, Equation (44). Compared to the MC simulation, this analytical approach reproduces quite well the spectral shape, though the “energy smoothing” due to the mosaicity is not taken into account. Using the analytical approximation has obviously the advantage of calculation time (a few seconds w.r.t. a few hours for the MC simulation) but, in the general case, it cannot easily reproduce the intensity map on the detector plane. These MC simulations, based on the basic principles and equations of the Darwin model of crystals, confirm the spectral and imaging properties of a Laue lens, as described above. The energy response of a narrow band lens is very sensitive to the depointing, while the impact distribution is only slightly modified. On the contrary, the spectral shape of the broad band lens is almost unchanged between 200 keV and 2 MeV, apart from the “sharp” features at 850 and 1800 keV (which are smoothed). Conversely, the impact distribution becomes a ring, whose radius is about 13 cm (=150 m ×3 ). 4. Theory vs. experimental results The CLAIRE project [20–24] was intended to test the validity of the Laue lens concept on an astrophysical source. A narrow band Laue lens has been developed at the CESR (Toulouse, France) and tested on ground and during a stratospheric flight (observation of the Crab Nebula). The characteristics (shape and flux) of spectra recorded during the lens tuning allowed the determination of the parameters of the crystals (mosaicity and mean length of the crystallites). These parameters were then used for the development of realistic numerical models (Monte-Carlo simulations), which can be compared with experiments in various conditions of pointing, source spectrum and distance, etc. A detailed description of the CLAIRE project is given in P. von Ballmoos et al. ([8], this volume). Hereafter, we only quote the experimental results for comparison with theoretical expectations. In order to estimate the diffraction efficiency of the lens, as well as its angular response, two experiments have been conducted on ground. First, a radioactive source of 57 Co was observed with the lens. This source emits a line at 122.06 keV, corresponding to a distance of 14.07 m according to Equation (3). At this distance, the angular size of each crystal is ∼2.4 arcmin (crystal height of 1 cm) or 1.7 arcmin (0.7 cm). Since these values are larger than the mosaicity, only a small fraction of the crystal Springer

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Fig. 4 MC simulation of a broad band Laue lens. Upper graph: diffracted spectra for an on-axis source (analytical approximation and Monte-Carlo simulation) and a 3 arcmin off-axis source. Lower graphs: MonteCarlo simulations of impacts density on the focal plane (left: 3 off-axis source, right: on-axis)

is diffracting, leading to a diffraction efficiency (diffracted fraction of the incident radiation on the lens area) of 3.2±0.1 % (see Paper 1, Section 7.1). The numerical simulations can then be used to correct this efficiency of a monochromatic, divergent beam into a polychromatic, parallel beam. Finally, taking into account the estimated uncertainties on the crystals’ parameters, a semi-empirical value for the peak efficiency at 170 keV (considering a diffracted peak of 3 keV FWHM) can be set to 7.7±1 %. Additional ground measurements with a source at 205 m were performed on an aerodrome in Figure as, on the Spanish Mediterranean coast [25]. This experiment led to a peak efficiency of 8.5±1 %, taking into account an estimation of systematic effects. Figure 6 shows the energy response of the lens for various depointing angles (from 30 to 270 arcseconds). Springer

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181

Fig. 5 MC simulation of a narrow band Laue lens. See Figure 4 for a description of the figures

The curves are compared with the results of a Monte-Carlo simulation of these experiments. The shape and deformation of the energy response are well reproduced by the model. In that sense, this experiment validated the theoretical instrumental response of the lens. On June 14 2001, CLAIRE was launched on a stratospheric balloon by the French Space Agency (CNES) from its site at Gap in the French Alps and landed near the Atlantic coast 500 km west of the launch site. After data analysis, the spectrum exhibits a significant excess of about 33 photons at 170 keV with an exposure time of 1h 12. This result leads to a peak +0 efficiency of 12.5±4−2 %, corrected for a perfect pointing and taking into account systematic effects. These experimental results are summarized and compared with numerical simulations in Table 3. Measurements and simulations are in good agreement and a value of 9±1 % of peak Springer

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Table 3 Comparison of experimental results and simulations Experiment

Measured eff.a,b

Simulated eff.a,c

Comments

Polychromatic source at infinity Polychromatic source at 205 m 57 Co at 14 m

12.5±4−2 %

8.88±0.02 %

8.5±0.5±0.5 %

8.53±0.02 %

3.17±0.02±0.1 %

3.668±0.004 %

Measurement derived from the 2001 flight analysis Long distance test (see text and [25]) Laboratory experiment with a radioactive sourced

+0

a

Peak efficiency assuming a peak FWHM of 3 keV for polychromatic sources, diffracted fraction of the incident flux on the lens for monochromatic sources. b Error bars include the statistical uncertainty (first figure) and an estimation of systematic effects (second figure). c Error bars are only statistical. d The low efficiency is due to the small diffracting volume for a monochromatic source at finite distance (see text). Rescaling gives a peak efficiency of about 7.7±1 % for a polychromatic source at infinity.

efficiency for a polychromatic source at infinity is compatible with both experimental and simulated data. Besides, the validity of the relationship between distance and diffracted energy (Equation 3) have been tested with various experiments using a continuum source: – tuning data (distance of 14.16 m) – source at 22.52 m with a partially tuned lens 6 Measurements MC simulations

5 4 3

Flux (cts/keV/s)

2 1 30 ’’ 0 60 ’’

90 ’’

210 ’’

270 ’’ 140

145

150

155

160

165

170

175

180

185

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Fig. 6 Response of the CLAIRE lens during the long distance test, for various off-axis angles. The solid lines represent the measurements, the dashed lines are from an MC simulation. Successive plots have been shifted down for clarity Springer

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1000 Distance [m]

D=f(E) 100

10

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1 14.162 m 22.52 m 205 m infinity

0.8

0.6

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0 110

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Fig. 7 Recorded spectra for continuum sources at various distances. Upper graph: theoretical positions of the peaks. Lower graph: results of the experiments

– long distance test (205 m) – stratospheric flight (infinity. . .) Figure 7 represents the recorded spectra for these experiments (lower graph), compared with the theoretical relationship given by Equation (3) (upper graph). The position of the centroids are in very good agreement with theory, slight departures from theoretical values (less than 0.5 keV) being the consequence of the incident spectrum shape and/or the detector calibration drifts.

5. Conclusion In the field of nuclear astrophysics, from a few tens of keV up to a few MeV, future spaceborne instruments will have to perform a significant sensitivity and angular resolution leap. Present technologies, such as coded masks or Compton telescopes, have equivalent collecting and detecting area. Thus, their point source sensitivity seem to be “intrinsically” limited. Based on X-ray diffraction in crystals, discovered almost 100 years ago, a Laue diffraction lens offer a way to overcome the present sensitivity dead-end, with also a unprecedented angular resolution in this energy range (typ. 1 ). In the present paper, the main characteristics and design options of this kind of instruments have been described. Additionally, the expected instrumental responses are confirmed by Monte-Carlo simulations, as well as by experimental results. Once the behavior, expectations and limitations of Laue lenses for astrophysics are correctly understood, the next step is to focus on the best design for a future spaceborne gamma-ray lens. . . Springer

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

10. 11. 12.

13. 14. 15. 16. 17. 18. 19.

20. 21. 22. 23.

24. 25.

Friedrich, P.K.W., Laue, M.: Annalen der Physik 41, 971 (1913) Gouy, M.: Ann. Phys. de Chimie 5, 241 (1916) Dardord, R.: J. Phys. Le Radium 3, 218 (1922) Fermi, E.: Nuovo Cimento 25, 63 (1923) Lindquist, T., Webber, W.R.: Can. J. Phys. 46, S1103 (1968) Smither, R.K.: Rev. Sci. Instrum. 53, 131 (1982) Lund, N.: Exp. Astron. 2, 259 (1992) von Ballmoos, P., Halloin, H., Evrard, J., Skinner, G., Abrosimov, N., Alvarez, J.M., Hamelin, B., Hernanz, M., Jean, P., Knödlseder, J., et al.: This volume (2006) Halloin, H., von Ballmoos, P., Evrard, J., Skinner, G.K., Hernanz, M., Abrosimov, N.V., Bastie, P., Hamelin, B., Lonjou, V., Alvarez, J.M., et al.: In: Citerrio, O., O’Dell, S.L. (eds) Optics for EUV, X-Ray, and Gamma-Ray Astronomy. Proceedings of the SPIE, vol. 5168. pp. 471–481 (2004) Halloin, H., von Ballmoos, P., Evrard, J., Skinner, G., Alvarez, J., Hernanz, M., Abrosimov, N., Bastie, P., Hamelin, B., Jean, P., et al.: ESA SP-552: 5th Integral Workshop on the Integral Universe. p. 739 (2004) Barriere, N., von Ballmoos, P., Halloin, H., Abrosimov, N., Alvarez, J., Andersen, K., Bastie, P., Boggs, S., Courtois, P., Courvoisier, T. et al.: This volume (2006) von Ballmoos, P., Halloin, H., Skinner, G.K., Smither, R.K., Paul, J., Abrosimov, N.V., Alvarez, J.M., Astier, P., Bastie, P., Barret, D., et al.: In: Citerrio, O., O’Dell, S.L. (eds) Optics for EUV, X-Ray, and Gamma-Ray Astronomy. Proceedings of the SPIE., vol. 5168. pp. 482–491 (2004) von Ballmoos, P., Halloin, H., Paul, J., Abrosimov, N., Andersen, K., Astier, P., Basa, S., Barret, D., Bastie, P., Bazzano, A., et al.: ESA SP-552: 5th Integral Workshop on the Integral Universe. pp. 747–753 (2004) Halloin, H., Bastie, P.: This volume (2006) Courtois, P., Andersen, K., Bastie, P.: This volume (2006) Abrosimov, N.: This volume (2006) Abrosimov, N., Lüdge, H.R. n. V.K.A., Borrissova, D., Halloin, H., von Ballmoos, P., Bastie, P., Hamelin, B., Smither, R.: J. Crystal Growth 275, e495 (2005) Frontera, F.: This volume (2006) Pisa, A., Frontera, F., De Chiara, P., Loffredo, G., Pellicciotta, D., Carassiti, V., Evangelisti, F., Andersen, K., Courtois, P., Hamelin, B., et al.: In: Citerio, O., O’Dell, S.L. (eds) Optics for EUV, X-Ray, and Gamma-Ray Astronomy II. Proceedings of the SPIE., vol. 5900. pp. 350–359 (2005) Naya, J.E., von Ballmoos, P., Smither, R.K., Faiz, M., Fernandez, P.B., Graber, T., Albernhe, F., Vedrenne, G.: Nucl. Instrum. Methods Phys. Res. Sect. A 373, 159 (1996) Kohnle, A., Smither, R., Graber, T., von Ballmoos, P., Laporte, P., Olive, J.-F.: Nucl. Instrum. Methods Phys. Res. Sect. A 408, 553 (1998) Laporte, P., Abrosimov, N.V., Bastie, P., Cordier, B., Di Cocco, G., Evrard, J., Laurent, P., Paltani, P., Skinner, G.K., Smither, R.K., et al.: Nucl. Instrum. Methods Phys. Res. Sect. A 442, 438 (2000) von Ballmoos, P., Evrard, J., Skinner, G.K., Abrosimov, N., Bastie, P., Di Cocco, G., George, M., Halloin, H., Hamelin, B., Jean, P., et al.: ESA SP-459: Proceedings of the 4th Integral Workshop ‘Exploring the Gamma-Ray Universe’. pp. 649–652 (2001) von Ballmoos, P.: Web page of the CLAIRE project, http://www.cesr. fr∼pvb/Claire/index.html (2003) Alvarez, J., Halloin, H., Hernanz, M., von Ballmoos, P., Jean, P., Skinner, G., Abrosimov, N., Smither, R.K., Vedrenne, G.: ESA SP-552: 5th INTEGRAL Workshop on the Integral Universe, pp. 757−+ (2004)

Springer


Mosaic and gradient SiGe single crystals for gamma ray Laue lenses N. V. Abrosimov

Received: 9 January 2006 / Accepted: 30 January 2006 C Springer Science + Business Media, B.V. 2006

Abstract Both Ge1−x Six mosaic crystals and Si1−x Gex crystals with gradient of composition could be grown using the modified Czochralski technique to produce the diffracting elements for the MAX gamma ray telescope. Although many elements cut from the mosaic crystal and used before for CLAIRE gamma ray telescope had an efficiency up to 20%, the overall efficiency of the lens was about 8.1 ± 0.7 %, which is more than twice lower than the theoretically predicted efficiency. Some causes of this behaviour are discussed. In addition to mosaic crystals, the growth of Si1−x Gex crystals with a gradient of composition and their properties are analysed. Such composition-gradient crystals could be a promising way to improve the diffraction efficiency of Laue lens for MAX. Keywords X-ray diffraction . Mosaic crystal . Gradient crystal . Crystal growth . Czochralski method . Germanium silicon alloys

1. Introduction One of the possible solutions on the way to gamma ray detection is a crystal diffraction lens telescope. In this case because of the focusing effect one can increase the collection area of gamma rays without increasing the detection area that is very important for the observation of extraterrestrial objects like super nova with a weak flux of radiation. There are some approaches to realize such telescope including Laue crystal lens as diffracting unit. But the question is: what crystals could be used to build the lens? Recently high quality Cu mosaic single crystals with a uniform and in this case very narrow intrinsic mosaicity between 30 arc sec and 5 arc min were grown by the Bridgman technique (Courtois et al. 2006). High homogeneity and high peak reflectivity make these crystals very promising for an application in crystal lens telescope. Other possible material candidates for the diffracting lens are bulk crystals of SiGe solid solutions in the form of N. V. Abrosimov () Institute for Crystal Growth, Max-Born-Str.2 D-12489 Berlin, Germany/Institute of Solid State Physics of Russian Academy of Sciences, 142432 Chernogolovka, Russia e-mail: [email protected] Springer

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both mosaic crystals and gradient crystals. In the last years, the growth of Si- and Ge-rich Ge1−x Six -single crystals with diameters of up to 50 mm using the Czochralski (Cz) technique opened new application areas like X-ray, gamma-ray and neutron optics (Abrosimov et al., 1996; Abrosimov et al., 1997). For example Si-rich crystals with an axial gradient of Ge are used as Bragg monochromators for synchrotron radiation to improve the spectral resolution and the spectral flux density of the diffracted X-ray beam by compensating the incident beam divergence (Erko et al., 2002). R. Smither in his new experiments used crystals with curved crystalline planes including Si crystals and Si-rich SiGe gradient crystals for diffraction of the high energy X-ray beam from Advanced Photon Source and gamma rays from radioactive source (Smither et al., 2005). It was found that using this approach there is a potential of increasing both the diffraction efficiency and the bandwidth by a factor of 5 as compared to what can be done with mosaic crystals. Nevertheless, Ge-rich Ge1−x Six mosaic single crystals are also a promising material for gamma ray optics. Some years ago the two balloon-borne experiments CLAIRE using the high energy γ -ray telescope for pointing at the Crab Nebula were launched by the French Space Agency (CNES) (von Ballmoos et al., 2004 (1)). This was the first astronomical observation with a gamma-ray lens telescope. Lately, the new concept of a space born crystal diffraction telescope MAX was presented by the MAX Scientific Advisory Group (von Ballmoos et al., 2004 (2)). The main feature of the telescope is based on the focusing γ -rays from the large collection area of a crystal diffraction lens onto a very small detector volume. As a consequence, the background noise is extremely low, making possible the unprecedented sensitivity. One of the main parts of the CLAIRE telescope was the γ -ray lens consisting of 556 Ge1−x Six diffracting elements, 1 × 1 cm2 cut from Ge1−x Six Cz grown mosaic crystals and mounted in concentric rings on a titanium frame. The mosaicity of the diffracting elements governs the flux throughput, the angular resolution and the energy bandwidth of the crystal lens. A mosaicity between 25 and 50 arc sec was found to be optimal for the CLAIRE experiments. For the MAX crystal lens telescope, the optimal mosaicity of diffracting elements was calculated using Darwin’s model for mosaic crystals to be about 30 arc sec (von Ballmoos et al., 2004 (2)). In the Darwin model, the real defect structure of the crystal, which may be due to dislocations, inhomogeneous strain, etc., is described by an agglomerate of perfect crystal blocks that are slightly angle-shifted against each other. The block size taking part in the scattering process should be microscopic or sub-microscopic to reach higher diffraction efficiency, and the angular distribution of the blocks can be defined as a continuous function. A FWHM of this Gaussian-like function is called the mosaic width, or here the mosaicity. This paper will describe the growth of both mosaic and gradient SiGe single crystals. 2. Crystal growth and characterization 2.1. Growth and characterization of mosaic crystals A reproducible growth of the Ge-rich SiGe mosaic crystals is different from the growth of perfect one. By the growth of the perfect crystals in two component systems one try to avoid the constitutional supercooling near the solid-liquid interface caused by the segregation of the second component, Si in this case. On the one hand constitutional supercooling leads to a morphological instability of the interface and to perturbations that can disrupt the single crystal growth. On the other hand one need such perturbations for the formation of cellular structure that gives the mosaicity of the grown crystals. The problem is to find such growth conditions and to keep them during the whole growth process. Springer

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Fig. 1 Longitudinal distribution of Ge in two Si1−x Gex single crystals of diameters 33 and 38 mm grown from the melt with the same initial charge of M0 = 360 g and Ge concentration of 7 at% Ge

The Ge1−x Six mosaic crystals were grown by a modified Cz technique applying Si feeding rods to replenish the loss of Si in the melt during the growth because of kSi > 1 (Abrosimov et al., 1997). Pulling was generally performed under normal pressure of Ar + 2% H2 and constant gas flow between 300 and 600 Nl·h−1 . The crystal growth begins with a Ge seed which is dipped in a pure Ge melt. When a neck is formed and the crystal begins to expand, the melt surface is contacted with the Si rods. The upward movement of the crucible with the melt gives the possibility to solve the Si rods continuously in the Ge melt. The rate of the crucible movement depends on the rods position in such a way that the silicon concentration gradient at the conical part of the crystal is maintained approximately constant. When the calculated concentration of Si in the crystal is achieved, the equilibrium between the solved Si and the crystallizing Si component is settled. It is supposed that the Si rods begin to solve immediately when they touch the surface of the Ge melt. Due to the relative movement between the rods and the melt, which is caused by the crucible rotation of about 10 rpm, the rods dissolve almost constantly. Using this technique it was possible to grow crystals of up to 35 mm diameter and 120 mm length with both constant and linear axial distribution of silicon (Figure 1). The mosaicity of the Ge1−x Six crystals was achieved by intentionally disturbing of the solid-liquid interface leading to a morphological instability and a cellular structure. Crystals of (100), (111), (211) and (130) orientations were grown with about 2 at%Si. The choice of the orientation was caused by the optimisation of the cutting process to fulfil the crystal preparation for 8 diffracting rings of the CLAIRE lens (von Ballmoos et al., 2004 (1)). The crystallisation rate during the growth was kept at about 6 mm·h−1 . The crystal structure and the shape of the solid-liquid interface of the grown crystals were studied by metallographic methods and the lateral photovoltage scanning (LPS) (Abrosimov et al., 2002) revealing the shape of impurity striations caused by segregation fluctuations Springer

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during the growth. In case of Ge1−x Six crystals, the second component (here Si) and the doping elements (P) are segregated similarly as such striations. The HF:HNO3 :CH3 COOHetchant was used for etching the samples. The mosaicity of the grown crystals was investigated with the hard X-ray diffractometer at the Institute Laue-Langevin, Grenoble, using the continuous high-energy X-ray spectrum (100 keV and 400 keV) (Hamelin et al., 2004). The crystal diffraction efficiency was measured twice, during the tuning procedure of the lens at the energy of 122 keV (efficiency of individual diffracting elements) and by a long distance test at the energy of 165 keV simulating the telescope flight experiment and showing the diffraction efficiency of the whole lens (Halloin et al., 2004). For the tuning procedure, the 122.06 keV photons from a 57 Co source situated 14.16 m in front of the lens on the optical axis were used. The diffracted photons were detected on the P01 INTEGRAL/SPI detector placed 2.33 m behind the lens on the optical axis. For the long distance test of the diffraction efficiency of the whole lens, an industrial X-ray generator with a 2.5 × 2.5 mm tungsten target (voltage 250 kV, current 1 mA) allowing a sufficient X-ray flux at 170 keV after absorption by 205 m on the air was used. 2.2. Growth of gradient crystals 2.2.1. Crystals with constant diameter Si-rich Si1−x Gex gradient single crystals were also grown by the Cz technique. The growth of gradient crystals is based on one of the peculiarities of a directional solidification: the segregation of the second component with distribution coefficient less than 1 leads to a nonuniform distribution of Ge along the crystal length. The Ge content increases with the rise of crystal length and solidified fraction g = Mcr /M0 , where Mcr – is the mass of the crystal s and M0 – the mass of the charge, 0 < g < 1. The Ge distribution in the crystal C Ge and the concentration changing in the melt C Ge are well described by the Scheil-Pfann expression: = C0,Ge (1 − g)k−1 , C Ge

s and C Ge = kC Ge

(1)

where C0,Ge - initial Ge concentration in the melt. In the range 0 < g < 0.6 the Ge concentration increases weakly with a quite constant gradient because of k = 0.35 and in the range g > 0.6 the gradient of the Ge concentration is increasing with increase of g. In the cylindrical part of the crystals g depends linearly on the crystal length according to the expression: g = Mcr /M0 = πρcr R 2 L/M0 ,

(2)

where ρcr , R and L are density, diameter and length of the crystal, respectively. Here, R and M0 are the parameters used for the choice of the required concentration gradient that will be obtained. In any case, if the initial mass of the charge is the same, the gradient is higher in the shorter crystals but in each crystal the gradient is rising from the begin to the end (Figure 1). 2.2.2. Crystals with variable diameter From the analyses of Equations (1) and (2) one can conclude that the crystals with the a constant gradient of doping impurity or the second component (Ge in our case) could be grown if the diameter of the crystal is gets smaller during the growth. Experimentally it is nearly impossible to grow such crystals with a constant gradient over the whole length, but Springer

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Fig. 2 Si1−x Gex single crystal grown from the melt with 7 at%Ge and the calculated profile for attaining the gradient ∼ 0.8 at%cm−1 (see explanation in text). The vertical straight line corresponds to the beginning of the experimental curve of the longitudinal Ge distribution in Figure 3

for the main part of crystal it could be realized (Abrosimov et al., 2004). The equation for the shape of the crystals was found as the dependence of the crystal radius R from the length L (Abrosimov, 2004)

R(L) =

2−k k−1 B M0 B L +1 . πρcr (1 − k)C0,Ge kC0,Ge

(3)

Here, B is the impurity gradient (in at%·cm in the case of SiGe solid solution). The possibility to grow Si1−x Gex single crystals with a nearly constant gradient of Ge was proved by the growth from the melt with 7 at% Ge· Figure 2. shows one of the grown crystals and the calculated profile of the crystal with constant gradient B = 0.8 at%·cm−1 . The dependence R(L) was calculated from Equation 3 for the following parameters: the initial charge M0 = 215 g, k = 0.32, and ρcr = 2.33 g · cm−3 . Here, we did not take into account that the crystal density changes with increasing Ge concentration. The calculated curve is given for the range 0.2 < g < 0.9; the crystal was grown upto g = 0.89. One can see from the comparison of the calculated profile and the shape of the grown crystal that they coincide well in the middle part of the crystal. This fact is also confirmed by Figure 3 that presents the Ge distribution measured along the crystal axis. In the middle part of the crystal, the Ge distribution is practically linear.

3. Results and discussion 3.1. Ge1−x Six mosaic crystals In general, the crystallographic defects like dislocations, cellular structures caused by dislocation rearrangement, low angle grain boundaries are undesired for the main applications of the crystals because the main task of the crystal grower is the growth of large perfect crystals (Rudolph). On the other hand such defects provide the mosaic structure being necessary for gamma-ray monochromators. Springer

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Fig. 3 Longitudinal distribution of Ge in Si1−x Gex crystal shown in Figure 2

It is difficult to grow defect-free SiGe single crystals. The crystal structure of SiGe is extremely sensitive to perturbations near the solid-liquid interface like melt convection and thermal fluctuations that are typical for the crystal growth from the melt. The main defects in these crystals are so-called rotational striations and dislocations. But the first experiments with Ge1−x Six crystals showed that the striations (fluctuations of Si concentration) and the grownin dislocations provide a mosaicity of less than 12

. Only the growth of Ge1−x Six crystals with a cellular structure gave us the possibility to achieve the mosaicity in the range of 30

and 60

. The density of the grown-in dislocations in such a crystal was in the range of 104 ÷ 105 cm−2 . The formation of a cellular structure in germanium crystals caused by constitutional supercooling near the solid-liquid interface was described in (Hurle et al., 1994). The crystals described were doped with Ga or In, both having distribution coefficients in Ge of less than unity and a limited solubility. Due to microsegregation on the disturbed interface, the cell boundaries become enriched with doping elements and solute-rich droplets trapped within the germanium crystal. The advantage of Si as a doping element (second component) is based on the miscibility over the complete range of compositions of Si and Ge. Because the distribution coefficient of Si in Ge is greater than unity, Si is preferentially segregated to the peaks of the cells, the cell boundaries become depleted, and no massive droplet formation is observed. Figure 4a shows the unstable microstructure detected by the LPS method and Figure 4b and Figure 4c show parts of detected region as etched pattern. During this growth stage the macroscopic growth parameters such as pulling rate, rotation rates of both crystal and crucible, and crucible translation rate were constant. The changes of morphology between stable and unstable state were caused by stochastic fluctuations. At least, two features could be seen from Figure 4 which are important for optimising the crystal growth process: (1) the cell size, small just after appearing, increases during the growth and (2) the cellular structure occurs reversible (if only in some range). The first point is important for controlling the cell size, which can be considered as diffracting element in the Darwin model of mosaic crystals. The latter shows that long crystals with a desired cellular structure can only be grown if the growth conditions are stable enough over a long time. Springer

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Fig. 4 Axial cut of a 112 -grown Ge1−x Six crystal, sample surface (220). Si concentration is 1.7 at%. (a) LPS measurement (38 mm × 10 mm), (b) and (c) micrographs showing the development of the cellular structure

As is known (Hurle et al., 1994), the morphology of the cellular structure depends on the crystal growth direction because, after initial perturbations, the micro-facets start to form on the solid-liquid interface and {111} plane faceting pyramids are developed. Figure 5 shows etched wafers of 100 , 112 and 130 orientated Ge1−x Six crystals with x = 0.02. All crystals have a convex (to the melt) solid–liquid interface. Size and form of the cells in the crystals with different orientation can be responsible for the different diffraction properties of the diffracting elements in CLAIRE’s lens. To fulfill the Bragg conditions in the 8 concentric rings, 8 diffraction planes – (111), (220), (311), (400), (331), (442), (333), Springer

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Fig. 5 Morphology of the cellular structure after the growth in a) 100 , b) 112 , c) 130 directions. Micrographs of the etched wafers

(440) were chosen. To optimise the cutting procedure, crystals of (100), (111), (211) and (130) orientations were grown with the diffracting planes being parallel to the crystal axis. Nearly all diffracting elements were checked for mosaicity, and each element was tuned in the diffraction position and the diffracting efficiency was measured. A large variation of the diffraction efficiency from 3% to 15% was observed between different optical elements, Springer

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and the best crystals were selected for the installation into the lens. (The theoretical peak efficiency was estimated to range from 25% at the best ((111) diffracting plane) down to roughly 10% ((333) diffracting plane)). The diffraction efficiency of the whole lens deduced during the stratospheric flight of the CLAIRE telescope was determined to be 6.7 ± 1.5% (von Ballmoos et al., 2004 (1)) which is in good agreement with the 8.1 ± 0.7% measured during the long distance experiment at the energy of 165.5 keV (Halloin et al., 2004). 3.2. Si1−x Gex gradient crystals The main feature of a gradient crystal, in which the component concetration varies monotonically over the crystal length, is that the lattice parameters vary also monotonically according to Vegard’s law. A lattice parameter gradient leads to the bending crystalline planes that can be used for diffraction of X-rays or gamma rays. The detailed analysis of the diffraction with such curved-plane crystals is given in detail by R. Smither (Smither et al., 2006). There are 3 different ways to produce diffracting elements with curved crystalline planes: through the temperature gradient, using the bending procedure and applaying two component gradient crystals like SiGe (Smither et al., 2006). The first two ways are very effective in practice they are rather simple in the realization only on a laboratory scale because one should have in-situ control of the temperature or bending conditions. In the case of gradient crystals, a build-in gradient of lattice parameter is achived at the stage of crystal growth. It can simplify the construction of the MAX lens and decrease its weight. Figure 6. shows three possibilities to cut diffracting elements (monochromators) from the Si1−x Gex gradient crystals. The laterally graded crystals shown in Figure 6d. were used for the double crystal monochromator with symmetrical Bragg reflection by BESSY KMC-2 beam line. The spectral flux density for such monochromator was found to be 4–6 times higher than others due to optimization of the Bragg conditions for a divergent beam using the lattice parameter gradient (Erko). For the MAX Laue lens application the diffracting elements can be cut along the crystals length as shown in Figure 6c. It should be taken into account that the different elements, in spite of the same gradient of the lattice parameter, have a different crystal composition that can influence the diffraction efficiency. The first measurements of the diffraction efficincy and FWHM of the rocking curve on the composition-gradient crystal are analysed in (Smither et al., 2005).

Fig. 6 The possibilities to cut the monochromators from the gradient crystal: (a) as-grown gradient crystal, (b) one non-banded monochromator, (c) banded monochromators, (d) two banded monochromators Springer

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There are some limits for the growth of Si1−x Gex gradient crystals. In general the higher gradient should be achieved, the shorter crystal could be grown. The maximal concentration gradient of 1.4 at% Ge per cm on 3 cm length with retantion of crystal quality was obtained by the growth from the melt with 7 at% Ge. The gradient of about 0.8 at% Ge per cm was achieved over a length of 8 cm. 4. Conclusion Both Ge1−x Six mosaic crystals and Si1−x Gex crystals with gradient of composition could be grown using the modified Czochralski technique to produce the diffracting elements for the MAX gamma ray telescope. To achieve a mosaicity of up to 60

, special growth conditions were needed which caused the interface perturbations and the development of the cellular structure. The morphology of the cellular structure depends on the growth direction and influences the mosaicity and the diffraction efficiency of the crystals. Although many elements have a diffraction efficiency of up to 20%, some elements show much lower diffraction efficiency. It was found that the overall efficiency of the lens is about 8.1 ± 0.7%, which is more than twice lower than the theoretically predicted efficiency. Further experiments are needed to improve the reproducibility of the growth process of Ge1−x Six mosaic crystals. In addition to mosaic crystals, the use of Si1−x Gex crystals with a gradient of composition could be a promising way to improve the diffraction efficiency of Laue lens for MAX. Further experiments are planned to study the influence of crystal quality and crystal composition on the diffracting properties of such composition-gradient crystals. References 1. Abrosimov, N.V., Rossolenko, S.N., Alex, V., Gerhardt, A., Schröder, W.: J. Crystal Growth 166, 657–662 (1996) 2. Abrosimov, N.V., Rossolenko, S.N., Thieme, W., Gerhardt, A., Schröder, W.: J. Crystal Growth 174, 182–186 (1997) 3. Abrosimov, N.V., Lüdge, A., Riemann, H., Schröder, W.: J. Crystal Growth 237–239, 356–360 (2002) 4. Abrosimov, N.V., Erko, A., Kurlov, V.N., Rossolenko, S.N., Rasin, I.G., Riemann, H.: Bull. Russian Academy of Sciences: Physics 68, 955–959 (2004) 5. Courtois, P., Andersen, K., Bastie, P.: Experimental Astronomy (this issue) (2006) 6. Erko, A., Abrosimov, N.V., Alex, V.: Crystal Res. Technol. 37, 685–704 (2002) 7. Halloin, H., von Ballmoos, P., Evrard, J., Skinner, G.K., Hernanz, M., Abrosimov, N., Bastie, P., Hamelin, B., Lonjou, V., Alvarez, J.M., Jean, P., Knödlseder, J., Smither, R.K., Verdenne, G.: Proc. SPIE 5168, 471–481 (2004) 8. Hamelin, B., Bastie, P.: Proc. SPIE, 4786, 29–39 (2002) 9. Hurle, D.T.J., Cockayne, B.: In: Handbook of Crystal Growth, Hurle, D.T.J. (ed.), (Elsevier Science B.V., 1994), pp. 99–211 (1994) 10. Rudolph, P.: Crystal Res. Technol. 40, 7–20 (2005) 11. Smither, R.K., Saleem, K.A., Roa, D.E., Beno, M., Kurtz, C., Khounsary, A., Abrosimov, N.: Rev. Sci. Instrum. 76, 123107 (2005) 12. Smither, R.K., Saleem, K.A., Roa, D.E., Beno, M., von Ballmoos, P., Skinner, G.: Experimental Astronomy (this issue) (2006) 13. von Ballmoos, P., Halloin, H., Evrard, J., Skinner, G., Abrosimov, N., Alvarez, J., Bastie, P., Hamelin, B., Hernanz, M., Jean, P., Knödlseder, J., Lonjou, V., Smither, R.K., Verdenne, G.: New Astronomy Rev. 48, 243–249 (2004) 14. von Ballmoos, P., Halloin, H., Skinner, G.K., Smither, R.K., Paul, J., Abrosimov, N.V., Alvarez, J.M., Astier, P., Bastie, P., Barret, D., Bazzano, A., Blanchard, A., Boutonnet, A., Brousse, P.,. Gordier, B., Courvoisier, T., DiCocco, G., Giuliani, A., Hamelin, B., Hernanz, M., Jean, P., Isern, J., Knödlseder, J., Laurent, P., Lebrun, F., Marcowith, A., Martinot, V., Natalucci, L., Olive, J.-F., Pain, R., Sadat, R., Sainct, H., Ubertini, P., Vedrenne, G.: Proc. SPIE 5168, 482–491 (2004) Springer

Exp Astron (2005) 20:195–200 DOI 10.1007/s10686-005-9018-x ORIGINAL ARTICLE

Copper mosaic crystals for Laue lenses P. Courtois · K. H. Andersen · P. Bastie

Received: 18 November 2005 / Accepted: 21 December 2005 C Springer Science + Business Media B.V. 2006

Abstract Large single crystals of copper with an uniform and very narrow mosaic spread between 25 seconds and 1 minute of arc are now available at I.L.L. This result is of great interest in the construction of a Laue lens for astrophysical applications for which such quality copper single crystals may be used. The X-ray diffraction properties of copper single crystals produced at I.L.L. were studied for x-ray energies ranging from 100 keV to 400 keV. Several monocrystalline plates with different thicknesses and mosaic distributions were then prepared from the as-grown crystals in order to measure their diffraction efficiency as a function of energy. As expected, the value of the peak reflectivity depends on the crystal thickness. Reflectivity measurements show the excellent properties of copper crystals for gamma-ray diffraction. A peak reflectivity of 24% was measured at 220 keV from a copper single crystal of 3.75 mm thickness having a mosaic spread of 1.5 minutes of arc. Some technical aspects on the preparation of copper single crystal plates are also discussed. Keywords Copper . Crystal growth . Mosaic crystal . Lens . X-ray diffraction . Reflectivity

1. Introduction A gamma-ray Laue lens for astrophysical applications based on mosaic copper single crystals requires crystals of high quality, with a homogeneous mosaic spread of less than 30 seconds of arc in order to achieve efficient focusing of high-energy gamma-rays (100 keV – 1 MeV) onto a small detector volume [1]. The aim of the present work is to show the feasibility of making such a gamma Laue lens which is a real challenge. We present recent progress in the growth of high quality copper single crystals at I.L.L. and we briefly discuss the difficulties P. Courtois () · K. H. Andersen Institut Laue Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble Cedex 9, France e-mail: [email protected] P. Bastie Laboratoire de Spectrométrie Physique de Grenoble, UMR 5588 du CNRS, Université Joseph Fourier, GrenobleI, BP 87, 38402 Saint Martin d’Hères cedex, France Springer

196 2.5

Copper Single Crystals Mo saic Spread (minutes of arc)

Fig. 1 X-ray mosaic spread distribution (fwhm) as a function of the vertical position on the as-grown copper single crystal, averaged over the horizontal cross-section

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2

1.5

june 2004

1

0.5 july 2005

0 0

5 10 15 20 relative position on the crystal (cm)

involved in the preparation of crystal pieces of small dimensions. We report hard X-ray scattering investigations of Cu200 in transmission geometry in the energy range from 100 to 350 keV showing the excellent quality of the crystals.

2. Crystal growth Faced with a growing demand for mosaic copper crystals for both neutron monochromators at I.L.L. [2] and Laue lenses for astrophysical applications [1;3], the I.L.L. has started a development program to optimize the crystal growth process in order to produce in-house high quality copper single crystals of large dimensions. This has been successful and detailed studies using hard X ray diffraction [4] have shown that it is now possible, since July 2005, to grow on a regular basis large ingots of 25 cm length and 8 cm diameter with a very narrow and uniform mosaic spread close to 30 seconds (Figure 1).

3. Crystal reflectivity The use of transmission geometry for the Laue Lens requires a careful optimization of the crystal thickness, with respect to both the (maximum) peak reflectivity and the integrated intensity. The optimum thickness also varies with x-ray energy. The peak reflectivity and the optimum thickness can be calculated using the model of the ideal imperfect mosaic crystal from Darwin’s theory [6]. However, because of primary and secondary extinction processes which are very difficult to predict, the experimental peak reflectivity is generally smaller than the theoretical value and the optimum thickness may also be different from theory. It is interesting, although not entirely trivial, to test the diffraction efficiency of the copper crystals using the hard X-ray facility at the I.L.L., which provides a white beam with energies close to the energies of the X-ray and Gamma-Ray continuum spectra from celestial sources. 3.1. Sample preparation Monocrystalline plates having different thicknesses and mosaic spreads were then cut from the as-grown crystals using EDM machining. The direction of cutting was parallel to the Cu(022) crystal planes in order to obtain Cu pieces with the Cu(200) crystal planes Springer

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Cu(200)

Reflectivity (arb.units )

Fig. 2 Peak profiles obtained from a copper single crystal before (the as-grown crystal) and after cutting a crystal plate of 4 mm thickness. EDM machining induces surface damages

197

After cutting t = 4 mm As-grown crystal

fwhm = 3.5 '

fwhm = 1 '

angle position (arb. units)

before etching

Cu(200)

after etching

Reflectivity (arb. uni ts.)

Fig. 3 Peak profiles from copper crystals pieces of 8 mm thickness before and after chemical etching. At least, a thickness of 0.6 mm has to be removed in order to obtain crystal pieces of high quality

t = 7.4 mm fwhm = 1.1 min

t = 8 mm fwhm = 2 min

angle position (arb. units.)

perpendicular to the surface. Detailed studies using hard X-ray diffraction have shown that spark erosion induces damage at the surface of the copper single crystal [6]. Figure 2 shows hard X-ray diffraction patterns before and after cutting a crystal of 4 mm thickness. After cutting, we observe that the mosaic has a complex structure giving rise to large tails in the peak profile and a larger width. The tails of the peak are weakened when cutting thicker crystals but defects are still present as indicated by the increase of the mosaic spread (Figure 3). The effect can be reduced by properly optimizing the machining conditions (minimum power and intensity) in order to minimize the electric discharge into the crystal but the problem of the formation of perturbed layers remains unsolved. Several methods were then tested with the aim of removing surface damage which are detrimental for X-ray diffraction applications. Since copper crystal is a very soft material, the use of classical mechanical machining or polishing is very difficult, leading to other defects in the crystal structure such as plastic deformation. Although it is a rather slow process, chemical etching was found to be the best way in order to remove the perturbed layers. Figure 3 shows peak profiles before and after chemical etching from a crystal of 8 mm thickness. After the removal of 0.6 mm thickness (i.e. 0.3 mm on each side), the peak profile is better, characterized by a Gaussian distribution and a mosaic spread very close to the original crystal, i.e.1 minute of arc. Springer

198 Fig. 4 Schematic representation of the quantities measured in hard X-ray diffractometry for reflectivity measurements. I0 = intensity of the direct beam, Id = intensity of the diffracted beam and It = intensity of the transmitted beam

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I0

θΒ

t Id

It

Thus, Starting from an as-grown crystal with a mosaic spread of 1.5 minutes of arc, we cut several pieces having different thicknesses (2 to 13 mm). Each crystal was etched in order to remove a total thickness of 1 mm. In this way, we successfully prepared several crystals having a mosaic spread around 1.5 minutes of arc. 3.2. Experiments We used the hard X-ray facility at I.L.L. which provides a white beam of X-ray energies ranging from 100 keV to 400 keV [4], to measure the peak reflectivity from the Cu200 reflection in transmission geometry as a function of both thickness and energy. The X-ray beam was 0.5 mm wide and 2 mm high and X-ray beam intensities were recorded using a cooled germanium detector having a high energy resolution (0.5% at 200 keV). The orientation of the Cu200 planes (Bragg angle θ B ) with respect to the incident X-ray beam allows the selection of a given energy band of diffracted photons which depends on the mosaic structure of the crystal (Figure 4). Both, the intensity of the incident beam I0 and the Bragg diffracted intensity Id were measured. The intensity of the transmitted beam It was also recorded. The peak reflectivity r is given by the ratio Id /I0 after subtraction of the detector background. 3.3. Principal results and discussion Typical intensity curves obtained from a copper crystal of 3.75 mm thickness are illustrated in Figure 5. It can be seen that the depth of the dip in the transmitted beam intensity corresponds

Fig. 5 Intensities of the direct, diffracted and transmitted beams measured onto the Ge detector from a copper crystal of 3.75 mm of thickness

1500 Direct beam (I ) 0

Transmitted beam (It )

Counts / 600s

1000

Cu(200) t = 3.75 mm

500 Diffracted beam (Id )

0 210

215

220 Energy (keV)

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Exp Astron (2005) 20:195–200 26 E = 300 keV - t E = 250 keV - t E = 200 keV - t

Peak reflectivity (%)

Fig. 6 Peak reflectivity as a function of the crystal thickness for three diffracted energies 200, 250 and 300 keV. The corresponding theoretical values of the optimum thickness tth are given for comparison

199

22

th th th

= 3.9 mm = 3 mm = 2.2 mm

18

14 Cu(200) fwhm = 1.5 ' 10

0

2

4

6

8

10

12

thickness (mm)

Fig. 7 Peak reflectivity as a function of the energy from copper single crystal of thickness 3.75 mm and 5.65 mm

30 Cu(200) fwhm = 1.5 '

Refl ectivity (%)

25

20

15 t = 0.565 cm

10

t = 0.375 cm 5 100

150

200

2 50

300

350

Energy (keV)

exactly to the diffracted intensities showing that no parasitic scattering occurs. This result confirms the excellent quality of the crystals. In Figure 6, the peak reflectivity as a function of the crystal thickness is reported for three diffracted energies 200, 250 and 300 keV, as well as the theoretical optimum thickness tth calculated using the model of ideal imperfect mosaic crystal [6]. As expected from the theory, the peak reflectivity exhibits a maximum value and then decreases with increases thickness, because of absorption. The experimental optimum thickness is close to the theoretical value tth . Figure 7 shows the peak reflectivity as a function of the energy for crystals of thickness t = 3.75 mm and t = 5.65 mm. The peak reflectivity increases with energy up to a saturation value of 24% at 220 keV for t = 3.75 mm and 22% at 300 keV for t = 5.65 mm. The width of the plateau observed in the measured curves depends on the thickness indicating that absorption plays an important role in the limitation of the reflectivity. We note, however, that the value of reflectivity exceeds 20% for a wide range of energies close to 100 keV. Springer

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4. Conclusion and perspectives Copper single crystals with a mosaic spread of 30 seconds of arc are now available at I.L.L. This result is of great interest in the construction of a Laue lens for astrophysical applications for which such quality copper single crystals may be used. Chemical etching was found to be necessary in order to remove damage induced by EDM machining at the surface of the copper crystals. Reflectivity measurements using a white beam of x-ray energies ranging from 100 keV to 400 keV confirm the excellent properties of copper single crystals and show the feasibility of making a Laue lens based on mosaic copper single crystals. The next step of this work will be the measurements of the absolute reflectivity of copper crystals for x-ray energies up to 900 keV at the European Synchrotron Radiation Facility (ESRF). In the future, we will also study the possibility of using bent copper single crystals which are interesting in order to improve the focusing properties of the lens.

References 1. Barrière, N. et al.: Experimental Astronomy 20, DOI:10.1007/s10686-006-9058-x 2. Courtois, P., Hamelin, B., Andersen, K.H.: Nuclear Instruments and Methods in Physics Research A529, 157–161 (2004) 3. Pisa, A.: SPIE Proc. 5536, 39 (2004) 4. Bastie, P., Hamelin, B., Courtois, P.: J.de Phys. IV France 10, 10–21 (2000) 5. Courtois, P.: ILL Annual Report, 100–101 (2002) 6. Schneider, J.R.: Nuclear Science Applications 1, 227–27 (1981)

Springer


High diffraction efficiency, broadband, diffraction crystals for use in crystal diffraction lenses Robert K. Smither · Khaliefeh Abu Saleem · Dante E. Roa · Mark A. Beno · Peter Von Ballmoos · Gerry K. Skinner

Received: 9 November 2005 / Accepted: 21 December 2005 C Springer Science + Business Media B.V. 2006

Abstract A major goal of the MAX program is to detect and measure gamma rays produced following the nuclear reactions that take place in a supernova explosion. To detect a reasonable number of supernovae, sensitivities of the order of a few times 10-7 γ cm-2sec-1 are needed – much better than possible with current instruments. The approach in the MAX program is to use a crystal diffraction lens to collect photons over a large area and concentrate them on a small well-shielded detector, greatly improving the signal to noise ratio. The crystals need to have both high diffraction efficiency and a relatively broad energy bandwidth. With mosaic crystals there is a trade-off between bandwidth and diffraction efficiency – one can have either high efficiency or large bandwidth, but not both without losing too much intensity through atomic absorption. A recent breakthrough in our understanding of crystal diffraction for high-energy gamma rays has made it possible to develop crystals that have both high diffraction efficiency and a relatively broad energy bandwidth. These crystals have near perfect crystal structure, but the crystalline planes are slightly curved. Such curved planes can be obtained in 3 different ways, by using mixed crystals with a composition gradient, by applying a thermal gradient, and by mechanically bending a near perfect crystal. A series of experiments have been performed on all three types of crystals using high-energy x-ray beams from the Advanced Photon Source at the Argonne National Laboratory. Experiments performed at 3 energies, 93 keV, 123 keV and 153 keV, with both the thermal gradient Si crystals and with the mechanically bent Si crystals, demonstrated that one can achieve diffraction efficiencies approaching 100% with moderate energy bandwidths ( E/E = 1.4%) and low atomic absorption (transmission = 0.65), in excellent agreement with theory. The use of this type of diffraction crystal is expected to increase the sensitivity of gamma ray telescopes by a factor of 5 over that possible with normal mosaic crystals.

Keywords Gamma-ray astronomy · Crystal diffraction · Thermal gradient · Bent crystal

R. K. Smither · K. A. Saleem · D. E. Roa · M. A. Beno · P. V. Ballmoos · G. K. Skinner Argonne National laboratory Springer

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1. Introduction In 1981, a program was started at Argonne National Laboratory to investigate the feasibility of constructing a Laue type crystal diffraction lens to focus high energy x-rays and gamma rays in the energy range from 100 keV to 1 MeV. Several different approaches were considered theoretically and partially tested [1–4]. The most successful was a set of concentric rings of single crystals where the crystals in each ring used a different set of diffraction planes to focus the incident radiation. By adjusting the radius of each ring, their foci could be superimposed in single spot. The first full-scale lens (55 cm dia.) was built at Argonne for the Department of Energy (DOE) Treaty Verifications Program. This lens used 8 crystal rings of Ge and made use of 8 different sets of crystalline planes to focus gamma-rays. The lens was tested with 8 different energies from 276.32 to 661.65 keV from 3 different radioactive isotopes. The lens demonstrated the feasibility of the concept and led to a collaboration between Argonne and CESR, Toulouse [5–8] This led to the demonstration of a lens for astrophysics in the CLAIRE program [8]. The Laue lenses built in these collaborations all used mosaic crystals, where one had to trade diffraction efficiency against energy bandwidth and visa versa. The success of Claire program has led to the proposal of the MAX space mission [7] As discussed by von Ballmoos et al. [7] the requirement to observe a reasonable number of supernovae per year places important requirements on the sensitivity. A factor of four improvement in diffraction efficiency allows one to see supernova in 8 times as many galaxies. Ideally, the crystals used in the lens should have both high diffraction efficiency and a relatively broad energy bandwidth. The later also implies a relatively broad acceptance angle for the incident gamma rays. With mosaic crystals there is a trade off between bandwidth and diffraction efficiency that limits the product of these two parameters. The maximum diffraction efficiency for a thick mosaic crystal is 0.50, but in order to achieve even a 0.30 diffraction efficiency with a modest energy bandwidth requires a thick crystal and a large loss of intensity by absorption. The product of the diffraction efficiency and the transmission through Laue crystals of Si and Ge, rarely exceeds 0.10 and is closer to 0.05 for higher energy gamma rays. One can do better with higher Z crystals, but it is very difficult to grow the near perfect crystals of these high Z materials that is needed to apply the “bent-crystal” approach. A recent breakthrough in our understanding of crystal diffraction for high-energy gamma rays has made it possible to develop crystals that have both high diffraction efficiency and a relatively broad energy bandwidth [9–15]. These crystals have near perfect crystal structure, but the crystalline planes are slightly curved. The curvature has a dramatic effect on the diffraction efficiency of the crystal. A particular wavelength photon passes through a Laue crystal having curved planes until it finds a region where the Bragg condition (nλ = 2dsin θ ) is satisfied. At this point the photon is diffracted. After diffraction, the photon does not encounter another region where the Bragg condition is satisfied, so it exits the Laue crystal in the diffracted direction. A photon of a different wavelength will pass through the crystal until it reaches a different region where it’s Bragg condition is met, where it too is diffracted and becomes part of the diffracted beam. The difference between the curved plane crystal and a mosaic crystal is that after the first diffraction, the diffracted beam in a curved plane crystal, will not see any crystalline planes that have the right Bragg angle to diffract them back into the undiffracted beam direction. This allows one to approach 100% diffraction efficiency.1 The net effect is a crystal that has both a high diffraction efficiency and a broad energy

1Note that efficiencies of diffraction quoted here do not include the effect of normal atomic absorption, which

must of course also be taken into account. Springer

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bandwidth, as well as a broad acceptance angle for a monochromatic beam. The crystal can also be thin enough that the transmission is high.

2. Crystals with curved crystalline planes This type of crystal can be produced in 3 different ways – (i) they can be grown as a twocomponent crystal where the relative concentration of two components is varied during growth [16–18], (ii) a thermal gradient can be applied to a near perfect crystal [19] and (iii) they can be produced by bending a near perfect crystal [20]. All three approaches have been explored in a series of experiments at Argonne National Laboratory with x-ray beams from the Advanced Photon Source. Figure 1(a) shows the curved crystalline planes in a two-component crystal of Si-Ge, where the higher concentration of Ge is at the top of the crystal. This is compared with the curved crystalline planes in a thermal gradient crystal where the hot surface is at the top of the crystal. In cross-section the crystal planes of a bent crystal will be appear similar to the latter but their form will be cylindrical, in contrast to the spherical shape found in the two-component and thermal gradient crystals. When an x-ray or gamma ray beam that is not monochromatic passes through a gradient crystal, the incident photons see a succession of crystalline planes at progressively changing incidence angle. Thus slightly different wavelengths are diffracted as a function of the distance the beam has traversed. This is illustrated in Figure 2. If a very small photon beam is incident on the convex side of the crystalline planes in a Laue crystal, it results in a divergent diffracted beam. Conversely, if it is incident on the concave side of the crystalline planes, a converging diffracted beam is produced. This effect can be used to focus the diffracted beam. A sharp focus will occur only for a beam with a small area. If one is diffracting 100 keV gamma rays from the [111] crystalline planes of silicon with a curvature of 5 arc sec per cm the focus will occur at a distance of 8 m. After that the diffracted beam will diverge. At 100 m from the diffraction crystal the gamma ray beam will have expanded to a width that is 2.5 mm larger than the original beam. A large area beam will show this increase in size at 100 m as well, as

Fig. 1 (a) The curved crystalline planes in a Si-Ge two-component crystal where the higher concentration of Ge is at the top of the crystal. (b) The curved crystalline planes in a thermal gradient crystal where the hot surface is the top surface. The planes of a bent crystal will be similar to (b) in cross-section Springer

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Fig. 2 (a) The diffraction of a gamma ray beam that is incident on the convex side of the curved crystalline planes. (b) The diffraction of a gamma ray beam that is incident on the concave side of the curved crystalline planes

will a beam incident on convex crystalline planes. This effect is small but it could become important for lenses with very long focal lengths.

2A. Measurements with thermal gradient crystals The major advantage of using thermal gradients to generate curved crystalline planes is that one can change the curvature by changing the thermal gradient. Thus one can measure the diffraction efficiency and FWHM of the rocking curve as a function of curvature for an individual crystal. If very perfect crystals such as Si are used, the curvature of the crystalline planes, which is spherical, can be very uniform. In the Argonne experiments the thermal gradient is applied by placing the silicon crystal between two large copper blocks that can either be heated or cooled. Thus the gradient applied to the crystal can be reversed without moving or changing diffraction system. This is illustrated in Figure 3 where a monochromatic x-ray beam from a monochromator enters from the right, is diffracted by the crystal, and detected by a photo diode. The undiffracted beam is monitored by a second photo diode. In these experiments, the thermal gradient is applied to a 1 cm cube of silicon. If the top of the crystal is cold and the bottom is hot, the x-ray beam is incident on the concave side of the crystalline planes, resulting in some focusing of the diffracted beam. Results from this Cold Top (CT) experiment with a 92.6 keV x-ray beam, are shown in Figure 4. The graphs are labeled with the temperature difference, T, applied to the crystal. The x-axis is the incidence angle of the diffraction process in arc sec and is defined as zero at the center of

Fig. 3 The experimental set up use in the thermal gradient experiments Springer

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Fig. 4 Data taken with a pure silicon crystal using the [111] planes with the cold top geometry and a 92.6 keV x-ray beam. The thermal gradients, T, are in units of ◦ C/cm

the peak. Both the diffracted peak (solid circles) and the intensity of the undiffracted beam (hollow circles) are shown. Figure 4 shows a set of 12 rocking curves where a series of thermal gradients is applied. The diffraction efficiency, defined as the ratio of the diffracted beam to the transmitted beam that exits the crystal when no diffraction occurs, is very small for zero thermal gradient but increases with increasing gradient to reach 95%. The FWHM increases almost linearly with thermal gradient. At the higher thermal gradients the rocking curve becomes flat topped suggesting that the curvature is quite uniform. Springer

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3. Bent silicon crystals Although the thermal gradient crystals are very useful for exploring the use of diffraction crystals with curved crystal planes, they are impractical for use in astrophysics. The power requirements for a large lens would be many kilowatts. The use of elastically bent crystals is much more attractive. Bent crystals of silicon were tested in a recent synchrotron run at the Advanced Photon Source. The experimental set up is shown in Figure 5. The crystal plate is pressed against a curved surface. The pressure was applied to the crystal through a soft material, either rubber or cardboard. In some experiments a soft material was used between the crystal plate and the curved surface as well. A typical rocking curve for a bent silicon crystal using the [111] crystalline planes to diffract a 93 keV x-ray beam is shown on the left, in Figure 6. Both the diffracted (filled circles) and the undiffracted (open circles) counting rates are shown. The form of the rocking curve and its FWHM of 31.8 arc sec, are very similar to the one in Figure 4, for a thermal gradient of 77◦ C/cm (FWHM 33 arc sec), shown on the right. Both curves are flat topped. The maximum diffraction efficiency of the bent crystal (0.997) diffraction is slightly higher than for the thermal gradient case (0.955). The dimensions of the bent silicon crystal were quite different from the 1 cm cube used in the thermal gradient experiments. The bent crystal was a single crystal 1 mm thick, 1 cm wide and 2 cm deep. The x-ray beam passed through the 2 cm dimension. The actual curvature per cm in the bent crystal (16 arc sec per cm) was one half of that in thermal gradient crystal (33 arc sec per cm). This lower curvature is better suited for the higher energy gamma rays. The x-ray beam from the monochromator used in the bent crystal experiments was 0.3 mm high and 2 mm wide. This is to be compared with the beam size of 1 mm high and 1 mm wide used Fig. 5 Is a schematic of the experimental set up

Fig. 6 Comparison of rocking curves using the [111] crystalline planes to diffract a 93 keV x-ray beam. Left: a bent crystal. Right; comparison measurements from Figure 4 for a thermal gradient crystal Springer

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Fig. 7 A plot of maximum diffraction efficiency verses the parameter α, defined as the ratio of the extinction length x the curvature per unit length, divided by the Darwin width, for the bent crystal data. The solid circles are the Si [111] data and the open circles are the Si [220] data. The solid line is the theoretical limit for the reflectivity of a silicon [111] and [220] crystal

in the thermal gradient experiments. The smaller vertical height made it possible to work at lower curvatures without distorting the rocking curve. The slight asymmetric shape of the bent crystal rocking curve is caused by slightly different bend at the ends of the crystal. This reflects the difficulty in controlling curvature over the whole crystal. Figure 7 is a plot of the maximum diffraction efficiency as a function of a parameter α, defined as the ratio of the extinction length in mm, times the curvature of the crystalline planes in arc sec per mm, divided by the Darwin width in arc sec. For Si, the extinction length for 93 keV x-rays is about 0.227 mm; the Darwin width is about 0.57 arc sec. Thus αis about 1.0 for a curvature of 2.5 arc sec per mm. The curvature needed for a given value of α decreases with the square of the energy, so the above value of 2.5 becomes 0.92 arc sec per mm at 153 keV. The theoretical limit [9–15] on the reflectivity as a function of α, is plotted as a solid line and given by I Re f = [1 − ex p(−2π/α)] The measured diffraction efficiency is always lower that the reflectivity because the diffraction efficiency includes the effect of the opening angle and energy spread of the synchrotron beam as well as any imperfections in the crystal and/or imperfection in the bending of the crystal. For very low values of curvature, the diffraction efficiency drops to ∼0.5, as is expected for a perfect, unbent crystal. The opening angle of the x-ray beam, about 2 arc sec, also plays a part in this decrease; if its effect is removed, the low curvature points move up and to the left. 4. Comparison of the different methods Apart from use of thermal gradients or mechanical bending, the third way to create curved crystalline planes in near perfect diffraction crystals is to grow a two-component crystal where the relative concentration of the two components changes as the crystal is grown. The Springer

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Fig. 8 The measured diffraction efficiency as a funtion of the curvature, θ/ L, times the extinction length divided by the Darwin Width for a perfect Si crystal. Circles show results for Si crystals in a thermal gradient experiment at 92.6 keV and the squares show the 153 keV data. Open and filled symbols are for the Cold Top and Hot Top thermal gradient data, respectively. The other sysmbols are data points from [9] for mixed Si-Ge crystals (+, ×.#,∗ correspond to 100; 120, 160 and 200 keV respectively)

best examples of the two-component type crystal have been grown at the Institute for Crystal Growth in Berlin [17–19]. They were Si-Ge crystals with starting concentrations of 3 to 7 percent germanium. Their properties were published in Keitel’s thesis [9] and in a series of articles [9–16]. The maximum diffraction efficiency obtained at Argonne in the thermal gradient experiments using pure Si crystals [20] are plotted in Figure 8 as a function of the parameter α defined above. Data from Keitel’s thesis [9], for [111] diffraction of Si-Ge crystals are shown for comparison. The data in Figure 8 can be compared with those for the bent crystal data in Figure 7. The data points at low curvature in the bent crystal data are higher and do not drop much below the value of 0.5 expected in this limit. This better agreement with theory is believed to be due to the smaller vertical size of the incident x-ray beam, 0.25 mm as compared to 1.0 mm (and thus the smaller opening angle of the x-ray beam) for the thermal gradient experiments.

5. Gradient crystals for satellite telescopes The Claire balloon-based telescope [8] had a focal length limited to a few meters and was designed with rings of crystals using different lattice planes to concentrate photons within a single narrow energy band. Formation flying satellite experiments now being planned, such as MAX [7] will have much larger focal lengths and larger lens radii. One of the favored designs uses only a few of the lowest diffraction orders in large diameter rings, each ring covering a slightly different energy band. When these overlapping responses are combined they cover one or more bands several hundred keV wide centered on energies of astrophysical interest. Springer

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Table 1 The optimized diffraction efficiency, transmission, their product and the effective area of a 200 cm radius by 2 cm wide ring. θ is the total curvature of the crystalline planes Energy keV

Thickness mm

θ arc sec

Diffraction efficiency (Diff. eff.)

Transmission (Trans.)

Diff. eff. × Trans

Effective Area cm2

80 100 150 200 400 600 800 1000 1200 1500 2000

5.5 6.5 10.0 11.5 18.5 24.0 30.0 35.0 39.0 46.0 56.0

50.9 40.7 27.2 20.4 10.18 6.79 5.09 4.07 3.40 2.72 2.04

0.899 0.885 0.942 0.852 0.786 0.736 0.713 0.688 0.661 0.640 0.606

0.747 0.759 0.706 0.703 0.650 0.628 0.598 0.584 0.577 0.562 0.545

0.672 0.672 0.665 0.599 0.511 0.462 0.427 0.402 0.381 0.360 0.330

1687 1686 1670 1504 1283 1160 1072 1009 956 904 828

A 200 cm-radius ring of Si crystals using the [111] planes to focus 400 keV gamma rays will have a focal length of 202.5 m. If the radial dimension of the crystals in the ring is 2 cm, than the area the ring will be 2514 cm2 . The 2 cm radial dimension will cover an energy range of 1 percent of the gamma ray energy, 4 keV, which corresponds to a Bragg angular change of 10.2 arc sec. Thus the angular bandwidth of the crystals should be at least 10.2 arc sec to cover the corresponding change in energy. The next ring would have a radius of 204 cm and cover the next 4 keV of the energy range, etc. The thickness, T, and curvature per unit length, θ/ L, of the crystals can be chosen to give the maximum product of the diffraction efficiency and transmission, the product of T × θ/ L being held at 10.2 arc sec. For a [111] Si crystal at 400 keV one finds optimum values of T = 18.5 mm and θ/ L = 0.550 arc sec/mm. This would result in a diffraction efficiency of 0.786 and a transmission of 0.650, giving for the product of these two terms = 0.511 and an effective area of this 200 cm radius ring with 2 cm × 2 cm × 1.85 cm crystals of 1285 cm2 . The gamma rays from a distant supernova could have an intensity of 2 to 4 photons per cm2 in 107 sec. Thus in 106 sec one could expect to focus 257 to 514 photons onto the detector from this ring. Larger rings and/or more rings would increase this number, but this performance is already attractive. Table 1 gives the results of similar optimization of a 200 cm radius ring with 2 cm by 2 cm area crystals for a range of gamma ray energies. Interestingly, one continues to get relativity high values for the product of the diffraction efficiency times the transmission even for energies as high as 2 MeV. The challenge is to demonstrate that this efficiency can be reached in practice. Acknowledgments The authors would like to thank Ruben Khachatryan of the Advanced Photon Source Optics Shop for orienting and cutting the silicon crystals used in the experiment and Peter Chupas for assisting in setting up the synchrotron experiment. This work was supported by the U.S. Department of Energy, Basic Energy Sciences, under contract no. W-31-109-Eng-38.

References 1. Smither, R.K.: Method for Focusing and Imaging X-Rays and Gamma-Rays with Diffraction Crystals, Sym. On Future X-Ray Experiments in the 80’s, GSFC, Oct. 1981, NASA Tech. Mem. No. 83848 (1981) Springer

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2. Smither, R.K.: New Method for Focusing X-Rays and Gamma-Rays, Rev. Sci. Instrum. 44, 131–141 (1982) 3. Smither, R.K.: Gamma Ray Telescope Using Variable-Metric Diffraction Crystals, 11th Texas Sym. On Relativistic Astrophysics, Austin Texas, Dec. 1982. Ann. of New York Acad. Sci. 44, 673 (1983) 4. Smither, R.K.: U.S. Patent No. 4,429,411, Instrument and Method for Focusing X-Rays, Gamma-Rays and Neutrons’ (1984) 5. Smither, R.K. et al.: Review of crystal diffraction and its application to focusing energetic gamma rays. Experimental Astronomy 6, 47–56 (1995) 6. Smither, R. K. et. al.: Crystal diffraction lens telescope for focusing nuclear gamma rays. Proc. SPIE, 2806, 509 (1996) 7. Ballmoos, P. von. et al.: MAX – a gamma-ray lens for nuclear astrophysics. Proc. SPIE 5168, 471 (2004) 8. Halloin, H. et al.: CLAIRE gamma-ray lens: flight and long distance test results. Proc. SPIE 5168, 471 (2004) 9. Keitel, S.: Ph.D. Thesis, Untersuchung von Si(1−x) Ge(x) -Gradientenkristallen und in-situ getemperten Silizium-Einkristallen als Monochromatoren für hochenergetische Synchrotonstrahlung, Physics Department, University of Hamburg (1999) 10. Keitel, S. et al.: Si1−x Gex gradient crystals: a new monochromator materiaal for hard X-rays. Nucl. Instrum. Methods Phys. Res. A 414, 427 (1998) 11. Penning P., Polder, D.: Anomalous transmission of X-Rays in elastically deformed crystals. Philips Res. Repts. 16, 419 (1961) 12. Kato, N.: Pendellösung fringes in distorted crystals I. Fermat’s principle for bloch waves. J. Phys. Soc. Japan 18, 1785 (1963) 13. Kato, N.: Pendellösung fringes in distorted crystals II. Application to two-beam cases. J. Phys. Soc. Japan 19, 67 (1964) 14. Kato, N.: Pendellösung fringes in distorted crystals III. Application to homogeneously bent crystals, J. Phys. Soc. Japan 19, 971 (1964) 15. Balibar, F., Chukhovskii, F. N., Malgrange, C.: Dynamical X-Ray propagation: a theoretical approach to the creation of new wave fields. Acta Cryst. A 39, 387 (1983) 16. Malgrange, C.: X-Ray Propagation in distorted crystals: dynamical to kinematical theory. Cryst. Res. Technol. 37, 662 (2002) 17. Abrosimov, N.V., Rossolenko, S.N., Alex, V., Gerhardt, A., Schröder, W.: Single crystal growth of Si(1−x) Ge(x) by the Czochralski technique. Journal of Crystal Growth. 166, 657–662 (1996) 18. Erko, A. et al.: On the feasibility of employing gradiënt kristal for high resolution synchrotron optics, Nucl. Instrum. Methods Phys. Res. A 375, 408–412 (1996) 19. Abrosimov, N.V., Rossolenko, S.N., Thieme, W., Gerhardt, A., Schroder, W.: Czochralski growth of Siand Ge-rich SiGe single crystals. Journal of Crystal Growth. 174, 182–186 (1997) 20. Smither, R., Abu Saleem, K., Beno, M., Kurtz, C., Khounsary, A., Abrosimov, N.: Diffraction efficiency and diffraction bandwidth of thermal gradient and composition gradient crystals, to be published in Rev. Sci. Instrum. 79, 1 (2005)

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An ‘‘ESA-affordable” Laue-lens Niels Lund


Abstract With ESA’s INTEGRAL mission gamma-ray astronomy has advanced to the point where major scientific advances must be expected from detailed studies of the many new point sources. The interest in developing focusing telescopes operating in the soft gamma-ray regime up to 1 MeV is therefore mounting rapidly. Telescopes based on Laue diffraction of gamma-rays from crystals appear as one promising route, although the practical difficulties of realizing a large scale Laue lens are certainly not small. In this paper I have attempted to develop an optimized lens design considering the size and mass constraints of a specific medium size launch vehicle. The introduction of the lens mass as a primary design driver has some surprising effects for the choice of material for the crystals and new tradeoff considerations are introduced. Keywords Instrumentation . Gamma-ray astronomy

1. Introduction Implicit in this study lies a number of assumptions and constraints: – The financial boundary conditions for a first space mission with a Laue lens. The validity of the Laue lens concept ought to be proven with a medium size mission. We accept here the mass and volume constraints of the Soyuz launcher [1]. – The INTEGRAL mission [9] has provided us with several hundred sources detected above the classical X-ray range. Most of these sources have been detected at the few mCrab level and requires an instrument with the same energy resolution as SPI [8] and about the same flux collection power as IBIS/ISGRI [4, 7], but with much lower background for a deeper study of their spectra and time variability.

N. Lund Danish National Space Center, Juliane Maries Vej 30, DK-2100 Copenhagen Ø e-mail: [email protected] Springer

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– The large focal lengths of Laue lenses naturally lead us to a concept of formation flying with a lens spacecraft and a detector spacecraft. Once the formation flying concept is accepted we are conveniently free to choose the focal length based on the crystal properties. – The formation flying configuration can only be maintained at large distances from the Earth – near the Earth the station keeping is disturbed by the gravity gradient between the two spacecraft. A mission at the Lagrange point is conceptually appealing, but is expensive in terms of launch mass, communication constraints and a protracted launch phase. An elliptical orbit around the Earth with an orbital period of 7 days may offer an acceptable gravity gradient environment and be beneficial regarding launch mass and communications [3]. – Rather than concentrating the lens response in a few energy bands which may appear particularly interesting today, I have chosen to optimize the lens for a continuous energy range between 200 and 1000 keV, with emphasis on the region around 511 keV. This choice may limit the sensitivity for certain spectral lines, but I am concerned about now designing a mission which is very specifically tailored to a limited range of astrophysical problems. – Given that the orbit must to go far away from the Earth the combined launch mass of the two spacecrafts (lens spacecraft and detector spacecraft) cannot be much higher than 2100 kg when basing the mission on the Soyuz ST launch vehicle. The dimensions at launch is limited to a diameter of 3.8 m and the height to 8 m. – In this study I have chosen not to consider imaging, but to go for the simplest possible focal plane design with just one (segmented) high-purity germanium detector. The dimension of this detector affects directly the lens design, I have assumed the diameter to be 60 mm. The detector thickness does not need to be specified at this stage.

2. A first design The design calculations presented here are based on the formalism presented in [5]. Two key parameters are the diffraction efficiency and the absorbtion cross section for the crystal material, both of these are fundamental properties of the chemical element and both are functions of the photon energy. A third parameter, which can be modified and tailored by the crystal growth and preparation processes is the degree of disorder in the crystal. A certain, low level of disorder, mosaicity in the crystal structure is very beneficial in order to maximize the integrated reflectivity of the crystals [2]. The mosaicity is usually characterized by the angular width of the reflectivity curve as the crystal is rotated past the Bragg angle. The response of a Laue lens to photons of a given energy peaks at a certain distance from the axis of the lens. We want our system to emphasize the response around 511 keV so for each crystal considered I have selected the focal length such that the ring diffracting 511 keV is placed at a radius of 180 cm, close to the maximum radius allowed by the launcher fairing. Higher energies, up to 1 MeV, will be diffracted by crystal rings lying at smaller radii (down to 92 cm), and lower energies, down to 200 keV will need crystals placed further out (out to 460 cm radius) – these latter ones will need to be placed on panels deployed after launch. When later comparing the qualities of various crystal candidates it is useful to recall that with these design choices the lenses all look exactly the same – the crystals diffracting any specific energy is lying in the same positions from lens to lens – only the focal length changes when switching from one crystal type to the other. To fulfill Braggs law for a lens of the above dimensions we will need a focal length of about 150 m – the precise value will depend on the d-spacing of the crystal material for the Springer

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213 Full lens area vs Energy. Fill factor: 0.85 Mosaic width 1’

4000

4000 Au (111) L: 174 m, M: 657 kg Ag (111) L: 174 m, M: 1098 kg Cu (111) L: 154 m, M: 1341 kg Ge (220) L: 148 m, M: 1855 kg Si (220) L: 142 m, M: 2442 kg

cm2

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Fig. 1 Effective area of full Laue lens, 1st order only, 85% crystal filling factor

lens. To achieve the highest throughput of the lens the mosaic width of the crystals should be chosen as large possible – keeping in mind that the mosaic width also leads to mosaic defocusing: the focal spot grows with increasing mosaic width. With our choice of detector diameter (60 mm) and focal length we can tolerate a mosaic width of one arcminute – at 150 m distance one arcminute corresponds to a displacement of 4 cm. This also means that we can use individual crystal elements of up to 4 cm diameter in the lens if we can reliably manufacture and handle this size of crystals. We can now calculate the response of a full, 9 m diameter, Laue lens covered 85 % with crystals of one arcminute mosaic width, and with the crystal thickness adjusted to maximize the peak reflectivity at each energy (see [5] for details). The result of this calculation is shown in Figure 1 for a number of candidate crystal materials. Only 1st order reflections are included in the calculations at this stage – higher orders will be included later. In the figures also the focal lengths and the total crystal mass for each lens is indicated. From Figure 1 one can draw some important conlusions: 1. 2. 3.

The flux collection area of a full Laue lens is strongly emphasizing the lower energies. Looking only at the overall efficiency of flux collection copper and silver appears as the best materials, while gold comes out best at energies above 400 keV. But surprisingly, considering also the crystal mass as a parameter, the advantages of gold as diffracting material for gamma rays suddenly becomes very apparent. The mass of crystals in the gold lens is only half of that in the copper lens and only a quarter of that of the silicon lens. Gold is light – silicon is heavy!! Measured in terms of diffraction cross section per gram, gold is way ahead of the other materials. The ordering of the materials is primarily decided by their atomic number, but the atomic packing density Springer

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also plays a role and there copper, silver and gold are close to peaks in the packing density distribution as function of the atomic number. Recalling that the maximum launch mass we have available using the Soyuz launcher is around 2100 kg we must conclude that we do not have the means to launch any of the lenses described in Figure 1. The mass allocation must first be split between the detector and the lens spacecraft – maybe in the ratio 300 kg for the detector and 1800 kg for the lens, and then we must allow for all the systems and structure on the lens spacecraft. My guess is that we need to reduce the mass of the crystals to below 400 kg to have a chance to see the ends meet.

3. Weight saving In the first calculations the thickness of the crystal was chosen to give the maximum intensity of the diffracted beam at each energy. This, however, is quite wasteful in terms of mass. Figure 2 shows a typical example of how the reflected power first increases rapidly with increasing thickness, then reaches a flat maximum and thereafter decreases slowly due to absorbtion in the crystal. One can note in Figure 2 that reducing the crystal thickness by a factor two from the peak reflectivity value only reduces the reflectivity by 15%. We shall accept this 15% loss in order to save a factor of two in the crystal weight. Another major weight saving can be achieved if we give up the idea that a Laue lens of necessity must be a nice complete disk. A full disk of the dimensions considered here would also need a very elaborate (and heavy) folding and deployment mechanism to fit inside the Soyuz fairing. To save weight and make life easier for the mechanical engineers we will in the following consider a lens consisting of a hexagonal central part and six rectangular panels

Reflectivity as function of crystal thickness. Au(111), 511 keV, mosaic width 1 ’ 30

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Fig. 3 Effective area of “flower lens” with the crystal thickness tapered to save weight and maintain a constant effective area below 511 keV – only considering 1st order reflections. The crystal thickness as function of energy is also shown. It varies from a fraction of a mm at 200 keV to a few mm at 1 MeV Fig. 4 Sketch of “flower lens” with the six crystal panels deployed

which can be folded up during launch. The hexagonal part is 3.7 m across corners and each panel measures 1.85 × 3.0 m. This flower lens concept is illustrated in Figure 4. The effective area of this flower shaped lens as function of energy is still increasing towards the lower energies and is still somewhat too heavy, at least if filled with copper or silver crystals. As a further weight saving measure I therefore reduced even further the crystal thickness for the crystal rings at large radii (low energies), now using the Springer

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Table 1 Characteristics of thickness tapered ‘flower’ lenses Effective area per energy range Crystal material Mass (kg) Length (m) 200–400 keV (cm2 ) 400–511 keV (cm2 ) 1000 keV (cm2 ) Gold

246

174

987

1146

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358

175

995

1141

605 549

Copper

401

155

964

1100

505

Germanium

526

148

740

838

368

Silicium

607

142

520

582

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1200 Au (111) L: 174 m, M: Ag (111) L: 174 m, M: Cu (111) L: 154 m, M: Ge (220) L: 148 m, M: Si (220) L: 142 m, M:

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Fig. 5 Effective area for the lens configuration of Figure 4, and including 2nd and 3rd order reflections. At the highest energies the effective area is increased by almost 50% by the higher order contributions

condition that the effective area should be constant below 511 keV. The resulting reflectivity curves are shown in Figure 3 together with the curves showing the crystal thicknesses as function of energy. The crystal weight now appear acceptable for copper, silver and gold crystals. In Figure 5 we show the reflectivity curves with 2nd and 3rd order reflections included.

4. Conclusions We have arrived at a lens design which we believe can be launched with a Soyuz. I have summarized the final lens characteristics in Table 1. This table is worth some comments. In terms of effective flux collection copper, silver and gold are almost equivalent except at the highest energies where gold is 10% better than silver and 20% better than copper. But the crystal mass required when using gold is 150 kg less than when relying on copper and 100 kg Springer

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less than when silver is used! This means that if 400 kg really is what Soyuz will allow us to use for the crystals then we may increase the area of the gold lens by 60% compared to the values shown in Table 1. Or we may use the extra kilos for extending the energy range to lower or higher energies. Although we can have misgivings about the security problems associated with building an instrument containing 250 kg of gold the price of the gold itself (∼ 3.5 MEuro in yesterdays prices) is not in itself preventive when we talk about a satellite project costing maybe 150 MEuro. But regardless of the crystal material chosen we have a number of difficult technical problems to solve before we can launch our first large scale Laue lens. The first problem to address will be the production in quantity of crystals with the required low mosaicity. Together with the production of the raw crystal boules the machining, handling and mounting of thin disks of these very soft materials must be developed and mastered. All these techniques should be worked out first for copper, where a large pool of experience already exist [1]. When we know how to deal with copper we may proceed to silver and gold. Most likely a support disk of a suitable material will be needed for each crystal. However, the very thin gold disks which appear to be required for the lowest energies (see Figure 3) can fortunately be replaced by silver or copper disks of more manageable thickness with only a marginal penalty in the total crystal mass. An important set of issues which must be addressed in some detail is whether an instrument offering “only” 1000 cm2 of collection area coupled with the energy resolution of SPI and a background rate lower than 5% of SPI is competitive as an ESA medium size mission? The limitation of this mission is that it strictly looks at one point source at a time. Are there sufficiently many targets which can provide enough photons in a short enough observation time? Is the probability of the bright transient high enough that this can be a significant argument for this mission? We need to find positive answers to this type of questions before we can hope to win a coming mission selection round.

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

Courtois, P., Andersen, K., Bastie, P.: Exp. Astron. 20, DOI 10.1007/s10686-005-9018-x (2006) Halloin, H.: Exp. Astron. 20, DOI 10.1007/s10686-006-9063-0 (2006) Hinglais, E.: Exp. Astron. 20, DOI 10.1007/s10686-005-9020-3 (2006) Lebrun, F., Leray, J.-P., Lavocate, Ph., et al.: A&A 411, L141 (2003) Lund, N.: Exp. Astron. 2, 259 (1992) Starsem, Co., Soyuz Users Manual. http://www.starsem.com (2001) Ubertini, P., Lebrun, F., Di Cocco, G., et al.: A&A 411, L131 (2003) Vedrenne, G., Roques, J. P., Schönfelder, V., et al.: A&A 411, L63 (2003) Winkler, C., Courvoisier, T. J.-L., Di Cocco, G., et al.: A&A 411, L1 (2003)

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Optical properties of Laue lenses for hard X-rays (> 60 keV) Alessandro Pisa · Filippo Frontera · Gianluca Loffredo · Damiano Pellicciotta · Natalia Auricchio

Received: 31 January 2006 / Accepted: 24 April 2006 C Springer Science + Business Media B.V. 2006

Abstract We report on preliminary results obtained with a Monte Carlo (MC) code developed to study the optical properties of Laue lenses for astro-physical observations. The MC code is written in the Python programming language and uses open source libraries. Among the physical quantities which can be investigated with the MC code, we paid our attention mainly to the estimation of the effective area, field of view (FOV) and point spread function (PSF) of the lens for observation of sources on-axis and off-axis. Keywords Laue lens . X-ray diffraction . X-ray telescope

1. Introduction A feasibility study of Laue lenses for the measurement of the continuum hard X-/γ -ray emission from celestial sources was already reported [9]. Here we summarize the main concepts and results. A Laue lens is a set of properly oriented crystals that focus X-ray photons via Bragg diffraction in the Laue geometry. X-ray diffraction can occur in perfect crystals because their lattice structure is periodic and its period is comparable with the wavelength λ of the X-rays: crystals are a natural diffraction grating for X-rays. Diffraction deviates photons from their incidence direction by an angle θ B (the Bragg angle) that depends on the wavelength λ and on the lattice interplanar distance dhkl , where hkl are the Miller indices of the planes. The Bragg angle can be obtained from the Bragg equation: 2dhkl sin θ B = nλ ,

(1)

A. Pisa () · F. Frontera · G. Loffredo · D. Pellicciotta · N. Auricchio Physics Department, University of Ferrara, Via Saragat 1, Ferrara, Italy e-mail: [email protected] F. Frontera IASF, CNR, Via Gobetti 101, Bologna, Italy Springer

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Fig. 1 Sketch of the cylindrical reference frame used for the Laue lens.

where n is the diffraction order. Taking a set of properly oriented crystals it is possible to build a lens capable of deviating photons from an X-ray source towards the focal point of the lens. However, perfect crystals are not suitable for building lenses for astro-physical investigations. Indeed they show a high reflection efficiency in a very narrow energy band (a small fraction of keV) and for a very narrow angular range (in the arcsecond range), while for studying the spectral properties of the continuum hard X-/γ -ray emission of celestial sources, a good reflection efficiency is required in a relatively broad energy band (tens to hundreds of keV, depending on the science goal), and a relatively large field of view (in the arcminute range) is needed. For these kinds of lenses, special crystals, with appropriate lattice deformations, appear to be more useful. Some examples of crystals with controlled imperfections are mosaic crystals, bent crystals and crystals with non constant lattice parameter induced by doping materials or thermal gradient. This paper deals with Laue lenses made of Copper mosaic crystal tiles. We will consider crystal tiles with the (111) planes normal to the tile cross section, which is assumed to be a square with side l, and parallel to two of the four lateral tile surfaces as shown in Figure 1. The thickness of the tiles is t. As it was also confirmed by our recent measurements results [2], the diffraction properties of the Copper mosaic crystals are consistent with the theoretical model proposed by Zachariasen [1]. To correctly focus photons, the direction of the lattice plane normal vector (which is parallel to the reciprocal lattice vector associated to the (111) planes, G111 ), has to intersect the focal axis and its inclination with respect to the focal plane should be equal to the Bragg angle θ B . The angle θ B depends on the tile center distance from the lens axis, ρ, and on the distance from the focal plane, focal length F (see Figure 1). The distances are measured with respect to the center of the upper surface of the tile. For a correct focusing, it is needed that: θB =

ρ 1 arctan . 2 F

(2)

Increasing the ratio ρ/F, the Bragg angle increases and thus also the wavelength of the focused photons. For a fixed value of ρ/F, and hence of θ B , the diffracted wavelength can be obtained by the Bragg law (1). Springer

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In this paper we will show the dependence from several parameters (tile size, mosaic spread, ratio between lens radius and focal length) of fundamental optical and physical properties of Laue lenses. In particular we are interested to the behaviour of the effective area, the Point Spread Function (PSF), the angular resolution and the Field Of View (FOV). All the lens properties are the result of the cooperation of all the crystals in focusing photons from X-ray sources. The task of determining these properties can be faced by means of numerical calculation. To this end a dedicated software has been developed.

2. Monte Carlo code The software developed to calculate the physical properties of the lens has been coded in the Python programming language [3]. Python has been chosen because it is a high level object oriented programming language and because plenty of scientific libraries are available. By using these libraries it has been possible to minimize the effort for the code development, debugging and testing. This code imports the libraries Numerical Python [4], Scientific Python [5], xraylib [6] and the GNU scientific library [7, 8]. The code is modular and each module faces a particular task. The code includes four main blocks: (1) lens geometry, (2) photon source, (3) photons interaction with the lens crystals tiles in which the story of each photon is followed, (4) distribution of the photons in the focal plane and their analysis. The main free parameters of the lens are the tile properties (material, lattice orientation, size, mosaic spread), its geometry (the disposition of the crystal tiles in the lens), the lens focal length and its nominal energy passband. Available tile dispositions include the Archimedes’s spiral geometry [9, 10], the concentric rings as proposed by von Ballmoos and coworkers for the MAX mission [11], a single ring (see Section 3). The photon source, whose spectral parameter can be controlled by the user, is simulated using randomly generated numbers.

3. Case of a ring lens For sake of simplicity we derive the properties of a ring lens made of Cu (111) crystal tiles. The assumed number of tiles is N and the ring is at a distance F from the focal plane (focal length). The ring radius is ρ = R (see Figure 1) and N is assumed to be 100. The inclination of the tiles in the ring satisfies Eq. (2). Via the Bragg equation it is possible to get the energy of the diffracted photons. Viceversa, given the photon energy it is possible to calculate the ring radius and the Bragg angle needed for focusing these photons. The tile thickness can be properly chosen to optimize the diffraction efficiency [9, 10]. Using the cylindrical reference frame of Figure 1, the radial coordinate ρ and the polar angle θ are the same for each crystal, while the azimuthal angle difference between two contiguous tiles is 2 π/N . It is implicitly assumed that the ring radius is large enough for the tiles allocation to be possible. There are important scaling laws which apply to ring lenses. Varying F but keeping fixed the ratio R/F, the Bragg angle does not change and so the lens focuses the same energy band (see Eq. 2). If the ratio l/F and the number of tiles, N, are kept fixed, the focal spot size is proportional to F and the effective area is proportional to F 2 . Springer

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The focal spot size was discussed in a previous paper [9]. With the developed software we can study in detail the variation of the spot size as a function of energy, of the l/F ratio and of the mosaic spread β. r For this study we make use of the radial photon distribution φ(r ) and its integral (r ) = 0 φ(ρ)dρ, which gives the encircled photon fraction. r is the radius of a circle centered in the origin O of the reference adopted frame (see Figure 1). In addition we will investigate the distribution of the photon positions in the focal plane projected on the x and y axes ( f x (x) and f y (y)).

4. Monte Carlo results We have tested our code assuming a lens made of a Cu (111) crystal tile ring optimized for 150 keV photons. We have studied the effects on the lens effective area and on the focal spot caused by the variation of the lens configuration parameters. 4.1. Reference configuration We assume as a reference configuration a lens made of a ring of Cu (111) crystals tiles with l = 10 mm, thickness of 2 mm and mosaic spread of 1 arcmin. The focal length of the reference lens is 50 m. The effective area of this configuration is shown in Figure 2, while Figure 3 shows the radial distribution of the photons on the focal plane (left panel) and the encircled photon fraction as a function of r/F. 4.2. Effect of a different tile thickness The value of the thickness affects not only the diffraction efficiency, and thus the lens effective area and the lens gain, but also the lens weight. Figure 4 shows the dependence of the effective area on the photon energy for three different crystal thicknesses (1.5, 2.0, 2.5 mm). As can be seen from the left panel of Figure 4, variations of the thickness of the order of 25% with respect to the reference configuration, result in small variations of the effective area for the first order diffraction, unlike the weight of the lens which varies proportionally to the thickness. However a higher thickness significantly increases the effective area due to the second order diffraction (right panel of Figure 4).

Fig. 2 Normalized effective area for the reference configuration. The two diffraction orders are shown

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Fig. 3 Radial distribution and encircled photon fraction for the reference configuration.

Fig. 4 Normalized effective area for different thickness values. (Left): First diffraction order; (Right): second diffraction order

4.3. Effects of different mosaic spread and tile size The increase of the mosaic spread leads to an increase of the energy passband of the lens, but also to a larger defocusing of the photons. Figure 5 shows the effective area vs energy for three different mosaic spreads (0.5, 1.0 and 2.0 arcmin) with an evident change of the energy passband and peak efficiency with the result that the number of focused photons increases with the mosaic spread. However the dispersion of the photons in the focal plane increases with the mosaic spread, with the result of a lower gain of the lens. This is shown in Figure 6, which exhibits the

Fig. 5 Normalized effective area for different mosaic spread values. (Left): First diffraction order; (Right): second diffraction order Springer

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Fig. 6 Encircled photon fraction for various values of the mosaic spread. In each figure are plotted the curves corresponding to different values of the ratio l/F

encircled photon fraction as a function of the circle radius for different values of the crystal mosaic spread and for different values of the l/F ratio. Thus a higher value mosaic spread implies higher spread of the focused photons, even though it also allows to use larger tiles with a reasonably negligible enlargement because the focal spot profile and size is mainly dominated by the enlargement due to the mosaic spread. A useful quantity to describe the spot size is the half power radius (R50 ), the radius of the circle that contains the 50% of the focused photons. Figure 7 shows that R50 /(Fβ) as a function of l/(Fβ) do not strongly depend on the mosaic spread in our range of interest. Springer

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Fig. 7 Normalized half power radius for different mosaic spread as a function of the normalized tile size.

Fig. 8 Reference configuration point spread function for a source on-axis (top) and for a source off-axis of 4 arcminutes (bottom).

5. Optical properties of the lens reference configuration 5.1. On-axis and off-axis response We will now study how the Laue lens PSF changes for photons coming from a point-like source offset by an angle α with respect to the lens axis direction. For the reference configuration, the on-axis PSF (α = 0) is shown in Figure 8 (top). Unlike the on-axis PSF, that obtained for an off-axis source (α = 4 arcmin) is no more symmetric. The photons are supposed to have a normalized wavevector that in Cartesian coordinate is (sin α, 0, cos α). Springer

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Fig. 9 Reference configuration radial distribution of the photons at different offset angles.

Fig. 10 Reference configuration photon distribution along the x axis.

Fig. 11 Reference configuration photon distribution along the y axis.

The PSF has the shape of a ring with larger width for negative values of x. Even if the ring shape is not symmetric, it is found that the photon barycenter is still in the lens focus. It is also visible the effect of the single tiles on the image. Each of the stripes visible in the PSF of Figure 8 (bottom) is the contribution of two tiles placed symmetrically with respect to the y axis. The distribution of the photons is shown in Figures 9–11 for various offset angle values. Figure 9 shows the radial photon distribution, while Figures 10–11 show the distribution of Springer

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the photons projected, respectively, along the x and y axes. As can be seen the distribution along the y axis is symmetric, while that along the x axis is distorted for negative values of the coordinate. This distortion gives information on the direction of arrival of the photons. 5.2. Angular resolution Looking at the radial distribution function of the focal spot (see Figure 9) it is possible to see that the peak position increases with offset. We assume that two celestial sources separated by an angle α can be resolved when their radial distributions are separated by at least the sum of their half width at half maximum (HWHM). With this assumption the angular resolution of the reference configuration lens is about 1.5 arcmin. 5.3. Field of view The numerical simulations show that the number of photons focused by the lens does not significantly vary as a function of the offset angle for values of the angle that are in the arcminute range. Even if the source counts for on-axis and off-axis sources is similar, offaxis photons are spread on a much larger surface (see Figures 9–11) and therefore need larger detectors. Being the background rate proportional to the detector surface, off-axis sources are detected with a lower signal to noise ratio (SNR). The FOV of the lens is thus determined by the detector radius. Photons from sources offset by an angle greater than the FOV are automatically discarded, given that they produce a ring with radius larger than that of the focal plane detector.

6. Conclusions The main properties of a lens made of a single ring of Cu (111) mosaic crystals have been investigated. Starting from a reference configuration of the lens, based on crystal tiles of 10 × 10 mm2 , 2 mm thickness, mosaic spread of 1 arcmin and a focal length of 50 m, we have investigated the effects of changing mosaic spread or thickness on the effective area and on the space distribution of the focused photons. The photon energy considered is 150 keV. As far as the crystal thickness on the effective area, its effect is relatively modest even for a significant thickness range (25%). Thus, compatibly with its feasibility, thickness lower than that optimized for reflection efficiency, can be taken into consideration with a sensitive reduction of the lens weight. As far as the mosaic spread is concerned, it appears that a value of 1 arcmin is a good compromise for the optimization of both the effective area and the encircled photon fraction. With 1 arcmin mosaic spread we have investigated the PSF of the lens for on-axis and offaxis sources suggesting a possible criterion for defining the lens resolution and we investigated the FOV, that for this kind of lens is basically limited by the detector size. The angular resolution is of the order of 2 arcmin. References Zachariasen, W.H.: Theory of X-Ray diffraction in crystals, Dover publications, Inc., New York, N.J. (1994) Pellicciotta, D. et al.: Laue lens development for hard X-rays (>60 keV), 2005 IEEE TNS, in press, (astroph/0511490). http://www.python.org http://www.numpy.org Springer

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http://www.scipy.org Brunetti, A. et al.: A library for X-ray-matter interaction cross sections for X-ray fluorescence applications, Spectrochimica Acta Part B, 59, 1725–1731 (2004) http://www.gnu.org/software/gsl/ http://pygsl.sourceforge.net/ Pisa A. et al.: Feasibility study of a Laue lens for hard x rays for space astronomy, Proc. SPIE 5536, 39–48 (2004) Pisa, A. et al.: “Development status of a Laue lens for high-energy x rays (>60 keV), Proc. SPIE 5900, 350–359 (2005) von Ballmoos, P. et al.: MAX: A gamma-ray lens for nuclear astrophysics. Proc. SPIE 5168, 482-491 (2004) Frontera, F. et al.: Exploring the hard X-/soft gamma-ray continuum spectra with laue lenses, Proc. 39th ESLAB Symposium, in press, 2005 (astro-ph/0507175)

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Exp Astron (2005) 20:229–239 DOI 10.1007/s10686-005-9017-y ORIGINAL ARTICLE

Development of a new photon diffraction imaging system for diagnostic nuclear medicine D. E. Roa · R. K. Smither · X. Zhang · K. Nie · Y. Y. Shieh · N. S. Ramsinghani · N. Milne · J. V. Kuo · J. L. Redpath · M. S. A. L. Al-Ghazi · P. Caligiuri

Received: 7 November 2005 / Accepted: 22 December 2005 C Springer Science + Business Media, B.V. 2006

Abstract The objective of this project is to develop and construct an innovative imaging system for nuclear medicine and molecular imaging that uses photon diffraction and is capable of generating 1–2 mm spatial resolution images in two or three dimensions. The proposed imaging system would be capable of detecting radiopharmaceuticals that emit 100–200 keV gamma rays which are typically used in diagnostic nuclear medicine and in molecular imaging. The system is expected to be optimized for the 140.6 keV gamma ray from a Tc-99m source, which is frequently used in nuclear medicine. This new system will focus the incoming gamma rays in a manner analogous to a magnifying glass focusing sunlight into a small focal point on a detector’s sensitive area. Focusing gamma rays through photon diffraction has already been demonstrated with the construction of a diffraction lens telescope for astrophysics and a scaled-down lens for medical imaging, both developed at Argonne National Laboratory (ANL). In addition, spatial resolutions of 3 mm have been achieved with a prototype medical lens. The proposed imaging system would be comprised of an array of photon diffraction lenses tuned to diffract a specific gamma ray energy (within 100–200 keV) emitted by a common source. The properties of photon diffraction make it possible to diffract only one specific gamma ray energy at a time, which significantly reduces scattering background. The system should be sufficiently sensitive to the detection of small concentrations of radioactivity that can reveal potential tumor sites at their initial stages of development. Moreover, the system’s sensitivity would eliminate the need for re-injecting a patient with more radiopharmaceutical if this patient underwent a prior nuclear imaging scan.

D.E. Roa · X. Zhang · K. Nie · N.S. Ramsinghani · J.V. Kuo · J.L. Redpath · M.S.A.L. Al-Ghazi University of California at Irvine – Medical Center, Department of Radiation Oncology Y.Y. Shieh · N. Milne University of California at Irvine – Medical Center, Department of Radiological Sciences R.K. Smither Argonne National Laboratory – Advanced Photon Source Division, Argonne, Illinois P. Caligiuri University of Chicago – Department of Radiology, Chicago, Illinois Springer

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Detection of a tumor site at its inception could allow for an earlier initiation of treatment and wider treatment options, which can potentially improve the chances for cure. Keywords Medical imaging . Lens . Photon diffraction . Radiopharmaceuticals . Nuclear medicine

1. Introduction The field of medical imaging has at its disposal a variety of modalities that are used for anatomical imaging, brain mapping, and diagnosis of organ diseases, to name a few. In many respects, these imaging modalities complement each other. For instance, in nuclear medicine, diagnostic imaging provides to the physician a pathophysiological view of the patient’s body, while computed tomography (CT) and magnetic resonance imaging (MRI) provide high-resolution images of the patient’s anatomy. Moreover, multimodality systems such as positron-emission tomography (PET) combined with CT or PET-CT provides these two forms of information in a single unit1−9 . Nuclear medicine relies on radiopharmaceuticals – biological compounds containing a radioactive isotope – to locate physiological abnormalities in the body. These isotopes are typically gamma-ray emitters of ∼100–200 keV in energy and with half-lives on the order of a few hours (see Table 1). The basic process for nuclear imaging involves introducing a radiopharmaceutical into the patient (usually by intravenous injection) which subsequently accumulates in the target site or biological process of interest. Advances in radiopharmaceutical manufacturing have resulted in compounds that specifically target certain sites or processes in the body with relatively low up-take in the surrounding body tissues. Higher concentrations of the radiopharmaceutical yield a higher gamma-ray emission rate relative to surrounding tissues and background. These gamma rays are captured by large detector arrays (e.g., gamma cameras, single-photon emission tomography – SPECT cameras) that subsequently send the data to a computerized system that generates a two- or three-dimensional image4−11 (Figure 1). Currently, most nuclear medicine imaging systems have limited spatial resolution that ranges from 7 to 15 mm. PET, the latest diagnostic system in nuclear medicine, can achieve resolutions of 4–5 mm at best. Furthermore, because the radiopharmaceuticals needed for PET imaging have significantly shorter half-lives (at most two hours), relatively large radiopharmaceutical doses must be prepared to leave enough activity to image the patient. In Table 1 Typical radiopharmaceuticals used in nuclear diagnostic medicine Nuclide

γ -Ray Energy (keV)

Purpose

320

Red cell volume

Cr-51

28 d

Ga-67

79.2 h

93, 185, 300, 393

Tumor location & inflammation

I-123

13.0 h

159

Imaging of thyroid

171, 245

Labeling white blood cells

140.5

Multi-purpose imaging Myocardial imaging

In-111 Tc-99m

67 h 6.02 h

Tl-201

73 h

135, 166

Xe-133

5.3 d

81

Ventilation imaging

1.83 h

511

Tumor imaging

F-18 Springer

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Fig. 1 Patient undergoing a scan using a gamma camera. Administration of a radiopharmaceutical (upper left display)

addition, most PET centers must be located in close proximity to a cyclotron facility, in order to minimize the transport time of the radiopharmaceutical from the preparation laboratory to the imaging room4−14 . The proposed imaging system uses an innovative approach based on photon diffraction for detecting gamma rays of a specific energy, within 100–200 keV, emitted by a radiopharmaceutical concentrated in a tumor site. Detection is carried out by focusing the incoming gamma rays into a small focal point on a detector’s sensitive area, analogous to a magnifying glass focusing visible light. Focusing gamma rays through photon diffraction has already been demonstrated with the construction of a gamma-ray diffraction lens telescope for astrophysics and a prototype lens for medical imaging15−20 . The application of this new system is envisioned to be for site specific scans of the patient’s body that can result in two- or three-dimensional images with a spatial resolution of ≤2 mm. If a patient has undergone a full-body scan and the data suggest the presence of a tumor or suspicious process (e.g., ischemia), a localized scan of that region could be performed with this imaging system without the need for injecting the patient with more radiopharmaceutical. This system may be better able to provide additional information to assess the size of the tumor or suspicious process and to more accurately define its location. 2. Materials and methods 2.1. Physics principles and conceptual view of a photon diffraction imaging system The proposed high spatial resolution imaging system relies on photon diffraction to redirect the trajectory of the gamma rays, emitted by a radiopharmaceutical concentrated in a tumor site, onto a detector. Photon diffraction is a three-dimensional process carried out by parallel planes of atoms within a crystal. This process is mathematically described by Bragg’s law21−26 , as: λ = 2d sin θ B

(1)

where “λ” is the photon’s wavelength, “d” is the spacing between atomic planes, and “θ B ”, known as the Bragg angle, is the angle subtended by the incoming gamma-ray trajectory and the lattice plane. The spacing between planes varies depending on the orientation of the lattice plane, which consequently varies the Bragg angle as well. Springer

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In the case of a cubic crystal, which is one of seven crystalline systems defined in crystallography, the spacing between the lattice planes is a function of their Miller indices (h, k, l) and it is defined as:

d= √

a h2 + k2 + l 2

(2)

where “a” is the crystal structure lattice constant. Subsequently, expressing the photon wavelength as:

λ=

hc Eγ

(3)

and incorporating equations 2 and 3 in equation 1 results in a re-defined expression of Bragg’s law as a function of gamma-ray energy, crystal lattice constant and crystal lattice plane: θ B = sin

−1

√ hc h 2 + k 2 + l 2 . 2E γ a

(4)

Equation 4 can be used to construct a photon diffraction lens consisting of concentric rings of crystals of different crystalline planes. Specific crystalline planes for each ring, can be selected based on the gamma-ray energy from a nuclear imaging radiopharmaceutical and from the gamma-ray incident angle determined by the source-to-lens distance and the concentric ring radius (Figure 2). The proposed imaging system consists of an array of photon diffraction lenses aligned to focus the gamma rays emitted by a common radioactive source. Each lens is mounted equidistantly between the source and its corresponding detector which defines a symmetric diffraction configuration. Gamma rays emitted within the boundaries of a lens’ solid angle are focused onto the sensitive area of the detector (Figure 3).

Fig. 2 Schematic diagram of the photon diffraction process carried out by a crystal diffraction lens Springer

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Fig. 3 (a) Conceptual view of the medical imaging system consisting of an array of 9 photon diffraction lenses. (b) Schematic diagram of a single lens with its corresponding detector and shield

This method of gamma-ray focusing and subsequent detection eliminates the need for high-spatial resolution collimators typically used in gamma cameras which causes significant reduction in sensitivity6−8 . Moreover, this photon diffraction imaging system can be tuned to diffract a specific gamma-ray energy (within ∼100 – 200 keV) by simply adjusting the source-to-lens and lens-to-detector distance such that the lens remains equidistant between the source and detector. This adjustment changes the Bragg angle to match the gamma-ray energy in order for photon diffraction to occur. 2.2. Construction of a prototype photon diffraction lens A prototype photon diffraction lens was constructed at Argonne National Laboratory to demonstrate the viability of using photon diffraction for detecting small concentrations of radioactivity. The prototype lens consists of 828 copper crystals cut in small cubes of 4 × 4 mm2 in cross-sectional area and 3–4 mm in thickness. Copper crystals were chosen due to their high diffraction efficiency for gamma-ray energies of 100–200 keV17 . Prior to cutting smooth circular slabs of copper crystal into small cubes, a set of measurements in a photon diffraction enclosure were carried out to determine the orientation of the crystalline plane to be used. These were transmission measurements that consisted of finding the maximum diffraction signal from that crystalline plane (orthogonal to the crystal’s circular surface) by irradiating the crystal piece with a 122 keV gamma-ray beam from a Cobalt-57 source and determining the crystal’s rocking curve. The copper crystals were distributed in 13 concentric rings assembled in two separate low-Z material substrates for the odd and even ring numbers, respectively, which facilitated the assembly process. Together they comprise a sensitive area of 132 cm2 (Figure 4). These substrates were disks of ∼16 cm in diameter with a thickness of 1.5 mm and with a flatness of approximately ±96 µradian. Although the substrates met this requirement around the central surface area, larger deviations were observed towards the edges. A dedicated lens assembly unit consisting of a Co-57 source, a 3-dimension translation stage, Pb collimators and a NaI detector was used to construct the prototype photon diffraction lens (Figure 5). Cobalt-57 with its 122 keV gamma-ray energy and 272 days half-life provided a suitable energy and time frame for assembly and determination of the diffraction response of the individual crystals in the lens. The diffraction response of a crystal was determined by isolating Springer

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Fig. 4 (a) Prototype crystal diffraction lens with its two substrates containing the concentric rings filled with crystals. (b) Mounting the two substrates for the actual lens configuration

Fig. 5 (a) Photograph of the lens assembly. (b) Schematic diagram of the assembly

the photons diffracted by that crystal using a Pb disc with a slot of 4-mm in width suspended at ≤1 cm above the crystal. Each crystal cube was cemented in place after maximizing its diffraction response signal.

3. Preliminary results and discussion Phantom measurements were performed with the prototype lens using Co-57 and Tc-99m sources mounted inside a 15 × 15 × 15 cm3 Lucite block. For the experiments using the Co-57 source, the lens was positioned at a distance of 84 cm from the source in order to maximize the diffraction of the 122 keV gamma rays emitted by this cobalt isotope. Springer

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Table 2 Data collected with different amounts of Tc-99m inside a Lucite phantom

Volume (cc)

Activity (mCi)

Peak Rate (Bkg Subtracted) (1-Lens)

0.126 0.031 0.008

3.6 0.7 0.04

382.4 c/s 57.8 c/s 4.0 c/s

Peak Rate (Bkg Subtracted) (9-Lenses)

Normalized Peak Rate 9-Lenses (cpm/µCi/cc)

3441.2 c/s 519.8 c/s 35.6 c/s

455.2 1437.2 6675.0

Background (Bkg): 1-Lens = 0.04 c/s = 2.4 cpm; 9-Lenses = 0.36 c/s = 21.6 cpm

Fig. 6 (a) Diffraction response of the prototype lens for a 122 keV gamma ray energy from a Co-57 source, FWHM = 3 mm. (b) Depth scan also using a Co-57 source – FWHM = 17 mm

For the 140.6 keV gamma rays from Tc-99m, the lens was positioned at 100 cm from the source. These experiments consisted primarily of scans along the horizontal (XY) axes that depicted the lens diffraction response at different source positions and provided information regarding the spatial resolution, defined as the full-width-at-half-maximum (FWHM) of the response signal. In addition, scans were performed to determine the lens’ sensitivity as a function of depth (Z-axis). Results from these scans using Co-57 yielded a diffraction response signal with a spatial resolution of FWHM = 3 mm for the horizontal scans and a depth sensitivity of FWHM = 17 cm (Figure 6). Measurements with Tc-99m were carried out using different amounts of this element in the form of sodium pertechnetate – a liquid substance. The Tc-99m was injected in 3 different cylindrical cavities of 0.126 cc, 0.031 cc and 0.008 cc, respectively. During a measurement, one of these cavities was mounted such that it was centrally located inside the Lucite phantom. The results are summarized in Table 2. As shown in Table 2, the data obtained for a single lens was extrapolated to the case of a 9-lens array like the one depicted in Figure 3a. Table 3 shows the estimated results expected Springer

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Exp Astron (2005) 20:229–239 Table 3 Estimated sensitivity data for a 9-lens array imaging system Volume (cc)

Diameter (mm)

cpm

√ S/N = Peak/ Bkg

1.0 0.5 0.01 0.005

12.4 9.8 2.7 2.1

2855.8 1427.9 28.6 14.3

614 307 6 3

Fig. 7 Calculated photon diffraction efficiency for a single lens

for a 9-lens system, assuming a tumor of spherical proportions with an activity of 1 µCi and using a normalized peak rate average of 2855.8 cpm/µCi/cc. However, it must be pointed out that in a clinical scan the tumor volume is not the only radioactive source. Surrounding organs adjacent to the tumor also absorb some of the radiopharmaceutical and the uptake is directly correlated to that organ’s volume. Consequently, these organs become a source of background during a clinical scan. Work in assessing the performance of the lens array system in a clinical scenario is currently in progress as described in the following section. In addition, efficiency calculations for a single lens based on photon diffraction theory resulted in a peak efficiency of 3% (Figure 7). This means that for a radioactive source emitting gamma rays isotropically, the overall efficiency -C1 for a single lens is:

- 1−Lens = (Diff. Eff.) × (132 cm2 /4π (100 cm)2 ) C - 1−Lens = 3.2 × 10−5 . C - 9−Lens = 2.9 × 10−4 , comparable For a 9-lens array, the overall efficiency becomes: C 8 with an overall efficiency for a gamma camera of Cγ −Camera = ∼3.0 × 10−4 . From the experimental data, the diffraction efficiency for the not fully optimized prototype lens was ∼1% which corresponds to an overall efficiency of 1.1 × 10−5 for a single lens and 1.0 × 10−4 for a 9-lens array. Springer

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4. Current status Monte Carlo calculations to assess the performance of the photon diffraction imaging system are currently in progress at the University of California at Irvine. These calculations are being performed using the Monte Carlo N-Particle (MCNP) computer code developed at Los Alamos National Laboratory27 . These calculations are aimed at determining the imaging system’s overall efficiency, sensitivity and specificity for detecting small tumors inside a patient’s body. This will be achieved systematically by:

r generating Monte Carlo calculations of the imaging system’s performance at different stages of development which will be used as benchmarks to assess the system’s experimental data, r assessing the overall efficiency of a fully assembled imaging system using Co-57 and Tc-99m radioactive sources inside a standard Lucite phantom, r assessing the imaging system’s overall efficiency using a Tc-99m radioactive source inside an anthropomorphic phantom, r assessing the imaging system’s overall efficiency using a Tc-99m radioactive source inside a small mammal. Also, measurements are currently in progress to determine the efficacy of using solid state rather than scintillation detectors in the new imaging system. In particular, we are interested in the 10 × 10 × 5 mm3 Cadmium Zinc Telluride (CdZnTe) detector array, which is already available commercially28 . This detector array is comprised of independent pixel size detectors that have an overall average energy resolution of ∼6.4 keV at 140 keV, compared to a resolution of 14 keV from a NaI detector. Such an energy resolution would allow us to set a narrower electronic window for acceptance of a specific gamma ray energy. This detector array coupled to a diffraction lens in the imaging system array could provide images with increased contrast due to reduction in the scattering background. Further, using a detector array rather than a single detector can provide information regarding tumor location.

5. Conclusion Preliminary work on a prototype lens done at Argonne National Laboratory has demonstrated that it is feasible to use photon diffraction for producing a high spatial resolution image. Although, we were able to achieve a spatial resolution of 3 mm with a not fully optimized photon diffraction lens, this spatial resolution is already about a factor of 2 better than a gamma camera’s spatial resolution. Moreover, these measurements have demonstrated that the lens is capable of focusing specific gamma-ray energies (122 keV for Co-57 and 140.6 keV for Tc-99m) by adjusting the source-to-lens and lens-to-detector distances. The limitation in spatial resolution observed in these measurements was due to the quality of the copper crystals used for the prototype lens. These crystals were too imperfect (400 arc sec ≤ mosaic width) for this imaging application. In addition, the deviations in flatness observed in the substrates also contributed to preventing us from achieving an optimal spatial resolution. However, we are confident that this technology can provide a significant contribution to diagnostic imaging in nuclear medicine and, furthermore, to the field of molecular imaging due to the high spatial resolution needed in this field. Finally, a considerable amount of work remains to be done to achieve the realization of a photon diffraction imaging system. Assessing the capabilities of a fully assembled Springer

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diffraction imaging system using Monte Carlo simulations is only the first step in the process towards realization. Measurements involving sophisticated anthropomorphic phantoms and subsequent, in-vivo measurements using small mammals will need to be carried out with this imaging system. Only upon successful results of these measurements could we move on towards a request for initiating testing of this system on patients. However, the benefits that this imaging system can provide are sufficient motivation to continue on this quest. Acknowledgements The authors would like to thank Edward J. Orlowski of the UCIMC Department of Radiation Oncology for some of the graphics work presented in this manuscript. Also special thanks goes to Algirdas Paugys for his work on making the lens setup and Lucite phantoms. This work was supported by a grant from the American Cancer Society – Institutional Research Grant #IRG-98-279-04 and the U.S. Department of Energy under contract W-31-109-Eng-38.

References 1. Beutel, J., Kundel, H.L., Van Metter, R.L.: Handbook of medical imaging, Vol. 1, SPIE Press, Bellingham, Washington (2000) 2. Curry, T.S., Dowdey, J.E., Murry, R.C., Jr.: Physics of diagnostic Radiology, Fourth Edition, Lea and Febiger Press, Philadelphia (1990) 3. Hall, E.J.: Radiobiology for the Radiologist. Fifth Edition, Lippincott Williams and Wilkins Press, New York (2000) 4. Adler, L.P., Weinberg, I.N., Bradbury, M.S., Levine, E.A., Lesko, N.M., Geisinger, K.R., Berg, W.A., Freimanis, R.I.: Method for combined FDG-PET and radiographic imaging of primary breast cancers. The Breast Journal 9(3), 163 (2003) 5. Carson, P.L., Giger, M., Welch, M.J., halpern, H., Kurdziel, K., Vannier, M., Evelhoch, J.L., Gazelle, G.S., Seltzer, S.E., Judy, P., Hendee, W.R., Bourland, J.D.: Biomedical imaging research opportunities workshop: report and recommendations. Radiology 229(2), 328 (2003) 6. Chandra, R.: Introductory physics of nuclear medicine. Third Edition, Lea and Febinger Press, Philadelphia (1987) 7. Wagner, R.H., Karesh, S.M., Halama, R.: Questions and answers in nuclear medicine. Mosby Press, Chicago (1999) 8. Palmer, E.L., Scott, J.A., Strauss, H.W.: Practical nuclear medicine. W.B. Saunders Company, Philadelphia (1992) 9. Khalkhali, I., Maublant, J.C., Goldsmith, S.J.: Nuclear oncology – diagnosis and therapy. Lippincott Williams and Wilkins Press, New York (2001) 10. Khalkhali, I., Villanueva-Meyer, J., Edell, S.L., Hanelin, L.G., Lugo, C.E., Taillefer, R., Freeman, L.M., Neal, C.E., Scheff, A.M., Connolly, J.L., Schnitt, S.J., Baum, J. K., Houlihan, M.J., Hale, C.A., Haber, S. B.: Diagnostic accuracy of Tc-99m SESTAMIBI breast imaging in breast cancer detection. J. Nucl. Med. 37, 74P (1996) 11. Boerman, O.C., Dams, E.Th.M., Oyen, W.J.G., Corstens, F.H.M., Storm, G.: Radiopharmaceuticals for scintigraphic imaging of infection and inflammations. Inflamm. Res. 50, 55 (2001) 12. Palmedo, H., Schomburg, A., Grunwald, F., Mallmann, P., Krebs, D., Biersack, H.: Technetium-99m-MIBI scintimammography for suspicious breast lesions. J. Nucl. Med. 37, 626 (1996) 13. Wagner, J.D., Schauwecker, D.S., Davidson, D., Wenck, S., Jung, S., Hutchins, G.: FDG-PET sensitivity for melanoma lymph node metastases is dependent on tumor volume. J. Surg. Onc. 77, 237 (2001) 14. Abella, H.: PET fails to match sentinel node biopsy for melanoma staging. Diagnostic Imaging Online, URL: www.diagnosticimaging.com/dinews/2003060201.shtml (2003) 15. Smither, R.K., Fernandez, P.B., Graber, T., von Ballmoos, P., Naya, J., Albernhe, F., Vedrenne, G., Faiz, M.: Review of crystal diffraction and its application to focusing energetic gamma rays. Exp. Astronomy 6, 47 (1995) 16. von Ballmoos, P., Smither, R.K., Naya, J.E., Albernhe, F., Faiz, M., Fernandez, P.B., Graber, T., Vendrenne, G.: A tunable crystal diffraction telescope for the energy range of nuclear transitions. Conf. Proc., Imaging in High Energy Astronomy, Anacapri, Italy (1994) 17. Kohnle, A.: A gamma-ray lens for nuclear astrophysics. Ph.D. Thesis, L’Universite Paul Sabatier, Toulouse, France (1998) Springer

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18. Smither, R.K., Roa, D.E.: Crystal diffraction lens for medical imaging. Proc. of SPIE: Medical Imaging 3977, 342 (2000) 19. Roa, D.E., Smither, R.K.: Copper crystal lens for medical imaging: first results. Proc. of SPIE: Medical Imaging 4320, 435 (2001) 20. Smither, R.K., Roa, D.E.: The physics of medical imaging with crystal diffraction lenses. Proc. of SPIE: Medical Imaging 4320, 447 (2001) 21. Bragg, S.L.: The development of X-Ray analysis. In: Phillips, D.C., Lipson, H. (eds.), Dover Publications, New York (1992) 22. Blakemore, J.S.: Solid state physics. Second Edition, Cambridge University Press, New York (1985) 23. Ahscroft, N.W., Mermin, N.D.: Solid state physics. Saunders College Press, Philadelphia (1975) 24. Warren, B.E.: X-Ray Diffraction. Dover Publications, New York (1990) 25. Zachariasen, W.H.: Theory of X-Ray diffraction in crystals. Dover Publications, New York (1994) 26. Tipler, P.A.: Modern Physics. Worth Publishers, New York (1987) 27. X-5 Monte Carlo Team: MCNP – A general monte carlo n-particle transport code. Version 5, Los Alamos National Laboratory (2003) 28. Laboratoire d’Electronique de Technologie de l’Information, 17 rue des Martyrs
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HAXTEL: A Laue lens telescope development project for a deep exploration of the hard X-ray sky (>60 keV) F. Frontera · A. Pisa · G. Loffredo · D. Pellicciotta · V. Carassiti · F. Evangelisti · K. Andersen · P. Courtois · L. Amati · E. Caroli · T. Franceschini · G. Landini · S. Silvestri · J. Stephen

Received: 3 February 2006 / Accepted: 18 May 2006 C Springer Science + Business Media B.V. 2006

Abstract A review of the HAXTEL project devoted to the development of a Laue lens telescope for hard X-/gamma-ray observation of the continuum spectra of celestial sources is presented. Main design properties, open issues, the status of the project and an example of multi-lens configuration with sensitivity expectations are discussed. Keywords Laue lenses · Gamma-ray instrumentation · Focusing telescopes · Gamma-ray source observations 1. Introduction The history of X-ray astronomy has shown that any advancement in our knowledge of the X-ray sky is strictly correlated with an increase in the instrument sensitivity. Above 10 keV, with respect to the traditional direct-viewing telescopes of the sky used till now, focusing optics appear the unavoidable solution to significantly improve the sensitivity level achieved so far. Now, while up to 60 keV the X-ray optics based on multilayer coatings (ML) now under development or the use of grazing incidence mirrors with high focal lengths (>50 m) can significantly improve the hard X-ray telescope sensitivity, above 100 keV, as we will see also in this paper, the best candidate technique appears the Bragg diffraction from mosaic crystals in transmission configuration (Laue lenses). The intermediate band (60–100 keV) can be covered with lower efficiency by the ML mirrors but also, as we will demonstrate here, F. Frontera () · A. Pisa · G. Loffredo · D. Pellicciotta University of Ferrara, Department of Physics, Via Saragat 1, 44100 Ferrara, Italy e-mail: [email protected] V. Carassiti · F. Evangelisti INFN, Section of Ferrara, Via Saragat, 1, 44100 Ferrara, Italy K. Andersen · P. Courtois Institute Laue-Langevin, Grenoble, France L. Amati · E. Caroli · T. Franceschini · G. Landini · S. Silvestri · J. Stephen INAF/IASF-Bologna, Via Gobetti, 101, 40129 Bologna, Italy Springer

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by Laue lenses, with a great advantage in sensitivity also in this band and the possibility of an inter-calibration of ML telescopes and Laue lenses in the case of satellite missions which include both. A huge increase in sensitivity (by a factor 100 or more) above 100 keV would open a new window of investigation of the high energy astrophysics, with the concrete possibility of fixing many open issues, apart from the prospect of unexpected discoveries. Among the open issues, we wish to mention (see also Frontera et al. [1]): – The properties of the high energy emission in presence of super-strong (>1013 G) magnetic fields (mass accreting X-ray pulsars, anomalous X-ray pulsars, Soft Gamma-Ray Repeaters); – The role of the Inverse Compton in compact mass accreting objects and in particular in Gamma Ray Bursts; – The role of non thermal mechanisms in extended objects (Supernova remnants, Galaxy clusters); – The role of the antimatter in the Universe from the study of the e+ − e− pair annihilation line and the effect on it of strong gravitational fields; – The study the star explosion mechanisms via the detection of the nuclear lines from synthesized elements (e.g., Co, Ni, Ti); – The high energy emission physics in AGNs from the study of the high energy cut-offs in their continuum spectra; – The origin of the high energy Cosmic X-/gamma-ray background (CXB). Synthesis models require a spectral roll-over with an e-folding energy of 100–400 keV in AGN. So far only a few spares measurements are available. Here we give an overview and the status of our HAXTEL (=HArd X-ray TELescope) project devoted to develop Laue lenses with a broad passband from 60 to 600 keV and beyond. This development is complementary to that which is being performed by other authors (e.g., von Ballmoos et al. 2004), devoted to the development of Laue lenses for the study of nuclear gamma-ray lines. 2. An overview of the results obtained thus far 2.1. Results of the feasibility study We summarize here the results of a theoretical feasibility study devoted to establish the best design of a Laue lens telescope along with its sensitivity expectations [3]. First of all the lens of our project is required to have a spherical shape with radius R and focal length f = R/2. If the crystals are available with flat geometry, which was our assumption, in order to best approximate the spherical geometry of the lens, crystal tiles with small cross sections are required. Among the best candidate materials for their high reflectivity, Cu (111) with mosaic crystal structure appears the most attractive in the hard X-/gamma-ray range (see Figure 1), and it is one of the few materials for which the technology for growing it with mosaic structure has already been developed with good results (see below). Thus for our feasibility study we have assumed Cu (111). Once the material choice has been fixed, crystal thickness and mosaic spread of the crystallites which make the mosaic crystal are the most crucial parameters to be fixed to optimize the lens performance. However their best values depend on the nominal Springer

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Fig. 1 Peak reflectivity of three materials which show high Bragg reflectivity and for which technology has been developed for mosaic structure. Cu (111) shows the best reflectivity above 100 keV. Reprinted from [3]

lens passband (E min , E max ), where E min =

hc hc f ≈ 2d sin θmax drmax

E max =

hc hc f ≈ 2d sin θmin drmin

(1)

with d being the crystal lattice spacing, and θmax and θmin being the maximum and minimum diffraction angles, respectively, permitted by the lens geometry, and thus dependent on the outer and inner radii rmax and rmin of the spherical segment, respectively (see Figure 2). The effect of the crystal thickness on the lens effective area is exemplified in Figure 3, in which a lens with 3 m focal length and a nominal passband from 60 to 200 keV are assumed. As can be seen, a single thickness is not the best solution for optimizing the lens effective area in its entire passband. While a thickness of 2 mm gives the highest effective area at low energies, a higher thickness (4 mm) optimizes the effective area at the highest energies. However the optimization of the lens effective area in a broad passband could imply a distribution of crystal thicknesses incompatible with lens weight constraints. We have investigated this issue elsewhere [5], finding that it is possible to find a good compromize. Also the mosaic spread β (FWHM of the angular misalignment of the crystallites), which defines the energy bandwidth (FWHM) of the photons reflected by a single crystal when they impinge on it at a given Bragg angle θ B ( E = Eβ/ tan θ B ), affects the lens effective area: a higher spread gives a higher effective area [3]. However a higher spread also produces a higher defocusing of the reflected photons in the focal plane. The best parameter which takes into account of both the effective area and the size of the focal spot in the focal plane is the focusing factor G given by: G = f ph

Aeff Ad

(2)

in which Aeff is the effective area of the lens and Ad is the area of the focal spot on which a fraction f ph of photons reflected by the lens fall. Taking into account that the sensitivity of Springer

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Fig. 2 Geometry of the Laue lens. Reprinted from [4]

the lens is given by nσ Imin (E) = n d Aeff f ph

Bd Ad T E

(3)

where Imin (photons cm−2 s−1 keV−1 ) is the the minimum detectable intensity in the interval

E around E, n σ is the significance level of the signal (typically n σ = 3–5), Bd is the instrumental background intensity (counts cm−2 s−1 keV−1 ), T is the exposure time to a celestial source, and n d is the focal plane detector efficiency at energy E, it can be seen that the lens sensitivity is inversely proportional to G. We have investigated the dependence of G on the focal length for three values of the mosaic spread (0.5, 1 and 2 arcmin) and for two different lens passbands: 90–110 keV (Low Energy, LE) and 450–550 keV (High Energy, HE). We find, for f ph = 0.50 which gives the fraction of photons corresponding to the Half Power Radius (HPR), and for crystal tiles of 15 × 15 mm2 , the result shown in Figure 4. As can be seen, G is significantly higher at low energies, it shows a saturation for high focal lengths, and, specially at high energies, a lower spread is more effective. This result has important consequences for the optimization the Laue lens design. It results that a lower spread is crucial to improve the lens sensitivity at high energies. However, compatibly with an acceptable G, a larger spread allows a higher effective area and thus Springer

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Fig. 3 Effect of the crystal thickness on the effective area. Reprinted from [3]

Fig. 4 Dependence of the focusing factor G on the focal length F for three different values of the mosaic spread in two different energy bands: 90– 110 keV (LE) and 450–550 keV (HE). See text

a better photon collection. A larger mosaic spread also requires a lower accuracy in the positioning of the crystals in the lens [3]. Another issue we have investigated is the disposition of the mosaic crystal tiles in the lens for a uniform coverage of the lens passband. The result is that the best crystal tile disposition is given by an Archimedes’ spiral (see Figure 5). As already discussed [3,4], this disposition, for low focal lengths, gives a smooth change of the lens effective area Aeff with energy, apart from jumps due to the contribution from higher diffraction orders (see, e.g., Figure 9). The advantage of the Laue lenses with respect to the direct-viewing telescopes, is better illustrated by the equivalent effective area S, defined, in the case of a lens, as S = G 2 Ad , while, in the case of a direct-viewing telescope, S is the useful detector area. In both cases the sensitivity (see Equation (3)) is inversely proportional to S 0.5 , which, for the lenses, is proportional to G, which increases with the focal length as shown in Figure 4. Special care has to be taken in the accuracy of the crystal tile positioning in the lens. A deviation of the crystal orientation with respect to the nominal position degrades the focusing factor. The accuracy required in the crystal tile positioning to get a negligible degradation of the nominal focusing factor not only depends on the mosaic spread, as above mentioned, but also on the focal length. Higher focal lengths require higher positioning accuracies, which is Springer

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Fig. 5 Disposition of the mosaic crystal tiles in the lens. The lens size is that required for a 210 cm focal length and a 60–200 keV nominal bandpass

at the current stage of development one of the major problems to be faced for the realization of a Laue lens. 2.2. Reflectivity measurements of Cu (111) mosaic crystal samples To test the reliability of the our feasibility study, we have performed reflectivity measurements of mosaic crystal samples of Cu(111). Samples of this material were provided by the Institute Laue Langevin (ILL), that has developed the technology for growing large single crystals of Copper with a small mosaic structure. The crystal samples of Cu (111) with different thicknesses and mosaic spreads were supplied to us for being tested at the Ferrara X-ray facility [7, 8]. Reflectivity curves were derived in different positions of the crystal surface to study the uniformity of the mosaic properties. Results of these measurements have been reported and discussed by Pellicciotta et al. [4]. An example of the derived reflectivity is shown in Figure 6. The reflectivity curves were fit with the theoretical model function derived by [9]. In most cases the results were found satisfactory. Figure 6 shows a typical result of the fitting analysis. However evidence of crystal inhomogeneity was observed near the crystal boundaries, mainly due to the crystal cutting procedure which perturbs the mosaic structure. Given that, for our goals, the crystals should be as homogeneous as possible the cutting procedure requires further refinement. In spite of that, the measurements results obtained substantially confirm the expectations of our feasibility study.

3. Status of our lens development project We are now developing a Demonstration Model (DM) to establish the best crystal assembling technique of the lens. The DM is a sector of the lens shown in Figure 5 and will be composed of 30 mosaic crystals with 3 arcmin spread and 15 × 15 mm2 front surface. A first mock-up of the DM, made of polycrystalline copper, has already been built for finding the best crystal assembly Springer

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Fig. 6 Example of measured reflectivity profile. Also shown is the best fit model and the residuals to the model (bottom panel). Reprinted from [4]

Fig. 7 Picture of the first DM mock-up during its development phase

technique which gives the needed mechanical accuracy in the crystal tile positioning. A picture of the first built mock-up during its development phase is shown in Figure 7. Once the DM has been developed and it is demonstrated to correctly work, a Prototype Model (PM) with the same focal length of the DM (210 cm) will be built, increasing the number of crystal tiles. The realization of the PM will be a good benchmark about our capabilities of scaling the assembling technology to larger lenses. Both DM and PM will be tested at the Ferrara X-ray facility which is now extended for this project [10]. Springer

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Fig. 8 Example of multi-lens configuration for the study of the continuum emission in the 60–1000 keV passband. The focal length assumed is 50 m. Part of the front surface of the Low Energy Lens (LEL) is taken by the four High Energy Lenses (HELs). See text for details

In addition to the hardware development, also a Monte Carlo (MC) code devoted to understand the optical properties of the lenses (point spread function, off-axis response, angular resolution) has been developed. Preliminary results have already been reported [5].

4. Example of possible multi-lens configuration for space astronomy As above discussed the gain of a Laue lens and thus its sensitivity approximately increase with the square of the focal length. We have already investigated different telescope configurations and focal lengths to efficiently cover the 60–1000 keV energy band. A multi-lens configuration appear the most sound solution. We show here (see Figure 8) a possible configuration with one large Low Energy Lens (LEL) with 60–600 keV energy passband and 4 High Energy Lenses (HELs) with 150–1000 keV nominal energy passband. All lenses have been assumed to have a focal length of 50 m and are designed according to the above discussed criteria, to study the continuum emission of celestial sources of gamma-rays. The main parameters of the lenses are summarized in Table 1. The advantage of this configuration is the achieved compromize between large collection area (see Figure 9 for LEL and for one HEL unit), which guarantees a good statistics of the collected photons up to the highest energies. The 4 units also guarantee a redundancy in the case of a failure of a detector, as it occurred in the case of one of the 3 units of the BeppoSAX MECS telescopes [11]. A drawback of the LEL with an energy threshold at 60 keV is its large diameter, which could be decreased by adopting a petal configuration to be launched folded and deployed in orbit. Also the lens weight is not negligible. The total weight of the crystals amounts to about 1600 Kg. A lighter solution can be obtained decreasing the number of HEL units. With 2 HELs the total crystal weight is 990 Kg. A possible further weight decrease could be obtained by decreasing the collection area of the LEL, e.g., adopting for the LEL a petal-like configuration. Springer

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Table 1 Main features of the Low Energy (LEL) and High Energy Lenses (HEL)

Parameter

LEL

HEL

Focal length (m) Inner radius (cm) Outer radius (cm) Mosaic crystal material Crystal tile size (mm2 ) Number of crystal tiles Crystal weight (Kg) Mosaic spread (arcmin) Nominal energy passband (keV) Half power radius of the focused photons (mm)

50 50 496 Cu (111) 10 × 10 × 2 221347 395 1 60–600 10

50 30 198 Cu (111) 10 × 10 × 4 83409 298 1 150–1000 10

Even the single HEL and LEL lenses show an unprecedented spectrum determination sensitivity. Assuming 106 s of exposure time and an energy bandwidth E = E/2, the sensitivity (see Equation (3)) of the LEL and that of one of the HEL units is shown in Figure 10. We have assumed a detection efficiency ηd = 1, f ph = 0.5 and a background intensity level B = 5 × 10−5 counts cm−2 counts cm−2 s−1 keV−1 , which is approximately the mean value measured with the PDS instrument aboard BeppoSAX in the 60–300 keV band. As can be seen, a sensitivity of a few ×10−8 cm−2 s−1 keV−1 or better, is achieved

Fig. 9 Effective area of the lenses. Left panel: Low Energy Lens (LEL); right panel: High Energy Lens (HEL), 1 unit

Fig. 10 Expected 3σ sensitivity of the lenses for an exposure time of 106 s. Left panel: Low Energy Lens (LEL); right panel: High Energy Lens (HEL), 1 unit Springer

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in the entire energy band (60–1000 keV), combining the LEL and HEL sensitivities. The maximum lens throughput is obtained between 100 and 550 keV, where the sensitivity could achieve values of a few ×10−9 cm−2 s−1 keV−1 , corresponding, in energy, to a few ×10−16 erg cm−2 s−1 keV−1 . Also for a deep study of the high energy nuclear lines (>600 keV), Laue lenses appear to be the best solution, but they require a specific design to maximize the sensitivity in a band around the expected energy of the lines (see, e.g., [2]). The focal plane detector performance is crucial for achieving the best lens sensitivity. In addition to a spatial resolution of the order of 1 mm and an energy resolution (FWHM) better than 2 keV at 500 keV (for the study of the annihilation line), a high detection efficiency is mandatory (for achieving the above sensitivity we have assumed ηd ∼ 1). The extension of the energy passband to energies lower than 60 keV (possibly down to 1 keV) is highly desirable for an accurate broad band study of the known high energy sources and for the identification of possible serendipitous sources we expect to discover with the unprecedented lens sensitivity. For spectral studies, a multilayer optics appears the best solution.

5. Conclusions The development of a Laue lens based on mosaic crystals for observing the hard X-ray sky in a broad continuum band has already successfully passed through a theoretical feasibility study to establish the best design of the lens and its expectations. Cu (111) has been suggested as a good candidate material. The experimental results obtained by the analysis of mosaic crystal specimens of Cu (111) produced at the ILL have encouraged our work and have demonstrated the correctness of our predictions. At the moment we are working on a Demonstration Model to establish the best assembling technique of the crystal tiles in the lens. After this phase a prototype model will be built and tested in our X-ray facility and, possibly, aboard a balloon flight. The expected sensitivity of our designed Laue lenses is unprecedented and is expected to open a new window in the high energy astrophysics. Acknowledgements We acknowledge the financial support by the Italian Space Agency ASI to the HAXTEL project. This research was possible also thanks to the received Descartes Prize 2002 of the European Committee.

References 1. Frontera, F. et al., Exploring the hard X-/gamma-ray continuum spectra with Laue lenses, Proc. 39th ESLAB Symposium, in press (2006) (astro-ph/0507175) 2. von Ballmoos, P. et al., MAX: a gamma-ray lens for nuclear astrophysics, Proc. SPIE 5168, 482 (2004) 3. Pisa, A. et al., Feasibility study of a Laue lens for hard X-rays for Space Astronomy, Proc. SPIE 5536, 39 (2004) (astro-ph/0411574) 4. Pelliciotta, D. et al., Laue lens development for hard X-rays (>60 keV), IEEE Trans. Nucl. Sci., in press (2006) (astro-ph/0511490) 5. Pisa, A. et al., Optical properties of Laue lenses for hard X-rays (>60 keV), Exp. Astron. 20, DOI 10.1007/s10686-006-9045-2 (2006) 6. Pisa, A. et al., Development status of a Laue lenses for hard X-rays (>60 keV), Proc. SPIE 5900, 350 (2005) 7. Loffredo, G. et al., X-ray facility for the ground calibration of the X-ray monitor JEM-X on board INTEGRAL, Astron. Astrophys. 411, L239 (2003) Springer

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8. Loffredo, G. et al., The X-ray facility of the Physics Department of the Ferrara University, Exp. Astr., in press (2006) 9. Zachariasen, W. H., Theory of X-rays Diffraction in Crystals, Wiley, New York (1945) 10. Loffredo, G. et al., The Ferrara hard X-ray facility for testing/calibrating hard X-ray focusing telescopes, Exp. Astron. 20, DOI 10.1007/s10686-006-9049-y (2006) 11. Boella, G. et al., The Medium-Energy Concentrator Spectrometer on board the BeppoSAX X-ray astronomy satellite, Astron. Astrophys. 122, 327 (1997)

Springer


CLAIRE: First light for a gamma-ray lens Peter von Ballmoos · Hubert Halloin · Jean Evrard · Gerry Skinner · Nikolai Abrosimov · Jose Alvarez · Pierre Bastie · Bernard Hamelin · Margarida Hernanz · Pierre Jean · Jurgen ¨ Knödlseder · Bob Smither

Received: 15 May 2006 / Accepted: 16 August 2006 C Springer Science + Business Media B.V. 2006

Abstract The objective of the R&D project CLAIRE was to prove the principle of a gammaray lens for nuclear astrophysics. CLAIRE’s Laue diffraction lens has a diameter of 45 cm and a focal length of 277 cm; 556 germanium-silicon crystals are tuned to focus 170 keV photons onto a 1.5 cm diameter focal spot. Laboratory measurements of the individual crystals and the entire lens have been used to validate a numerical model that we use to estimate the lens performance for a source at infinity. During a stratospheric balloon flight on 2001 June 14, CLAIRE was directed at the Crab nebula by a pointing system able to stabilize the lens to within a few arcseconds of the target. In 72 min of valid pointing time, 33 photons from the Crab were detected in the 3 keV bandpass of the lens: CLAIRE’s first light! The performance of CLAIRE’s gamma-ray lens, namely the peak reflectivity for a polychromatic source (9 ± 1%), has been confirmed by ground data obtained on a 205 meter long test range. CLAIRE’s measured performance validates the principle of a Laue lens for nuclear astrophysics, opening the way for a space-borne gamma-ray lens telescope P. von Ballmoos () · H. Halloin · G. Skinner · P. Jean · J. Knödlseder CESR, 9, av. du Colonel-Roche, 31028 Toulouse, France e-mail: [email protected] J. Evrard CNES, 18 Avenue Edouard Belin, 31401 Toulouse, France N. Abrosimov Institut für Kristallzüchtung, Max-Born-Str. 2, 12489 Berlin, Germany J. Alvarez · M. Hernanz IEEC, Edif. Nexus, 08034 Barcelona, Spain P. Bastie Laboratoire de Spectrométrie Physique, BP 87, 38402 St Martin d’Hères, France B. Hamelin Institut Laue-Langevin, BP 156, 38042 Grenoble, France B. Smither Argonne Natl. Lab, 9700 South Cass Avenue, Argonne, Il 60439, USA Springer

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that will achieve one to two orders of magnitude improvement in sensitivity over present technologies.

Keywords Instrumentation . Nuclear Astrophysics . Gamma Ray Optics . Laue Crystals

Introduction Nuclear astrophysics presents an extraordinary scientific potential for the study of the most powerful sources and the most violent events in the Universe. Ranging from the life cycles of matter to the behaviour of matter under extreme conditions, the gamma-ray Universe is mostly non-thermal. Its principal science themes, cosmic explosions and cosmic accelerators, are discussed in Section 1 of this volume. Today, traditional telescope concepts for nuclear astrophysics are reaching the physical limits for space missions; disadvantages whose impact increases with detector size – mostly related to the high background in space borne gamma-ray detectors – have lead gamma-ray astronomy to an impasse where “bigger is not necessarily better”. Present telescope concepts for nuclear astrophysics are based on inelastic interaction processes making use of geometrical optics (shadowcasting in modulating aperture systems) or quantum optics (kinetics of Compton scattering). Improvements in the sensitivity of an instrument can usually be obtained by a larger collection area – in the case of “classic” gamma-ray telescopes this involves a larger detector surface. However, since the background noise is roughly proportional to the volume of a detector, a larger photon collection area is synonymous with higher instrumental background. For “classic” gammaray telescopes, the sensitivity is thus increases at best as the square root of the detector surface. A possible way out of this dilemma consists of taking advantage of the wave character of the photons. Gamma rays can interact coherently inside a crystal via Bragg diffraction, i.e. through the interference between the periodic nature of radiation and the periodic structure of matter in a crystal lattice. The principles of crystal diffraction are discussed by Halloin and Bastie [8]. In a Laue diffraction lens, a large number of crystals are oriented so as to deflect incident photons towards a common focal spot: γ -rays are focused from a large collecting area onto a small detector volume. As a consequence, the background noise – which scales with detector volume – is extremely low, making possible unprecedented sensitivities. With the R&D project CLAIRE we took up the challenge of proving the principle of a gamma-ray lens for nuclear astrophysics, namely by demonstrating a prototype Laue lens and measuring its actual performance when observing a celestial source. As a first step, a ground-based Laue lens system had been set up and successfully tested by our collaboration [13]. The diffraction efficiencies of individual Ge crystals, were measured at the APS synchrotron at Argonne National Laboratories [11] and agreed with those expected from the Darwin model (efficiencies of 20 to 31% depending on energy and crystal planes). The next logical step towards a space-borne crystal lens telescope was to demonstrate a diffraction lens under space conditions and with an astrophysical target. This objective was realized between 1999 and 2003 with the CLAIRE project. Springer

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CLAIRE’s lens Concept and design Demonstrating the principle of a Laue diffraction lens during a short balloon flight implied the observation of a dependable γ -ray point source. At declinations compatible with the latitude of the available launch site of CNES at Gap-Tallard (French Alps) the Crab nebula, one of the rare standard candles at γ -ray energies, was an obvious choice. Whereas the limited energy band of a Laue lens is not a handicap when nuclear lines are to be detected, observing the Crab nebula’s continuum spectrum with a narrow bandpass Laue lens is a challenge. However, for a strong continuum source such as the Crab, and within the mass and size constraints for an exploratory balloon flight we found it advantageous to use all the crystal rings for a single, narrow energy band. To keep complexity and cost within the scope of a balloon project, it was clear that the energy to which the lens is tuned would be fixed, even though a tunable lens prototype had been demonstrated [10]. The choice of the energy band to be diffracted was then guided by practical considerations : the structural rigidity of the telescope, the upper limit of 500 kg for balloon payloads flying over France, and the severe pointing requirements for a balloon-borne lens made a short focal length preferable (see Equation 2 below). Since the focal length of a lens of a given diameter increases with energy, these arguments favoured energies below 200 keV for our 45 cm diameter lens frame. With the above constraints in mind, the energy to be diffracted was more or less arbitrarily chosen to be 170 keV for a source at infinity (511 keV being the 3rd harmonic. . .), this energy is sufficiently far away from two strong lines that are known to appear in a GeD background spectra at 139.7 and 198.4 keV (Ge isomeric transitions) and which are useful for a precise energy calibration. Geometry In a Laue-type crystal diffraction lens, crystals are disposed on concentric rings such that they will diffract the incident radiation of a given energy onto a common focal spot (Figure 1). In order to be diffracted, an incoming gamma-ray must satisfy the Bragg-relation 2d sin θ B = nλ

(1)

where d is the crystal plane spacing, θ B – the incident angle of the photon (Bragg-angle), n – the reflection order, and λ – the wavelength of the gamma-ray. See Halloin [9] for a thorough discussion of the principles of diffraction optics. Fig. 1 The basic design of a crystal diffraction lens in Laue geometry

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Fig. 2 CLAIRE’s lens during tuning on the optical bench at CESR. In the centre of the lens is a small telescope and CCD camera mounted on precision ball bearings. The direction of a source whose image remains on the same pixel during rotation (the “invariant pixel”) defines the optical axis

In a narrow bandpass Laue lens such as CLAIRE, every ring of crystals uses a different set of crystalline planes [hkl] in order to focus photons in a single energy band (E 2 = E 1 = E i in Figure 1) onto a common focal spot. For a given focal distance f of the lens, ri is the radius of ring “i” is given by ri = f tan[2θ B,i ] ≈ f

λ , di

(2)

where di is the crystalline plane spacing of ring “i” and λ is the wavelength of the radiation to be focused. Table 1 lists the ring radii and dimensions of CLAIRE’s lens; the parameters are for ˚ concentrating 170 keV photons onto Germanium crystals (lattice parameter a = 5.65 A) a common focal spot at a distance of 277 cm. Since mosaic defocusing (see e.g. [8, 9]) is negligible for CLAIRE’s short focal length (beam broadening on the focal plane 0.4–1.5 mm), the size and shape of the focal spot is dominated by the size of the crystal tiles projected on Table 1 The eight rings of CLAIRE’s gamma-ray lens

Springer

Ring

plane (Hkl)

d (hkl) ˚ A

Number of crystals

Crystal size (mm)

Mean radius (mm)

Scatter angle

0 1 2 3 4 5 6 7

111 220 311 400 331 422 333 440

3.27 2.00 1.71 1.41 1.30 1.15 1.09 1.00

28 52 56 72 80 88 96 104

10 × 10 10 × 10 10 × 10 10 × 10 10 × 7 10 × 10 10 × 7 10 × 10

61.7 100.8 118.2 142.6 156.2 174.7 188.2 201.7

0.64◦ 1.04◦ 1.22◦ 1.48◦ 1.61◦ 1.81◦ 1.92◦ 2.09◦

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the focal plane: in CLAIRE’s tuned lens, almost 100% of the diffracted photons are contained in a 1.5 cm diameter focal spot. Crystals CLAIRE’s crystals were produced by N. Abrosimov at the Institut für Kristallzüchtung (IKZ) in Berlin. The width of a crystals energy bandpass – and thus the lens efficiency – are governed by the mosaicity of the crystal [9]. In order to obtain homogeneous, constant quality crystals with the required optimal mosaicity (25–50 arcs), small amounts of Silicon are added to the Germanium melt during the growth process. The Germanium-rich Ge1−x Six crystals (x ≈ 0.02) were grown by a modified Czochralski technique using Silicon feeding rods to replenish the loss of Si in the melt during the growth [1]. The mosaicities of the Ge1−x Six crystals range between roughly 30 arcsec and 2 arcmin, leading to a field of view of about 1.5 arcmin and a diffracted energy bandwidth of about 3 keV at 170 keV. A correlative study between crystal structure, mosaicity and diffraction efficiency of the CLAIRE crystals is presented in [2]. After cutting of the crystals ingots at IKZ Berlin, most of the crystal tiles were characterized (mosaicity) at the Hard X-Ray Diffractometer of ILL Grenoble. Lens assembly and tuning At CESR Toulouse, the individual crystal tiles were mounted on flexible aluminium supports, which in turn are mounted on the lens frame. The reinforced 45 cm diameter titanium frame that holds up to 576 crystals on 8 rings (Table 1) was designed and manufactured at the Argonne National Laboratory, Argonne, USA. The tuning of the lens consists of tilting each crystal tile to the appropriate Bragg angle so that the diffracting energy is 170 keV for a source at infinity. Instead of directly calibrating the lens for a parallel beam of 170 keV photons, crystal tuning on the 20 m optical bench at CESR uses a 150 kV X-ray generator situated on the lens optical axis at a distance of 14.16 m. At this distance, a crystal will be correctly tuned (170 keV at infinity) if it diffracts 122.28 keV photons. A co-aligned mask (brass-lead sandwich) of the size of the entire lens, placed on the optical axis just in front of the lens, was used to select an individual crystal for tuning, while shielding already tuned crystals. The continuum spectrum of the X-ray generator allows us to quickly find the diffraction peak as soon as it shows up at any energy (typically between 90–140 keV, corresponding to an angular tolerance of 0.4◦ to 1.4◦ depending on the ring). The crystal inclination is then manually fine adjusted (by a screw pushing against the crystals aluminium support plate – 1% of a full turn corresponds to a shift of about 1 keV) so that the diffraction peak shifts until it reaches 122.28 keV. The CLAIRE crystals were tuned to within a precision of ± 0.3 keV, corresponding to a precision of ±8

(innermost ring) to ±25

(outermost ring), respectively. The configuration of the CESR optical bench was chosen to allow for swift tuning/detuning verification using the 122 keV line of a 57 Co source (see below). Pointing and alignment In order to be able to point the lens at a source (during tuning, ground tests, as well as in flight), the lens optical axis has to be visualized. For this purpose, a small optical telescope equipped with a CCD camera is mounted in the centre of the lens frame on precision ball bearings; Springer

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the ball bearings allow the telescope to rotate around its optical axis. When observing a light source while this telescope is rotated, the image on the CCD describes a circle whose centre gives the direction of the rotating axis. This invariant pixel is then made the gamma-ray lens optical axis. The method provides an alignment accuracy better than 10 arcsec and was used throughout all operations of the lens – from crystal tuning to flight alignment. Even when refocusing of the optical telescope becomes necessary (from the 14 m source to infinity) or if the CCD camera is to be changed, the lens axis remains unchanged within the required precision. On the optical bench at CESR, the light source was a small lamp positioned on the optical axis as close as possible in front of the target of the X-ray generator tube. Performance of the individual crystals The spectra recorded during the tuning campaigns (2000, 2001, 2003) represent large databases with 400 to 600 individually measured crystals. The characteristics of the recorded spectra, mainly the integrated flux, the width and the shape of the diffraction peak, permit the determination of the crystals’ parameters (mosaicity and mean size of the crystallites, see [6]). During the tuning campaign 2003, the integrated flux in the diffraction peak was measured for 559 individual crystals. Figure 3 compares the statistics of these fluxes in the eight rings. Two main lessons are conveyed by this graph: a. the innermost rings ([111] and [220] crystals) are roughly 4 times more efficient than the outermost rings ([333] and [440] crystals). This behaviour is in agreement with theoretical peak efficiencies. Note that the largest part of the crystals is situated in the outer rings – where efficiencies are unfortunately lowest. b. the large spread of the measured fluxes in a single ring means that the quality of the CLAIRE crystals is quite heterogeneous. The efficiency of the individual crystals within a ring varies by factors of 2 to 10, depending on the ring! The tuning data, however, also prove that real crystals can be as good as the Darwin model predicts: the best crystals of the lens have peak efficiencies above 20%.

1.5 111

2

diffracted photons [cm s µA]

Fig. 3 Diffracted fluxes of 559 individual Ge1−x Six crystal from the 2003 tuning campaign. Boxes enclose 50% of the data set of each ring, the median value of the flux is displayed as a line. The lines extending from the top and bottom of each box mark the minimum and maximum values within the crystal data set of each ring

220

311

400

331

422

333

440

CLAIRE 2003 tuning data of 559 Ge crystals 1

0.5

0 0

1

2

3

4

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The parameters from the database were used for the development of a realistic numerical model of our lens (Monte-Carlo simulation). The lens model turned out to be essential for comparing and scaling the different experiments with their various conditions of pointing, source spectrum and distance. Ground tests In order to estimate the diffraction efficiency of the lens, as well as its angular response, several experiments have been conducted on the CESR optical bench, at the launch site in Gap-Tallard (French Alps) and during a “long distance” test near Figueras (Catalonia). The 57 Co standard The gamma-ray line at 122.06 keV from a small radioactive 57 Co source was observed at a distance of 14.07 m. This test was performed on the optical bench at CESR and on the launch site where an X-ray generator can not be operated. The resulting global reflectivity turned out to be merely 3.2 ± 0.1%; the reflectivity being defined as the ratio of photons concentrated onto the focal spot over the number of photons incident on all the crystals of the lens. This low reflectivity is the consequence of two effects – the parallax of the crystals for a source at finite distance and the high absorption of the crystals whose thickness was optimized for 170 keV. At a distance of 14 m, the angular size of a 1 × 1 cm footprint crystal is ∼2.4 arcmin ∼1.7 arcmin for the crystals with 0.7 cm height). Since these values are typically 3–4 times larger than the mosaicity of the crystals, the Bragg condition is only satisfied in a fraction of the crystal volume, leading to an apparently low diffraction efficiency. We have used our numerical model to extrapolate the efficiency of the 57 Co tests (monochromatic, divergent beam at 122 keV) for an astrophysical target (polychromatic, parallel beam at 170 keV). Taking into account the estimated uncertainties on the crystals’ parameters and considering a diffracted peak width of 3 keV FWHM, the peak efficiency for parallel radiation at 170 keV estimated from the 57 Co data is 7.7 ± 1%. The 57 Co standard tests were performed before and after transferring the lens to the launch site, showing that the lens did not suffer significant detuning during the 6 hour drive from CESR Toulouse to Gap-Tallard. X-ray beam tests on CESR optical bench In addition to crystal tuning, the optical bench at CESR also allowed measurements of the reflectivity in a polychromatic, though divergent, beam at energies below 150 keV. Although the continuum spectrum of the X-ray generator can “cover” the entire volume of each crystals with photons satisfying the Bragg condition, the peak reflectivities measured were too low (typically 3.5 ± 0.4%) for a reason very similar to the one that made the 57 Co standards look to low (see above): The total energy band “covered” by a single crystal is in fact determined by its angular width as seen from the source. However, at any one given energy within this band, only a slice of the crystal’s volume actually satisfies the Bragg condition and contributes to the diffracted flux. The width of this energy slice is determined by the crystal’s mosaicity. As a consequence, the ratio of the total crystal volume to active volume is again the ratio of mosaicity to angular extent of the crystal. The semi-empirical value that is deduced from the laboratory X-ray generator data for the peak efficiency at 170 keV is 8.7 ± 1%. Springer

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1000 C preflight

normalized counts in focal spot

Fig. 4 The diffractions peak of CLAIRE’s lens for two “lens totals” performed on the CESR optical bench using the x-ray generator. Preflight data were taken in May 2001, post flight data are from September 2002. The best fits (Lorenzians) show widths of 3.0 and 3.4 keV FWHM, respectively

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The overall diffraction efficiency of the lens was verified in this manner just before the 2001 balloon campaign, and again more than a year later, after the balloon flight. The energy spectrum of the two diffraction peaks, normalized for equivalent experimental conditions (generator current, absorber thickness), are shown in Figure 4. In spite of a rough parachute landing (>50 g) and recovery, the two tests show virtually identical integrated reflectivities (roughly 2% reduction mostly due to crystals that detached during landing and recovery) and only a slight detuning. So although the CLAIRE lens had not been designed for this, its robustness has demonstrated that a gamma-ray lens can be made sturdy enough to withstand high-g shocks and vibrations. CLAIRE “TGD” In May 2003 the CLAIRE telescope was tested on a 205 m long optical bench, set up on a small airfield near Figueras in northern Catalonia. At this “quasi infinite” distance (TGD : Test a` Grande Distance) the diffracted energy is 165 keV. Three mobile cabins were installed on the airstrip : the gamma-ray lens and germanium detector were set up in a first cabin, a second cabin about 200 meters away from the first one was used to accommodate the X-ray source, a third cabin served as control room; its location, about 15 m from the lens/detector container, was chosen to be well out of the X-ray beam. The X-ray source consisted of an industrial X-ray generator with a 2.5 × 2.5 mm tungsten target. The voltage and current were set to 250 kV and 1 mA respectively, allowing for sufficient X-ray flux at 165 keV after absorption by 205 m of air. CLAIRE was pointed to the X-ray source with an alignment method similar to that used in the laboratory and in flight: the X-ray tube was positioned such that a lamp mounted immediately in front of it coincided with the invariant pixel of the rotating CCD camera. The peak efficiency (205 m, diffracted energy 165 keV) was measured to be 8.5 ± 1%, in agreement with the lens simulations for this test, and compatible (considering the error bars) with the other ground tests. Springer

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Fig. 5 CLAIRE TGD energy response of the lens for various depointing angles

The different values for the lens efficiency measured on the ground (rescaled 57 Co standards, 7.7%; rescaled X-ray beam tests, 8.7%, and TGD, 8.5%) will be discussed below. Figure 5 shows the energy response of the lens for various off-axis angles of the source (from 30 to 270 arc seconds). The curves are compared with the results of a Monte-Carlo simulation of these experiments, using the crystal parameters as deduced from the tuning data. The shape and deformation of the energy response are well reproduced by the model, validating the theoretical instrumental response of the lens. For a detailed discussion of the CLAIRE TGD see [3].

The balloon instrument Gondola The lens module, detector package, and pointing systems are integrated into a telescope structure made of composite materials (Figure 6). The 3 m telescope structure, consisting of 18 carbon fibre spars and 3 honeycomb platforms only weighed 100 kg. The structure was conceived, manufactured and tested by the University of Birmingham. The upper platform holds the lens and its fine pointing system. The detecting system (detector matrix, Dewar, anticoincidence shield/collimator and electronics) are mounted on the lower platform. The entire payload weighs 500 kg. Detector Diffracted photons are collected on a small 3 × 3 array of high-purity germanium detectors, housed in a cylindrical aluminium cryostat. Each of the individual Ge bars is an n-type coaxial detector with dimensions of 1.5 cm × 1.5 cm and 4 cm long, with an internal electrode bore hole (35 mm depth, 5 mm diameter). Preamplifier electronics are located in a pressurized Springer

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Fig. 6 The CLAIRE telescope at Gap during the 2001 balloon campaign. On the first platform, the gamma-ray lens in its two-axes gimbal

aluminum capsule directly behind the detector matrix. The detector is cooled by a liquid nitrogen dewar that was also pressurized during the flight. The detector is actively shielded by a CsI(Tl) side shield and BGO collimators. The focal spot of the gamma-ray lens is visualized by the circle produced on the detector plane by a small laser mounted on the rotating alignment telescope. During flight the spot may wander around on the Ge-detector matrix as the primary stabilization seeks its central position. The focal spot ideally is on the central detector of the Ge matrix. The surrounding detectors can be used either to enhance the detection efficiency of source photons having undergone a Compton scatter in the center detector, or alternatively they may be used for background rejection. Stabilization and pointing The CLAIRE stabilization and pointing system was developed by the balloon division of the French Space Agency CNES with the help of the Observatoire de Genève, Switzerland. Two almost independent pointing stages allow the observation of a target located within a few degrees of the sun (on June 14 and 15 the Crab is within 1◦ of the sun). The primary pointing system stabilizes and points the entire telescope to within 10 arc minutes; azimuthal control is performed by a torque swivel (that also measures the torque between gondola and balloon), and by using azimuthal information from a magnetometer and a gyrometer. A screw jack in conjunction with an inclinometer is used for the elevation control. The system is completed by a device for passive damping of gondola motions. The fine pointing system consists of a two-axes gimbal that stabilizes and points the gamma-ray lens only. Fast control of the gimbal is performed through two custom-made high precision actuators, the pointing is controlled by mechanical gyrometers and a sun sensor mounted on a two-axis turret for offset. The absolute offset is calibrated and controlled by the central CCD camera and a wide field CCD camera. The stabilisation of the gamma-ray lens has been shown to be better than 3 arc seconds during the balloon flights. Springer

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Table 2 The 2001 CLAIRE balloon flight Launch Instrument weight Balloon Float altitude Targets Termination

6:29 UT, June 14, 2001, Aerodrôme de Gap-Tallard 500 kg Zodiac, 600 000 m3 ≤3 hPa (41 km), attained at 9:02 UT Crab nebula, Sun – active region 9489 (9h45–9h52) 15:12 UT, landing close to Bergerac

Before pointing the Crab, the sun was simultaneously observed by the central telescope, by the wide field CCD camera and by the sun-sensor. This operation allowed us to relate the invariant pixel and the zero point of the pointing system during the balloon flight. A thorough description of the gondola and pointing system is given in Laporte et al. [12]. Balloon flight On June 14 2001, CLAIRE was launched by the balloon division of the French Space Agency CNES from its base at Gap-Tallard in the French Alps (see Table 2). As for the technological maiden flight a year earlier [14], the CNES crew succeeded again to launch in a narrow two day window (!) defined by the sun’s angular proximity to the Crab nebula. The 500 kg payload was lifted from the Gap airfield by a 600 000 m3 Zodiac balloon at 06:29 UT. Thanks to the auxiliary balloon technique routinely used by CNES the launch went very smoothly. The float altitude of 2.8 hPa (corresponding to 41 km) was reached in about 2.5 h, termination took place after nearly 6 h at float, close to Bergerac in southwestern France. Telemetry data indicated that the fine pointing system performed very well with an error ≤0.01◦ elevation/cross-elevation for 89% of the time at float, and that the primary pointing system stabilized the focal spot so that it stayed within the detector for 77% of the good fine pointing spells. According to telemetry, we therefore expected roughly four hours of recorded Crab data. All nine germanium detectors showed nominal performance during the flight, the energy resolution at 170 keV was about 2.5 keV FWHM. The anti-coincidence shield reduced background noise by a factor of 10, resulting in a rate of about 2.3 × 10−4 cts s−1 keV−1 cm−3 at 170 keV for single events (see top of Figure 7) – four background-lines dominate the spectrum: three Ge isomeric transitions (53.4, 139.7 and 198.4 keV) and the e− e+ annihilation line (511 keV). A thorough discussion of the detector and anticoincidence system is given by Halloin [6]. First light A comprehensive simulation of the observation (Crab spectrum, atmosphere, flight – and pointing-data, lens reflectivity, detector efficiency) showed that a 4.5 σ detection was expected. Although both the fine pointing quality of the lens, and the primary pointing of the gondola seemed to have worked satisfactory, an initial data analysis did not result in a positive detection of the Crab [7]. The key for finding a signal turned out to be the discovery of an offset of the lens axis, both in the fine pointing system (the Crab pointing) and in the primary pointing system (position of the focal spot on the detector). The offset in the Crab pointing was due to an incomplete Springer

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Fig. 7 Top: Spectrum for single events at float altitude (background noise spectrum); bottom : spectrum for single events recorded during time intervals with good Crab pointing: at 170 keV, an excess of 33 photons is detected

measurement of the prismatic effect in the CCD’s sun-filters. We were able to measure the direction and amount (70 arcsec) of the effect a posteriori in our laboratory. Reassembling and testing the telescope structure revealed that the focal point moves by 4.5 to 6 mm in elevation (Y-axis) when in the observing position, and that of its position in the X-axis is indeterminate to within a range of about −15 and 15 mm. These mechanical problems would have been taken care of by optical tracking of the alignment laser that materializes the focal spot during the observation. A detailed discussion of CLAIRE’s primary and fine pointing is given by Halloin [6]. Crab detection The offset in the fine pointing of the Crab led to a broadening of the peak of diffracted source photons to 8 keV FWHM – akin to the effect illustrated in Figure 5. This effect is readily taken into account in the data analysis. The corresponding broadening of the focal spot is negligible Springer

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since the size of the crystal tiles dominates the beam size in the case of CLAIRE’s short focal length. As a consequence of the remaining uncertainty in the focal spot position, we made 30 data-analysis trials in the mechanically possible range. The maximum significance was found by assuming offsets of +5 mm in the vertical and +10 mm in the horizontal directions. With this detector offset and event discrimination the useful exposure time is reduced to 72 minutes, but now the spectrum (Figure 7 bottom) shows an excess of 33 photons at 170 keV, a 3.5 σ effect corresponding to a probability of 99.976%). For comparison, a spectrum of all single events for every detector at float altitude (reference for background) is shown in the top part of Figure 7. To obtain the actual significance of the detection, the number of trials has to be taken into account. The trial positions are strongly dependent since spectra from adjacent positions (1 mm apart) contain a large number of common events. A series of flight simulations using background noise only (no Crab signal) showed that our 30 trials are equivalent to about 4.2 independent trials – the actual significance of our detection is hence 3σ (0.999764.2 ≈ 0.99898). Flight performance For an off-axis source, the diffraction peak is broadened (i.e. 8 keV) but its integral remains roughly constant. Assuming a Crab flux of (1.42 ± 0.02) × 10−4 ph s−1 cm−2 keV−1 at 170 keV [5], the detection of 33 photons implies a peak efficiency of ≈12.5 ± 4+0 −2 % (error bars: the first figure is the statistical uncertainty, the second figure is an estimation of systematic effects), corresponding to an effective area of about 64 cm2 at 170 keV. The above efficiency is obtained using the following instrumental parameters: a mean detector efficiency of 45.5% (at 170 keV), a deadtime of 15%, a bandpass of 3 keV FWHM for the perfectly pointed lens, and a mean atmospheric transmission of 67% (at 170 keV, altitude of 41 km).

Conclusion Experiments with continuum sources at distances of 14.16 m, 22.52 m (CESR optical bench), 205 m (long distance test) and infinity (Crab nebula) have demonstrated the performance of our Laue lens. Figure 8 represents the recorded spectra for these experiments (lower graph), compared with the theoretical energy-distance relationship for a diffracted source (upper graph). The energies of the centroids are in very good agreement with theory, slight departures from theoretical values (less than 0.5 keV) being the consequence of the incident spectral shape and/or the detector calibration drifts. Table 3 summarizes the measured peak efficiencies of these experiments, and compares them with equivalent simulations. Measurements and simulations are in fairly good agreement. Rescaling the measured efficiencies of the ground tests for a polychromatic source at infinity (diffracted peak width of 3 keV FWHM), obtains values compatible with a peak efficiency of 9 ± 1%. CLAIRE’s stratospheric flight has provided the first observation of an astrophysical source with a gamma-ray lens. In combination with the long-distance test on the ground, these results validate the theoretical models and demonstrate the principle of Laue lens. Moreover, CLAIRE’s stratospheric flight represents a first demonstration of the Laue lens technology in space environment. In this article, we have described the performance of CLAIRE on the ground and in flight. Springer

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Fig. 8 Recorded spectra for various source distances (lower graph). The upper graph represents the distance of the source as a function of diffracted energy. The vertical lines show the theoretical corresponding energies. 14.162 m corresponds to the tuning distance (E th = 122.29 keV). The measurement at 22.52 m (E th = 136.5 keV) was performed on the optical bench at CESR with a partially tuned lens. 205 m is the distance of the generator on the long distance test range (E th = 165.5 keV). The peak for an infinite distance is taken from the stratospheric flight of June 2001 (see above)

Extrapolating this performance to the case of a space-borne instrument [4], this volume) reveals an outstanding potential for nuclear astrophysics : a gamma-ray telescope using a Laue diffraction lens has the potential to combine narrow line sensitivities of a few 10−7 ph s−1 cm−2 , with high spectral and angular resolution, and the capability of measuring the polarization of the incident photons. The sensitive gamma-ray spectroscopy that Table 3 Comparison of experimental results and simulations

Experiment source

Dist. (m) Energy spectrum

Predicteda,b Measureda,c Rescaled eff.a efficiency (%) efficiency (%) at 170 keV, ∞ (%)

57

CESR optical bench Co isotope 14.1 CESR optical bench 150 kV X-ray generator 14.2 CLAIRE TGD 300 kV x-ray generator 205 CLAIRE balloon flight Crab nebula a Peak

∞

122.1 keV narrow line 3.668±0.004

3.17±0.02±0.1 7.7±1

122.3 keV continuum

3.5±0.1±0.3

8.7±1

165.5 keV continuum 8.53±0.02

8.5±0.5±0.5

8.5±1

170 keV continuum

8.88±0.02

+0

12.5±4−2

12.5±4

efficiency assuming a energy bandpass of 3 keV FWHM for polychromatic sources, diffracted fraction of the incident flux on the lens for monochromatic sources. bars are only statistical. c Error bars include the statistical uncertainty (first figure) and an estimation of systematic effects (second figure) b Error

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can be performed by such an instrument addresses a wide range of fundamental astrophysical questions such as the life cycles of matter and the behaviour of matter under extreme conditions. Acknowledgments The authors wish to thank the balloon division of the French Space Agency (CNES), which built the pointing system and operated the CLAIRE flights from the launch to the gondola recovery. This work was partly supported by the U.S. Department of Energy under contract W-31-109-Eng-38. The team at CESR is grateful for continuing support from the French Space Agency CNES. The authors of this article acknowledge valuable contributions of the two referees.

References 1. Abrosimov, N.V., Rossolenko, S.N., Thieme, W., Gerhardt, A., Schröder, W.: J. Crystal Growth 174, 182 (1997) 2. Abrosimov, N.V., Lüdge, A., Riemann, H., Kurlov, V.N., Borissova, D., Klemm, V., Halloin, H., von Ballmoos, P., Bastie, P., Hamelin, B., Smither, R.K.: J. Crystal Growth 275, e495–e500 (2005) 3. Alvarez, J., Halloin, H., Hernanz, M., von Ballmoos, P., Jean, P., Skinner, G., Abrosimov, N., Smither, R., Vedrenne, G.: Proceedings of the 5th INTEGRAL Workshop, Munich 16–20 757, ESA SP-552 ( 2004) 4. Barrière, N. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9058-x (2005) 5. Bartlett, L.M.: High resolution gamma-ray spectroscopy of the Crab. PhD thesis, Univ. of Maryland (1994) 6. Halloin, H.: Premières lumières pour une lentille gamma, PhD, U. Paul Sabatier, Toulouse (2004) 7. Halloin, H., von Ballmoos, P., Evrard, J., Skinner, G.K., Abrosimov, N., Bastie, P., Di Cocco, G., George, M., Hamelin, B., Jean, P., Knödlseder, J., Laporte, Ph., Badenes, C., Laurent, Ph., Laurens, A., Smither, R.K.: Proc. SPIE (Intl. Soc. for Optical Engineering), Vol. 4851, p. 895, 2003 8. Halloin, H., Bastie, P.: Exp. Astron. 20, DOI 10.1007/s10686-006-9064-z (2005) 9. Halloin, H.: Exp. Astron. 20, DOI 10.1007/s10686-006-9063-0 (2005) 10. Kohnle, A., Smither, R.K., Graber, T., Laporte, Ph., Olive, J.F., von Ballmoos, P.: Nuclear Instr. Meth. Phys. Res. Sect. A 408, 553–561 (1998a) 11. Kohnle, A., Smither, R.K., Graber, T., Fernandez, P., von Ballmoos, P.: Nuclear Instr. in Meth. in Phys. Res. Sect. A 416, 493 (1998b) 12. Laporte, Ph., Evrard, J., Laurens, A. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9067-9 (2005) 13. Naya, J., von Ballmoos, P., Smither, R.K., Faiz, M., Fernandez, P., Graber, T., Albernhe, F., Vedrenne, G.: Nuclear Instr. Meth. Phys. Res. Sect. A 373, 159 (1996) 14. von Ballmoos, P., Evrard, J., Skinner, G.K., Abrosimov, N., Bastie, P., Di Cocco, G., George, M., Halloin, H., Hamelin, B., Jean, P., Knödlseder, J., Laporte, Ph., Laurent, Ph., Laurens, A., Smither, R.K.: ESA Symp. Proc., Exploring the Gamma-Ray Universe, SP-459, 649 ( 2001)

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Exp Astron (2005) 20:269–278 DOI 10.1007/s10686-006-9058-x O R I G I NA L A RT I C L E

MAX, a Laue diffraction lens for nuclear astrophysics N. Barrière · P. von Ballmoos · H. Halloin · N. Abrosimov · J. M. Alvarez · K. Andersen · P. Bastie · S. Boggs · P. Courtois · T. Courvoisier · M. Harris · M. Hernanz · J. Isern · P. Jean · J. Knödlseder · G. Skinner · B. Smither · P. Ubertini · G. Vedrenne · G. Weidenspointner · C. Wunderer Received: 1 June 2006 / Accepted: 27 June 2006 C Springer Science + Business Media B.V. 2006

Abstract The next generation of instrumentation for nuclear astrophysics will have to achieve a factor of 10–100 improvement in sensitivity over present technologies. With the focusing gamma-ray telescope MAX we take up this challenge: combining unprecedented sensitivity with high spectral and angular resolution, and the capability of measuring the polarization of the incident photons. The feasibility of such a crystal diffraction gamma-ray lens has recently been demonstrated with the prototype lens CLAIRE. MAX is a proposed

N. Barrière () · P. von Ballmoos · M. Harris · P. Jean · J. Knödlseder · G. Skinner · G. Vedrenne · G. Weidenspointner Centre d’Etude Spatiale des Rayonnements, 9, avenue du Colonel Roche, BP 4143 - 31028 Toulouse Cedex 4, France e-mail: [email protected] K. Andersen · P. Bastie · P. Courtois Institut Laue Langevin, 6, rue Jules Horowitz BP 156 – 38042 Grenoble Cedex 9, France N. Abrosimov Institut für Kristallzüchtung, Max-Born-Strasse 2, D-12489 Berlin, Germany H. Halloin APC, collège de France, 11, place Marcelin Berthelot, 75231 Paris, France S. Boggs · C. Wunderer Space Sciences Laboratory #7450, University of California, Berkeley, CA 94720-7450, USA T. Courvoisier ISDC, Chemin d’Ecogia 16, 1290 Versoix, Switzerland J. M. Alvarez · M. Hernanz · J. Isern IEEC-CSIC, Campus UAB, 08193 Bellaterra (Barcelona), Spain B. Smither Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA P. Ubertini Istituto di Astrofisica Spaziale e Fisica Cosmica, Via del Fosso del Cavaliere 100, 00133 Roma, Italy Springer

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mission which will make use of satellite formation flight to achieve 86 m focal length, with the Laue lens being carried by one satellite and the detector by the other. In the current design, the Laue diffraction lens of MAX will consist of 13740 copper and germanium (Ge1−x Six , x ∼ 0.02) crystal tiles arranged on 36 concentric rings. It simultaneously focuses in two energy bands, each centred on one of the main scientific objectives of the mission: the 800–900 keV band is dedicated to the study of nuclear gamma-ray lines from type Ia supernovae (e.g. 56 Co decay line at 847 keV) while the 450–530 keV band focuses on electron-positron annihilation (511 keV emission) from the Galactic centre region with the aim of resolving potential point sources. MAX promises a breakthrough in the study of point sources at gamma-ray energies by combining high narrow-line sensitivity (better than 10−6 cm−2 s−1 ) and high energy resolution (E/dE ∼ 500). The mission has successfully undergone a pre-phase A study with the French Space Agency CNES, and continues to evolve: new diffracting materials such as bent or composite crystals seem very promising. Keywords Instrumentation: Gamma-ray Laue lens . Gamma-ray astrophysics . Mosaic crystals PACS: 95.55.Ka, 29.30.Kv, 61.10.-i

1. Introduction Observing gamma-ray lines is first and foremost a matter of extracting a weak signal swamped in an intense and complex instrumental background. This is partly due to the fact that all existing instruments are based on concepts where the collecting area is equal to the sensitive area. Since the instrumental background in a detector operating in space is roughly proportional to its volume, decoupling the instrument effective area from the detector volume would lead to a dramatic improvement of sensitivity. That is why focusing gamma rays appears today as the only way to study point sources with a sufficient sensitivity to further our understanding of explosive nucleosynthesis and compact objects. MAX is a mission concept for a space-borne gamma-ray telescope using a Laue lens to focus nuclear gamma-ray lines from a large area onto a small detector. The lensing effect is based on Bragg diffraction in the volume of crystalline materials. CLAIRE, a prototype of such a Laue lens has already been realized in a CESR – CNES (the French space Agency) collaboration, and has demonstrated the feasibility of this concept [11, 23]. In this paper we first provide an overview of the MAX mission: its principal scientific objectives, the characteristics of the current instrument design, sensitivity estimates for various crystal types and detector options. We then describe ongoing R&D on new diffracting materials, such as composite crystals or bent crystals.

2. Scientific motivations Gamma-ray astronomy presents an extraordinary scientific potential for the study of the most powerful sources and the most violent events in the Universe. While at lower wavebands the observed emission is generally dominated by thermal processes, the gamma-ray sky provides us with a view of the non-thermal Universe, where particles are accelerated by still poorly understood mechanisms to extremely relativistic energies and nuclear reactions and decays are creating the basic elements that constitute our world (see the first section of this volume). Springer

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MAX aims to observe radioisotopes produced in Type Ia supernovae (SN) (see e.g. [19]) and around compact objects through their emitted nuclear lines. Type Ia supernovae (SN), with classical novae [12] and core collapse SN (Type Ib, Ic, II,. . .), are the main contributors to the production of heavy elements, playing a major role in the life cycle of matter in the Universe. The exceptional luminosity of SN Ia has made them a valuable tool for the measurement of extragalactic distances and for determining the metric of the Universe. The optical light produced in Type Ia SN is mostly powered by the decay chain 56 Ni → 56 Co → 56 Fe, which is directly observable mainly in two gamma-ray lines at 812 keV and 847 keV. Despite their great interest in many areas of astronomy, fundamental questions remain about all types of SN. Establishing the actual 56 Ni and 56 Co decay line intensities and shapes is a primary goal that will lead to a breakthrough for our understanding of the detailed physics at work in these explosions. A sensitivity of ∼10−6 cm−2 s−1 to broadened gamma-ray lines would allow at least one Type Ia SN per year closer than 20 Mpc to be observed with a detection significance of 25σ , which would allow discrimination between various models [16]. Up to 5 y−1 could be detectable with a significance of 3σ , in a radius of 50 Mpc. The search for potential sources of the positrons whose presence is implied by the 511 keV radiation observed with SPI/INTEGRAL constitutes the other main scientific theme of the MAX mission. Compact objects (microquasars, neutron stars and pulsars, X-ray binaries, . . .), active galactic nuclei, solar flares and the high energy afterglow from gamma-ray bursts may release significant numbers of positrons leading to 511 keV annihilation line emission. The shift and the shape of this line carry a lot of information about the region and conditions where positrons have annihilated [14]. Fine spectroscopy of the annihilation line combined with a good spatial resolution could elucidate the nature of these objects.

3. The MAX mission MAX was proposed in response to an announcement of opportunity issued by the CNES concerning a formation flight demonstrator mission. It consists of a lens spacecraft and a detector spacecraft flying in formation to form a gamma-ray telescope of 86 m focal length. The pre-phase A study led by the CNES/PASO group that ended in November 2005 confirmed the feasibility of the mission, and indicated a mass margin of 400 kg. As a consequence we have updated the MAX design (which becomes MAX 3.0) with an increase of 72% in the focusing area (crystal tiles), resulting in dramatic increases in the effective areas of both bandpasses. MAX is still under development and so is continuously evolving. The version 3.0 presented here is based on crystals representing the current state of the art and which are relatively conservative compared to new diffracting materials that are highlighted by the current R&D program (see below). 3.1. Lens features In the current MAX design, the lens is made of 13740 crystal tiles of 1.5 cm × 1.5 cm including 90% copper crystals [8] and 10% germanium crystals [1]. The thicknesses, T0 , of crystal tiles are optimized for each ring according to the following formula which comes from the maximisation of a mosaic crystal peak diffraction efficiency for a given mosaicity: 1 2σ cos θ B T0 = ln 1 + . 2σ µ Springer

272 Table 1 MAX crystals masses and geometrical areas. LE: low energy band; HE: high energy band

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Focal length f Crystal mosaicity Geometrical area Mass of crystals Number of HE rings Mass of HE crystals Geometrical area of HE rings Number of LE rings Mass of LE crystals Geometrical area of LE rings

86 m 30 arcsec. 30915 cm2 235 kg 20 172 kg 15966 cm2 16 62 kg 14949 cm2

σ is the diffraction coefficient for the crystalline material, µ is the absorption coefficient (without coherent scattering which is precisely the origin of the Bragg diffraction), and θB is the angle of incidence of rays on the diffracting planes (called Bragg angle when diffraction occurs). The value of σ is calculated according to the dynamical theory of diffraction (see Halloin, Bastie [5, 6] for complete treatment). The crystal tiles are arranged on 36 concentric rings with radii ranging from 56.25 to 76.35 cm and from 93.05 to 129.05 cm. The resulting lens focuses simultaneously in two broad energy bands corresponding to the previously described scientific objectives (Figure 1): the lower energy band is centred on 500 keV. Its width permits the observation of red-shifted e− − e+ annihilation lines from compact objects (e.g. the supermassive black hole in the centre of our Galaxy), as well as the study of the 478 keV decay line from 7 Be. The bandpasses of the 14 Cu rings and 2 Ge rings combine to cover an energy band from 450 to 530 keV, with a total effective area of 1200 cm2 at 511 keV. The second energy bandpass is obtained with 18 Cu rings and 2 Ge rings whose responses superimpose to cover an energy band from 800 to 900 keV, with a total effective area of 660 cm2 at 847 keV. In addition, the second order diffraction of the crystals covering the lower energy bandpass extends this band up to 1050 keV. Details of masses and geometrical areas of both bandpasses are given in Table 1. 3.2. Detector features The baseline detector for MAX is a Compton camera consisting of a stack of planar germanium strip detectors (GeD). The stack is made of 5 GeD modules similar to the ones used in the balloon borne Nuclear Compton Telescope, which was successfully tested in 2005 (NCT, [4]). Each GeD is approximately 8 cm × 8 cm and 1.5 cm thick, and the strips are 2 mm pitch, which ensure a 1 mm3 3D-positionning. The design used to estimate sensitivities [24, 25] assumes a gap of 0.7 cm between two GeD. To reduce the background count rate, the detector is separated from the spacecraft by being placed on a 1 m “tower”. In addition, the Compton camera is encapsulated in a plastic veto shield, and a 5 cm thick active BGO crystal screens it from the emissions produced in the structure of the spacecraft. It has been established during the MAX pre-phase A study that cooling of the Compton camera can be achieved with a 1 m diameter radiator. Alternative solutions to the above baseline are being considered, including a high sensitivity Si/CdTe narrow field of view Compton camera [17, 22], or Compton CdTe pixel detector [7]. The advantages of using a detector providing localization of the interactions are multiple: besides following any excursions of the focal spot across the detector plane, such a system allows the simultaneous measurement of signal and background. Most importantly, in a system with three-dimensional event localization, a significant background reduction can be achieved by reconstructing the arrival direction of the photons using Compton Springer

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Fig. 1 Effective area of the lens for a perfect pointing on a point source. Each Gaussian curve is the contribution of a single ring. The second order diffraction of low energy (LE) rings extends the high energy (HE) bandpass up to 1050 keV. Various sets of Bragg planes in copper and germanium at different radii contribute to the two main energy bands: Cu(111), Cu(200) and Ge(111) are used for the LE band, whereas Cu(111), Cu(200), Cu(220), Cu(222) and Ge(311) diffract in the HE band. In this sense, this lens is a hybrid between a broad-band lens and a narrow-band lens

kinematics. This allows the rejection of photons not coming from the lens direction. In addition, a Compton camera is inherently sensitive to gamma-ray polarization. Lastly a fine pixellated focal plane allows the limited imaging capabilities of the lens to be used. One drawback of a Compton camera is at present their low detection efficiency (ranging between 6–7% for a Ge- strip Compton stack). First steps in the optimisation for the particular case of a Laue lens have been performed [25] and this works will continue in the future. 3.3. Sensitivity estimates The modelled narrow line sensitivity of MAX in both energy bandpasses is shown in Figure 2. Lens efficiency estimates are derived from the diffraction efficiency given by the Darwin model, which are in agreement with the diffraction efficiencies measured for the lens prototype CLAIRE [11] and recent measurements made at the European Synchrotron Radiation Facility (ESRF, Grenoble, France) [5, 6]. The upper curve (a) in Figure 2 shows the sensitivity with current technology, based on the lens MAX 3.0 and the baseline Compton camera described in Section 3.2. The lower curve in Figure 2b shows a sensitivity requiring advanced technology: a lens using bent crystals (see below) focusing onto an optimized Compton camera (the “LARGE” geometry in [25]). At this early stage, these estimates are rough but conservative. Numerous optimizations could still be done, as for example, improving the treatment of the Compton-rejected photons (93% of the signal), or the optimization of the detector geometry or the lens efficiency. 3.4. Lens PSF – imaging capabilities Although a crystal lens telescope is not a direct imaging system, the spatial response does depend on the source position in the field of view. For an on-axis point source, the response is a Springer

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Fig. 2 The modelled narrow line sensitivity of MAX in both energy bands. Curve (a) is the sensitivity with current technology, using the baseline Compton camera (see above) and the current lens MAX 3.0. Curve (b) is the sensitivity reachable with a lens using bent crystals and an optimized Compton camera. The circle and the triangle are the sensitivities for a broad line (3%) at 847 keV

Fig. 3 MAX baseline detection plane (8 cm × 8 cm, 1 mm2 pixels) response for a point source. Flux is coded both by a grey square root scale and by square root contours. Left: image of an on-axis point source. Right: image of an off-axis point source when the lens is pointing 60 arcsec away from the source. The Monte-Carlo code used for these simulations was developed by Halloin [11] Springer

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Gaussian-like spot centred on the optical axis of the lens (Figure 3, right). For an off-axis point source, the focal spot becomes a donut shape (centred on the lens optical axis) presenting an azimuthal intensity modulation [18]. The average radius ra of the focal ring and the angular position of the maximum intensity ϕ m give the zenithal (off-axis) (θ s ) and the azimuthal (ϕ s ) angles of the source through the very simple relations: θ S = a tan ra/f , ϕ S = ϕm + π

where f is the focal distance of the lens for a source at infinity. The minimum thickness of the focal ring (where the intensity is maximal) approaches the radial size of the crystals with increasing zenith angle of the source (individual square crystals are arranged on rings such that one side is tangential). Thus, mosaicity and crystal sizes dictate the angular resolution of the instrument. The field of view of MAX is limited by two parameters: firstly, the size of the detection plane (8 cm × 8 cm) limits the radius of the recorded focal ring to 4 cm. Taking into account crystals radial size, the maximum radius of observable focal ring is 3.25 cm. The field of view of MAX is therefore ±78 arcsec. The second limiting parameter is the decrease of the lens effective area when the zenithal angle of the source increases (Figure 4). For an angle of 60 arcsec, the effective area goes down by 45% and 40% at 511 keV and 847 keV respectively.

Fig. 4 Effective area as a function of position in the field of view at 511 keV and 847 keV Springer

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4. The R&D towards a spaceborne Laue lens 4.1. Lens structure A first design of the structure of the lens has been made in order to study its thermo-elastic deformations. The design is based on the ALCATEL structural concept [10, 13]: a main circular carrier structure supports 32 independent modules onto which the individual crystals are attached. The central carrier structure homogenizes the temperature and transmits mechanical forces to the satellite structure through four titanium links. Due to the penetrating nature of gamma rays it is possible to put the lens in a multilayers insulator (MLI) cocoon to ensure sufficient thermal stability. Even with such a passive system the temperature would already be within ±3 K of the nominal temperature, whatever the orientation of the sun. For a 86 m focal distance, the diffracting planes of a crystal have to be oriented within ∼10 arcsec with respect to the lens line of sight to keep the position of the crystal footprint within ±1 cm of its nominal position. This value dictates the specification for the lens out of plane deformation: modules have to keep their nominal orientation within ±10 arcsec. It has been shown in the MAX pre-phase A study that a ±2 K active thermal control around the nominal temperature (ambient) is sufficient to satisfy this deformation specification, a requirement that seems easily attainable [13]. 4.2. Diffracting materials 4.2.1. Lessons from the CLAIRE lens The CLAIRE lens was made of 556 crystals mounted on eight rings (see [11, 23] for an in-depth description of the CLAIRE project). These crystals, that are actually a solid solution of silicon in germanium (Ge1−x Six , x < 0.1), were grown using a modified Czochralski technique at the Institute of Kristalzüchtung (IKZ, Berlin, Germany) by [1]. CLAIRE was a narrow bandpass Laue lens, it focused radiation centered on 170 keV (for rays coming from infinity) using a different family of crystalline planes for each ring. The overall diffraction efficiency of the lens was found to be about 10%, though some of the best crystals had a peak reflectivity of 25%. There are two reasons to explain the relatively low efficiency of the entire lens compared to that of the best crystals. Firstly, the theoretical diffraction efficiency decreases with increasing Miller index. For example, the eighth ring used the [440] reflection that has a theoretical integrated reflectivity 7.5 times lower than that of the (111) planes. Secondly, even on a given ring where all crystals are supposed to be identical, differences do exist. These differences that translate into differences in absolute reflectivity and energy bandpass, are due to mosaicity and crystallites length variation. Basically, the larger the crystallites, the worse is the reflectivity. A larger mosaicity offers a larger energy bandpass, but it, too, decreases the reflectivity. The CLAIRE project has emphasized the need to use preferentially sets of crystalline planes of lower Miller index, and to ensure that the quality of the crystals grown can be maintained consistently during the production of a large number of boules. 4.2.2. Existing crystals MAX lens would be mainly made with copper crystals, with 10% germanium-silicon crystals to provide enhanced collecting area in the energy bands of interest. Copper crystals combine high theoretical diffraction efficiency (higher than germanium) with inherent mosaic Springer

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structure. The challenge was to grow crystals with a mosaicity of about 30 arcsec, a value which is very small for this material. In 2005, this goal was achieved for the very first time by [8] at ILL. Such a low mosaicity copper crystal have shown a peak reflectivity reaching 30%. Concerning germanium crystals, since the time when CLAIRE’s crystals were grown the quality of crystals obtained by the modified Czochralski technique has been improved. Using only the most efficient reflections (low Miller index), we can count on peak diffraction efficiencies exceeding 25%. Nevertheless, the only way to completely avoid variation of the crystalline parameters, such as those noted in the CLAIRE lens, would be to characterize every crystal and to select only the best. 4.2.3. New generation of crystals Alternative crystalline materials are also being considered. One possibility is germanium ‘composite crystals’, made of perfect single-crystal germanium wafers that are stacked with a slight mis-oriention from one to the next (like the crystallites in a mosaic crystal). This kind of crystal presents potentially advantages with respect to mosaic crystals: single crystal wafers are easily reproducible and it is possible to optimize the wafer thickness according to the energy that the stack will have to diffract. Since wafers are perfect single crystals, the formulae given in subsection 3.1 do not apply any more, the optimal thickness of a wafer equals half of the Pendellösung period (the period of the oscillations of the diffracted intensity as a function of the thickness of the crystal; [3]). Of course the key point is to manage to build the stack properly. Indeed, a recent measurement run at the ESRF [5, 6] on a prototype composite crystal showed that the angular separation between wafers was greater than their angular bandpass1 , leading to an undesirable comb-like response. This still-evolving technique, especially the surface treatment of the wafers, has yet to be optimised. Bent crystals are another alternative that seem very promising. Smither [21] have already measured Si crystals with efficiency close to 100% (disregarding absorption2 ) in an angular bandpass of 30 arcsec. Bent diffracting planes can be obtained in 3 ways: by applying a thermal gradient to a crystal, by elastically bending a crystal, or by growing a composition-gradient crystal (Ge1−x Six ) [2]. In the latter case, a spherical curvature of atomic planes perpendicular to the gradient direction appears, due to the fact that Ge atoms are larger than Si atoms [21]. Bent crystals present two main advantages with respect to mosaic crystals: their peak diffraction efficiencies are not limited to 50% as is the case for mosaic crystals (see for instance Halloin, Bastie [5, 6]), and their rocking curves (curves representing the range of angles through which an incident beam can be diffracted) can have a square shape. As a comparison, mosaic crystals exhibit a Gaussian-like rocking curve, which is good for the lens field of view, but degrades the focusing on the detector (since each crystal diffracts a diverging beam whose spatial distribution is Gaussian). Preliminary estimates of the sensitivity achievable with a lens made of bent crystals show a gain of a factor 2 with respect to the current version of MAX. 1 Even a perfect single crystal has an angular bandpass that is called the Darwin width. In addition, the cutting process induces deformations that increase the angular bandpass. 2 If we do not consider the absorption, when a beam goes through a crystal, it is shared in two complementary parts: the diffracted beam and the transmitted beam. In the case of a mosaic crystal, these two parts tend to be equal if the crystal is thick enough: the maximum diffraction efficiency without absorption is 50%.

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5. Summary With its Laue lens consisting of Cu and Ge crystals rings MAX promises a breakthrough for the study of point sources at gamma-ray energies by combining narrow line sensitivities better than 10−6 cm−2 s−1 and high energy resolution (E/dE ∼ 500). MAX features a Laue lens consisting of rings of Cu and Ge crystals, covering simultaneously two broad energy ranges: 800–900 keV and 450–540 keV. A small detector, maintained at a distance of 86 m by a second spacecraft flying in formation, collects the focused radiation. A pre-phase A study of the French Space Agency CNES has established the feasibility of the mission with present technologies [10]. The performance of a future Laue lens depends mainly on the diffraction properties of its individual crystals. Despite the fact that mosaic crystals produce a focal spot not ideally concentrated on the detection plane, the copper crystals grown at ILL show peak reflectivities up to 30%. The growth of copper crystals can be fairly well controlled at present, with mosaicities ranging from a few minutes down to 30 arcsec. It is hence already possible to build an efficient gamma-ray Laue lens using a combination of copper and germanium mosaic crystals. We have shown that Laue lenses can benefit either from crystals having a composition gradient (causing curvature of the crystalline planes) or from “composite crystals” (having an “artificial mosaic structure” produced by assembling wafers with slightly different alignments). In either case, the efficiency-limitation, which prevents Laue mosaic crystals of having a reflectivity higher than 50%, can be exceeded. We also show the importance of improving the crystals point spread function to obtain a compact focal spot and thus a enhanced signal/noise ratio. Acknowledgements The authors acknowledge continuing support from the French Space Agency CNES.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

Abrosimov, N. et al.: J. Crystal Growth 275, e495–e500 (2005) Abrosimov, N.: Exp. Astron. 20, DOI 10.1007/s10686-006-9036-3 (2006) Authier, A.: Dynamical theory of X-ray diffraction. Oxford Science Publications (2001) Boggs, S.E. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9051-4 (2006) Bastie, P. et al.: ESRF User report, http://ftp.esrf.fr/pub/UserReports/32513 A.pdf (2006) Halloin, H., Bastie, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9064-z (2006) Caroli, E. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9048-z (2006) Courtois, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-005-9018-x (2006) Cosmic Vision, ESA, BR-247 Duchon, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9070-1 (2006) Halloin, H.: Phd Thesis, University Toulouse III, (2003) http://www.cesr.fr/∼pvb/MAX/publis/Diss Halloin 03.pdf Hernanz, M. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9036-3 (2006) Hinglais, E. et al.: Exp. Astron. 20, DOI 10.1007/s10686-005-9020-3 (2006) Jean, P. et al.: A&A 445, 579–589 (2006) Knödlseder, J. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9031-8 (2006) Leising, M.: Exp. Astron. 20, DOI 10.1007/s10686-006-9052-3 (2006) Limousin, O. et al.: NIM A 504, 24–37 (2003) Lund, N.: Exp Astron 2, 259 (1992) Prantzos, N.: In Proc 5th INTEGRAL Science Workshop (ESA SP-552), 15 (2005) Smither, R. et al.: RSI 76, 123107 (2005) Smither, R. et al.: Exp. Astron. 20, DOI 10.1007/s10686-005-9019-9 (2006) Takahashi, T.: Exp. Astron. 20, DOI 10.1007/s10686-006-9059-9 (2006) von Ballmoos, P. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9071-0 (2006) Weidenspointner, G. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9035-4 (2006) Wunderer, C. et al.: Exp. Astron. 20, DOI 10.1007/s10686-006-9034-5 (2006) Springer


The gamma ray lens – an ESA technology reference study Craig Brown · Nicola Rando · Alexander Short · Aleksander Lyngvi · Tone Peacock

Received: 14 October 2005 / Accepted: 10 April 2006 C Springer Science + Business Media B.V. 2006

Abstract The Science Payload and Advanced Concepts Office (SCI-A) of the ESA Science Directorate conducts a number of Technology Reference Studies (TRS) on hypothetical scientific missions that are not part of the approved Science programme. Such TRS activities allow identifying, at an early stage, technology development needs as well as exploring future mission scenarios. As part of this effort, the Gamma Ray Lens (GRL) mission, a future generation gammaray observatory, has been the subject of a preliminary internal investigation. The present paper provides an overview of the science goals assumed for this study, the selection of the reference mission profile, together with a preliminary description of the spacecraft design. The reference payload is also described, as well as the list of technology development activities derived from the study.

1. Introduction Technology Reference Studies (TRS) are conducted by the Science Payload and Advanced Concepts Office (SCI-A) of the ESA Science Directorate, with the aim of establishing key technology development requirements necessary for the realisation of similar, future science missions [1]. A TRS consists of the investigation of a hypothetical future mission of scientific worth that is not currently part of the ESA science programme. Each study aims to highlight areas requiring technology development, as well as to establish mission drivers and areas of complexity. There are four primary areas for investigation within the TRS programme: planetary science, fundamental physics, solar physics and astrophysics missions. Increasing sensitivity of a gamma-ray mission is widely considered as the next important development in gamma-ray astronomy. The required leap in sensitivity implies the need of focussing optics that, in this high-energy range, is very difficult to achieve. The Gamma Ray Lens (GRL) was an ideal candidate for an astrophysics TRS due to its challenging nature,

C. Brown () · N. Rando · A. Short · A. Lyngvi · T. Peacock Science Payload and Advanced Concepts Office, European Space Agency, ESTEC, The Netherlands e-mail: [email protected] Springer

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and was studied in order to establish the technology development requirements needed to realise such a mission in the future. This paper will introduce the reference mission requirements used in this study, and will present the preliminary mission design for the Gamma Ray Lens.

2. Reference science requirements In order to conduct the Technology Reference Study, preliminary science requirements need to be assumed. There are two primary source types of interest that lead to three main energy bands for the GRL. Positron-electron annihilation, and the subsequent single, double and triple Compton backscattering processes, leads to two energy bands: 50–200 keV and 460– 522 keV. The band widths take potential red-shift into account, as well as intrinsic broadening of the spectral lines. The second source types of interest are sources of explosive nucleosynthesis and, in particular, type Ia Supernovae due to their use as cosmological candles. The primary energy of interest associated with these sources is the 847 keV 56 Co decay line, leading to an energy band of 825–910 keV. Table 1 shows a summary of the reference science requirements for the GRL mission. The requirements are compatible with those presented on behalf of the gamma-ray science community at the 2005 INTEGRAL Workshop at ESTEC [2].

3. Orbit selection The GRL mission has the following orbit requirements to best meet the mission goals.

r Long, stable observations for formation flying between two spacecraft r Typical observation times of ∼2–3 weeks (80 days for SNe Ia) r Large portion of the sky visible at any one time r Stable thermal environment r Low number of eclipse periods r Minimal radiation damage to the detectors and other systems r Low v for orbit insertion and maintenance Table 2 outlines the orbit tradeoff that was performed in order to establish the most appropriate orbit for the Gamma Ray Lens. Note that a 5-point scale, ranging from –2 to +2, is used to demonstrate in detail the advantages and disadvantages between the differing orbit types. Table 1 Summary of preliminary assumed science requirements

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Attribute

Requirement

Energy band Effective area Angular resolution Energy resolution Line sensitivity Continuum sensitivity Typical integration time Sun restraint angle Nominal mission lifetime

425–522 keV, 825–910 keV, 50–200 keV 10000 cm2 @ 511 keV, 5000 cm2 @ 847 keV 1 Arcminute 2 keV @ 600 keV ∼5 × 10−7 ph.cm−2 s−1 ∼10−8 ph.cm−2 s−1 ∼106 sec. @ 511 keV, 2 × 105 sec. for SNeIa 30◦ , half cone ∼10 years (extendable to 15)

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Table 2 Outline of the trade-off between orbit types based on the GRL mission requirements Mission requirement

LEO

GEO

HEO

L2

Weighting

Stability and maintenance v Observation period Visibility of the sky Thermal environment stability Eclipse periods Radiation environment Communications and ground operations Launcher capacity Total Weighted total

−2 −2 −2 −1 −2 −1 0 2 −8 −5.75

0 −1 0 1 −1 1 2 −2 0 −2.25

−1 0 1 0 −1 −1 1 0 −1 −0.50

2 2 2 2 2 1 0 −1 10 7.25

1 1 1 0.5 0.5 0.25 0.25 1 – –

Table 3 Laue lens dimensions for the MAX [3], Soyuz Fregat and Ariane 5 configurations Configuration

Focal length [m]

Rin Ge [cm]

Rout Ge [cm]

Rin Cu [cm]

Rout Cu [cm]

MAX Soyuz fregat Ariane 5

133 436 504

97 318 365

110 360 450

87 285 328

96 314 363

It is clear from this trade-off that an orbit at L2 is the most desirable. For the purpose of this study it has therefore been assumed that the GRL will utilise a Halo orbit at L2. 4. The gamma ray lens The energy bands of interest for the GRL mission (see Table 1) suggest two separate optic technologies: Multilayer Silicon Pore Optics, expected to perform well up to 200 keV, and Laue crystals which are suitable for the focusing of gamma rays from 200 keV to 2 MeV. Due to the focusing geometry of the Laue lens, a large (∼500 m) focal length is required. This implies the need for two separate spacecraft: A focusing optic spacecraft (OSC) housing the lens and a detector spacecraft (DSC) orbiting at the optic focal spot. Two mission profiles were investigated as part of the GRL TRS: a medium sized mission utilising two separate Soyuz Fregat launchers in a dual launch scenario and a single Ariane 5 launcher in a single launch scenario. The smaller Soyuz Fregat launcher capacity results in a limited payload capability. A silicon pore optic is not included in the Soyuz payload, meaning that only the two higher energies of interest are considered in this configuration. The primary advantages of using the larger Ariane 5 configuration are: (1) a larger payload capacity allowing observation of all energy bands of interest at increased effective areas; (2) the removal of any problems associated with a dual launch; (3) further potential for payload expansion. For comparison, the MAX mission has been considered in this study as a third, smaller mission concept. MAX is a gamma ray focusing mission based on Laue crystals, proposed by CESR (Centre d’Etude Spatiale des Rayonnements), Toulouse [3]. The mission is sized to fit both detector and lens spacecraft into a single Soyuz Fregat launcher. The dimensions and specifications for MAX were input into the models developed for the Gamma Ray Lens TRS and are also presented in this paper in order to compare the GRL with MAX. Table 3 outlines the key dimensions of the Laue lens used for the MAX, Soyuz Fregat and Ariane 5 profiles. Springer

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Fig. 1 The modelled effective area for the Ariane 5, Soyuz Fregat and MAX Laue Lens configurations

An effective area and sensitivity model was created in order to analyse and compare the various Laue lenses proposed for different GRL configurations. Figures 1 and 2 show the effective area and sensitivity results, respectively, for the Soyuz Fregat and Ariane 5 configurations. The reported dimensions of the MAX lens were also input into the model, with the results shown here for comparison. Note that a real measured SPI INTEGRAL background [4], was used in the GRL sensitivity analyses presented in Figure 2. As such we have assumed a SPI INTEGRAL-style Ge spectrometer with a similar background rejection capability through anticoincidence shielding. It can be seen from Figures 1 and 2 that the Ariane 5 configuration comfortably meets both effective area and sensitivity requirements outlined in Table 1. An improvement of ∼100 times better sensitivity than SPI INTEGRAL is achieved by the Ariane 5 configuration.

5. Preliminary spacecraft design For the purpose of this section, only the Ariane 5 configuration will be discussed. As noted, two separate spacecraft flying in formation are required for the GRL mission: the OSC housing the Laue lens and Silicon Pore Optic, and the DSC supporting the SPI INTEGRALstyle germanium detector. Here, the preliminary spacecraft design is described. Figure 3 shows a diagram of the deployed OSC. The cylindrical bus was chosen due to the ring structure of the Laue lens and the ability to more easily stow the large structure during launch. In order to maintain a clear load path through the spacecraft during launch, the OSC bus was designed to match the diameter of the 2624 cm Ariane 5 launch adapter. Ensuring a clear load path will minimise the stress on the stacked configuration during launch. Springer

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Fig. 2 The modelled sensitivity for the Ariane 5, Soyuz Fregat and MAX Laue Lens configurations, assuming a spectrometer based on an array of cooled Ge detectors

The ring-shaped bus was used due to the necessity of an unobstructed view for the multilayer silicon pore optic. Housing the silicon pore optic inside this ring provides a clear line of sight between the optic and the detector spacecraft. The silicon pore optic will be designed to have a focal spot that coincides with that of the Laue lens, thus enabling simultaneous observations in different energy ranges. The deployment mechanism is designed to fit the lens within the Ariane 5 fairing during launch and then deploy the lens to the full 9 m diameter after spacecraft separation. It can be seen that the lens is composed of 30 separate petals. These are sized to simplify the construction, metrology and testing of the lens. When in stowed configuration, the mass of the lens is concentrated towards the top of the OSC bus. The height of the bus is therefore determined by the need to secure the large crystal mass in the stowed configuration, with stiffening rings used to re-enforce the structure. The thrusters are positioned to allow for full, three-axis stabilisation and transverse motion. Star trackers and sun sensors are placed around the craft providing attitude measurements, while the antennae provide omni-directional communication capability. Figure 4 shows the DSC spacecraft configuration. The bus consists of two main parts: an outer octagonal wall and an internal cylindrical wall. The stacked configuration is a primary driver in the design of the DSC, as this spacecraft has to be able to support the large mass of the OSC during launch. The cylindrical wall is designed to transfer the load path through the stacked configuration (Figure 5), and has a 2624 cm diameter to match both the OSC diameter and the Ariane 5 adapter. The main detector payload, a cooled germanium spectrometer, is placed in the centre of the spacecraft. The spectrometer assumed in the GRL study consists of an array of 52 Springer

Fig. 3 (a) A 3D picture of a possible configuration for the deployed OSC, (b) a face-on picture showing the dimensions of the OSC and (c) a side-on view

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Fig. 4 (a) A 3D picture of a possible DSC configuration and (b) the DSC dimensions

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Fig. 5 (a) A 3D drawing of the GRL stack inside the Ariane 5 short 5660 SPELTRA fairing and (b) the dimensions of the stacked configuration

hexagonal germanium detectors, covering an area of 405 cm2 . An anticoincidence vetoing shield surrounds the detector array at the focal plane. The spacecraft thrusters were positioned on the DSC to allow full three-axis stabilisation and transverse motion. Star trackers and sun sensors are placed around the craft to provide attitude measurements, while the antennae on the craft provide omni-directional communication capability. The formation-flying package is assumed to be similar to the one baselined for the XEUS mission [5], modified to account for the large increase in focal length from 50 m to ∼500 m. The metrology system has three subsystems; (1) coarse radio metrology, (2) fine radio metrology and (3) optical metrology. Radio metrology will bring the two spacecraft within 120 m of each other with an accuracy of a few centimetres. The optical metrology system for XEUS is very accurate at a focal length of 50 m (∼10’s µm laterally and 100’s µm longitudinally). The attitude requirements for the GRL are less stringent than that of XEUS, being ± 0.08 m laterally and ± 1 m longitudinally based on a 1 σ point spread function of 60 cm2 . It is therefore assumed that this system can be scaled for the GRL formation-flying package. The larger, more active part of the metrology system will be located on the DSC. A laser will be located on the DSC and is reflected from the OSC in order to perform the optical metrology measurements and both fine and coarse radio metrology can be performed by the same set of transmitters.

6. Conclusions The Gamma Ray Lens Technology Reference Study has highlighted a number of areas requiring further work if such a mission is to be viable in the future. Table 4 summarises the key GRL mission drivers and the associated areas of future activities required if the mission is to be realised. One of the key outcomes of the study is the fact that increasing the size of the mission eventually results in a limited sensitivity improvement due to the role of background. In order to become photon limited rather than background limited, vast improvements in background rejection should be a priority. Springer

• Need to strictly control mosaicity • Inter-crystal alignment • Deployment mechanism alignment accuracy • Thermal control to minimise spacecraft warping • Silicon Pore Optics development • Multilayer coating design for efficient, broad energy coverage; 50–200 keV

PSF size

• Relatively long mission lifetime of 10–15 years. Poses potential difficulties for detector life since Ge isn’t radiation hard. • This has been noted as a desirable capability for a future gamma-ray mission

Mission lifetime

∗ Areas

envisaged to require major work or development

Gamma-ray polarisation∗

• ‘Better’ ACS detectors • Designing out intrinsic background lines from the spacecraft

Background rejection∗

Silicon Pore Optics∗

Petal Deployment

Laue Crystals∗

Metrology system

• AOCS design, constant formation control in order to maintain required accuracy • Scaling of current technology from missions such as XEUS, Darwin and LISA for a focal length of ∼500 m • Crystal growth • Crystal characterisation • Mounting on the lens–optimising packing factor • Crystal alignment, metrology and calibration • Deployment mechanism

Formation flying and rendezvous

Key Mission Drivers

Table 4 Summary of key mission drivers and possible future activities required for the GRL mission

• Design of a detector capable of simultaneous spectroscopy and polarisation measurement, with possible balloon flight test

• Development of ‘better’ ACS materials, e.g. LYSO, LuAP • Investigation of novel background rejection techniques e.g. Compton kinematic rejection • Possible development of other high-resolution, radiation hard focal plane detectors–LaI, LuI • Gamma-ray polarisation techniques

• Effective area and energy response modelling

• Design and characterisation of the SPO • Design of the multilayers

• Development of simple, accurate, large - scale deployment mechanism • Crystal mounting and alignment techniques • Full thermal analysis of the GRL spacecraft

• Design and testing of a metrology system capable of achieving the GRL requirements • Investigation of crystal growth and classification techniques • Crystal mounting and alignment methods • Investigation of gradient crystals

• Establish a formation flying package for the GRL

Future work

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The mission and spacecraft design presented here are the results of the preliminary science goals assumed at the start of the study. Nevertheless the suggested technology development activities would be still applicable if the science requirements would be changed. Acknowledgements The authors would like to acknowledge the work by Alan Owens, Alex Jeanes, Arvind Parmar, Christoph Winkler, Dave Lumb, Hubert Halloin, Peter von Ballmoos, Richard Griffiths and Thijs van der Laan.

References 1. Lyngvi, A. et al.: Technology reference studies, 55th international astronautical congress. Vancouver, Canada (2004) 2. Knödlseder, J. et al: Prospects in space-based gamma-ray astronomy, 39th ESLAB symposium proceedings, Experimental Astronomy 20, DOI: 10.1007/s10686-006-9031-8 (2005) 3. Von Ballmoos, P. et al.: MAX: A gamma-ray lens for nuclear astrophysics, Proc. SPIE 5168, 482–491 (2004) 4. INTEGRAL special edition, Astronomy and Astrophysics 411, No. 1 (2003) 5. Bavdaz, M., Lumb, D., Peacock, A.: XEUS mission reference design, Proc. SPIE 5488, 530–538 (2004)

Springer


Gamma ray Fresnel lenses – why not? G. K. Skinner

Received: 17 November 2005 / Accepted: 30 January 2006 C Springer Science + Business Media B.V. 2006

Abstract Fresnel lenses offer the possibility of concentrating the flux of X-rays or gammarays flux falling on a geometric area of many square metres onto a focal point which need only be a millimetre or so in diameter (and which may even be very much smaller). They can do so with an efficiency that can approach 100%, and yet they are easily fabricated and have no special alignment requirements. Fresnel lenses can offer diffraction-limited angular resolution, even in a domain where that limit corresponds to less than a micro second of arc. Given all these highly desirable attributes, it is natural to ask why Fresnel gamma ray lenses are not already being used, or at least why there is not yet any mission that plans to use the technology. Possible reasons (apart from the obvious one that nobody thought of doing so) include the narrow bandwidth of simple Fresnel lenses, their very long focal length, and the problems of target finding. It is argued that none of these is a ‘show stopper’ and that this technique should be seriously considered for nuclear astrophysics. Keywords Gamma-ray . Astronomy . Optics

1. Introduction: Focusing as a phase control problem ‘Gamma-wave’ is a convenient term to employ when considering optics for high energy radiation (gamma-rays, or hard X-rays) in which the wave-like properties of the radiation need to be taken into account. We commence with a discussion of the general principles of focussing ‘gamma-waves.’ In its simplest form Fermat’s principle states that the path of radiation through an optical system is that which takes the least time. To be more precise, the time has a stationary value with respect to a small deviation in the path. In this form, Fermat’s principle does not take into account the wave aspect of the radiation – for example it does not work for diffraction gratings. However if restated in the form that the phase of the radiation at the destination

G. K. Skinner () Centre d’Etude Spatiale des Rayonnements, 9, avenue du Colonel Roche, 31028, Toulouse, France e-mail: [email protected] Springer

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Fig. 1 The phase at which radiation must be scattered to focus incoming radiation with plane horizontal wavefronts. At each position the intensity indicates the (relative) phases such that radiation will be focussed at the point indicated, with from 0–2π coded white to black. A cross-section is shown above the main figure. In three dimensions the iso-phase surfaces are paraboloids of revolution about the vertical axis

has a stationary value, then it is applicable quite generally. Thus the various paths through an optical system must result in the radiation arriving at the focal point with the same phase, modulo 2π . This is of course equally obvious if one considers Huygen’s principle and the fact that one wants all wavelets to interfere constructively. Suppose that we wish to bring parallel incoming radiation to a focus by scattering from elements within an optical system (‘scattering’ should here be thought of as generation of a Huygen’s wavelet; one could equally write ‘reflection’ or ‘diffraction’). Figure 1 shows the phase change necessary as a function of the position of the scattering element in the case of plane incoming wavefronts (source at infinity). Often each scattering takes place with the same phase change (diffraction by identical atoms, reflection from surfaces . . . ). In this case the scatterers need to be distributed on isophase contours, which form a system of nested paraboloids. Figure 2 illustrates how grazing incidence mirrors, multilayer optics, and Laue diffraction ‘lenses’ use respectively reflecting surfaces, alternating layers, and planes of atoms to aim to populate parts of iso-phase surfaces. In each case only an approximation to the ideal is achieved. For Laue lenses, the planes of atoms are flat and equispaced and so cannot perfectly follow the surfaces. In this case, and for grazing incidence or multilayer optic, practical tolerances are such that the scattering is coherent only very small regions. Lack of coherence means that on larger scales intensities are added, not amplitudes. 1.1. Changing the phase of a gamma-wave The requirements for focussing can be met exactly if the phase of the gamma-wave can be controlled. Figure 2(d) indicates how the phase change needs to vary across the surface of a planar focussing component in order to concentrate plane incoming wave onto a point. How does one change the phase of a gamma-wave? It turns out to be surprisingly easy (Skinner, 2002). It is well known that grazing incidence reflection relies on the fact that for X-rays and gamma-rays refractive indices are slightly less than unity. Conventionally one writes n = 1 − δ, where δ is small and positive. Thus the phase of X/γ -ray radiation will be changed Springer

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Fig. 2 The relationship of different focussing systems to isophase contours of Figure 1. (a) Nested grazing incidence mirrors should ideally follow a subset of the isophase surfaces of Figure 1. (b) The layers of multilayer mirrors follow also follow such surfaces. (c) In the case of a Laue lens, crystals planes approximate iosphase surfaces. (d) A cut along the line shown gives the phase change needed in a planar focussing device

by any material that it passes through. It is useful to define t2π = λ/δ, which is the thickness of material which leads to a phase change of 2π with respect to the phase in vacuo. This is of course the largest phase change ever needed. Table 1 gives an indication of orders of magnitude of t2π for some example materials and photon energies, as well as of the Springer

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Exp Astron (2005) 20:289–298 Table 1 Examples of the thickness of material necessary to change the phase of X/γ -ray radiation by 2π , and the corresponding absorption loss. Low atomic number materials show the least absorption. Gold is an example of a high density material which though having poor transmission at low energies minimises the lens thickness

Material

t2π µm

5 keV Absorption %

t2π µm

100 keV Absorption %

t2π mm

500 keV Absorption %

Polycarbonate Silicon Gold

23 13 2.1

6.3 51 93

470 260 39

0.9 0.9 32

2.4 1.3 0.19

2.6 2.7 5.2

transmission losses associated with this amount of material. Over a wide range of materials and energies, dimensions are convenient for manufacture and losses are very low. 1.2. An example Phase Fresnel lens for gamma-rays A consequence of the possibility of modulating the phase of a gamma-wave with a convenient thickness of material is that one can make a lens for focussing gamma-rays simply by giving a disk of material a thickness profile with the form shown in Figure 2(d). This is essentially a Fresnel lens, but as the term is often applied to a simple lens whose thickness is stepped without consideration to maintaining phase, we term it a Phase Fresnel Lens, or PFL. As an example, such a lens for 500 keV gamma-rays might consist of a 5 m diameter disk of (say) aluminium with a thickness varying between tmin = 0.25 mm (to provide a substrate) and tmax = tmin + t2π = 1.4 mm. The absorption losses would be 1.6%. We shall consider below the example of such a lens in which the finest pitch, p, of the pattern (at the periphery) is ∼1 mm. 2. Advantages of Phase Fresnel lenses Phase Fresnel lenses seem to offer major advantages for gamma-ray astronomy. Angular resolution The diffraction-limited angular resolution of a PFL of diameter d at wavelength λ is given by the usual formula for a circular aperture, θ D = 1.22λ/d. In appropriate circumstances there is no reason why resolution close to this limit should not be achieved. For a 5 m diameter lens at 500 keV the diffraction limit is 0.12 micro seconds of arc (µas). Sub micro arc second resolution is exactly what is needed to image the space-time around a black hole – a specific objective of NASA’s ‘Beyond Einstein’ program. Simple manufacture Because the refractive index is very close to unity, the manufacturing tolerances necessary in the construction of a PFL are often relatively lax. For an aluminium lens working at 500 keV, λ/40 optical precision requires only 30 micron accuracy. In such circumstances Gamma-ray lens ‘polishing’ can be done with regular machine-shop tools! Collecting area Because of the low transmission losses and the large geometrical collecting area possible with PFLs, the effective area of a PFL-based telescope can be enormous. Even allowing for absorption, for reasonable detector efficiency (50%), and for rms wavefront Springer

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errors corresponding to λ/10, the effective area of the example 5 m diameter lens would be 65000 cm2 . Low aberrations and non-critical alignment With the typical dimensions which are being considered here, a PFL is an extreme example of a high aperture-ratio ( f -number), thin lens. Consequently geometrical aberrations are low (in fact entirely negligible for any conceivable size focal plane detector) and any tilt of the lens with respect to the viewing direction has little effect (tilts of ∼ 1◦ can be tolerated). In addition the depth of field is relatively large.

3. The downside For a given lens diameter and λ the focal length of a Fresnel lens is given by f = pd/2λ. Table 2 gives some example values for a 5 m diameter lens. It can be seen that unless one reduces p to the atomic scale (as in Laue lenses), to the nanometric scale (as in multilayer mirrors), or at least to that entailing micromachining, then focal lengths are very long, particularly for high energies. Minimising the focal length of a PFL by adopting very small p is difficult because the necessary thickness (depth) of the structure remains that discussed in Section 1.1 and the ‘aspect ratio’ (pitch/depth) of the required profile becomes very high. Also, although it was argued in Section 2 that tolerances on the thickness are easily achieved, radial tolerances need to be p if diffraction limited focussing if not to be compromised. However, there are reasons for not trying to minimise f. The diffraction limited resolution will not be obtained if the detector does not have adequate spatial resolution or if chromatic aberration is too important. Combining the above expression for the focal length in terms of p with θD = 1.22λ/d shows that the physical dimension of the diffraction spot is simply 0.66 p, independent of λ. A detector with spatial resolution x which is of this order of magnitude or worse will cause blurring on an angular scale x/ f . Thus any PFL system with x > p, or equivalently f < x d/2λ, will be limited by detector resolution, not by diffraction. In the case of chromatic abberation, a spectral band of width λ leads to a blurring θC = 0.15(d/ f ) ( λ/λ). Thus both detector resolution problems and those of chromatic aberration ease with increasing f .

Table 2 Examples of the focal length f of a PFL having diameter, d = 5 m for various values of finest pitch p and photon energy. The aspect ratio is indicative (t2π / p) and supposes a moderately dense material (ρ ∼ 10).The first two lines illustrate energy/pitch/focal-length combinations for which PFL aspect ratios are probably impracticable and for which Laue diffraction (Figure 1c) is more appropriate Pitch p

Energy (keV)

Aspect ratio

Focal length f

Notes

0.5 nm 0.5 nm 200 nm 25 microns 1.0 mm

100 1000 5 100 500

1.3 × 105 1.3 × 106 16 2.5 0.32

100 m 1 km 2 km 5000 km 106 km

Typical atomic spacing ” ” ” Note 1 Note 2 Example used here

Note. 1 Same pitch as the Chandra HEG grating [2]. Note. 2 Same aspect ratio as the Chandra HEG Diffraction grating. Springer

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Fig. 3 Continuous lines: the contributions to the angular resolution of a 5 m diameter PFL for 500 keV gammarays. That for chromatic abberation assumes a 2 keV band. Dashed lines show the corresponding values for a 2 m diameter PFL (the detector is of course unchanged). In each case the curves show the combination of the three components

Figure 3 shows the effect on the contributions to the angular resolution of changing the design focal length of an example Fresnel lens having d = 5 m and working at 500 keV. For the baseline design it is supposed that the detector resolution is limited by the track length of the electron receiving the energy of the incoming to x ∼ 0.5 mm. Similarly, the spectral band is assumed to be no narrower than the typical resolution of a Germanium detector,

E ∼ 2 keV at 500 keV. It can be seen that unless f > ∼ 106 km, then chromatic abberation will limit the angular resolution to no better than about one µas. Thus the two main problems which need to be addressed are chromatic aberration and long focal length. 3.1. Chromatic aberration The problems caused by chromatic aberration include both the loss of angular resolution due to blurring of the image and the decrease in sensitivity to which this blurring leads through the necessity of collecting the signal from a larger, and hence higher background, region of the detector. We have seen that the former effect is mimimised by using long focal lengths. The latter bears some discussion. Suppose one accepts that chromatic abberation is inevitable. Obviously for mono-energetic radiation there is not a problem. For broadband emission, one will properly focus only the radiation in a small fraction of the spectrum. With an energy resolving detector, radiation outside a band E can be ignored. One can then pose the question – how wide should E be for the best sensitivity? Suppose the sensitivity is limited by noise on the detector background, B, in a focal spot of diameter dd . We may take the detector background to be proportional to

E dd2 . If dd is dictated by chromatic aberration then it will be proportional to E. For a continuum source, so will the signal S. Consequently, assuming that the dominant source of noise is statistical background fluctuations, the signal-to-noise ratio S/B 1/2 is proportional Springer

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Fig. 4 The efficiency of a 500 keV PFL if the detector distance is adjusted to match the focal length for each energy (note - the corresponding curve in reference Skinner (2002) is slightly incorrect)

to E −1/2 . One thus reaches the counter-intuitive conclusion that, in these circumstances, the best signal-to-noise ratio is obtained by using a band as narrow as the detector energy resolution will allow. This is of course also best for angular resolution. Using a narrow energy band, the sensitivity to a broadband signal will of course not be as good as if a wider bandpass had been possible without compromising the focusing, but given the large collecting area and the tiny background in a small focal spot and in a narrow energy range, it can be amazingly good. The narrow line sensitivity of our example 5 m, 500 keV lens could be 70 keV), are in an advanced stage of development [1–3]. Accurate test and calibration of these focusing telescopes are crucial in order to correctly derive their response function and thus to avoid systematic errors in the determination of spectral, temporal and energetic properties of the X-ray celestial sources. In order to perform these calibrations, monochromatic and parallel hard X-ray beams are desired. The beam

G. Loffredo () · D. Pellicciotta · A. Pisa Physics Department, University of Ferrara, via Saragat 1, I-44100, Ferrara, Italy V. Carassiti · S. Chiozzi · F. Evangelisti · L. Landi · M. Melchiorri · S. Squerzanti Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Ferrara, Italy F. Frontera IASF, CNR, Via Gobetti 101, Bologna, Italy Springer

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Fig. 1 Sketch (not to scale) of the recent configuration of the Ferrara X-ray facility. From the left: the X-ray tube, the monochromator system, the sample holder and the detector holder. The X-ray beam travels partially within an evacuated tube and partially in a helium atmosphere.

energies have to cover the energy passband of these new telescopes (up to several hundreds of keV). Either for testing or calibrating these new telescopes, suitable hard X-ray facilities are needed. The Ferrara X-ray facility has already been used to, e.g., perform the ground calibration of the JEM-X (Joint European Monitor for X-rays) detectors on board the INTEGRAL satellite [4], reflectivity measurements of mosaic crystals (graphite [7], Cu (111) [5]) and non linearity tests of hard X-ray detectors ([8]). Here we summarize the past configuration of the Ferrara X-ray facility and the current extention.

2. The X-ray facility and its applications The X-ray facility of the Ferrara University was initially motivated to test the PDS aboard BeppoSAX [6] in the range from 15 to 140 keV. The configuration of the X-ray facility used for the most recent measurements/calibrations is shown, not to scale, in Fig. 1. The main components include two alternative X-ray tubes as sources of polychromatic X-ray beam (one working at lower energies (6–60 keV) and the other at higher energies (15–140 keV)), a hybrid vacuum-helium system with vacuum tubes and an helium box where a fixed–exit double-crystal monochromator is installed, a system of collimators plus a Pb shield to stop the scattered radiation in the testing room, a six-axis table used as sample holder, and a four-axis table as detector holder. Currently the facility is being extended in the LARge Italian X-ray facility (LARIX), see Fig. 2. As the figure shows, LARIX includes two large experimental rooms and a 100 m long tunnel linking these rooms. The X-ray facility described in Fig. 1 is now positioned in the large experimental room. The sample holder, the detector holder and the holder which measures the position of the sample holder, can be movedon 10 m long rails as Figs. 3 and 4 Springer

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Fig. 2 Plan of LARIX. From the left: large experimental room where the facility is actually positioned, the tunnel and the second experimental room.

Fig. 3 Plan of the facility installed in the large experimental room of LARIX. The wall around the facility are Pb shield in order to devide the X-ray environment and the console room. On the optical table are positioned the X-ray tubes, the monochromator system, the collimation system. The sample holder and the detector holder can be moved on the rails.

show. The sample holder has 6 degrees of freedom, three translations and three rotations, the detector holder is improved with a rotation in addition to the three linear stages. We see in Fig. 4 the walls 2 meter high, made of Al + Pb which separate the X-ray equipment from the console room. This is equipped with three computers which manage the X-ray facility instrumentation. The X-ray tubes are shielded by a box made of a Pb layer 5 mm thick. An overhead travelling crane (1000 kg weight–bearing, 20 m long) is installed parallel to the 10 m long rails. The facility in the current configuration can be used for calibrating position sensitive detectors, for a detailed study of the response function of hard X-ray detectors, e.g. the study of linearity discontinuities in X-ray detectors (e.g. [8], for hard X-ray reflectivity measurements (mosaic crystals, multilayers, etc) and calibration of hard X-ray optics and other applications, such as transparency measurements of complex materials. Springer

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Fig. 4 Picture of a part of the X-ray facility in the present configuration. It shows the 10 m long rails hosting the sample holder, the detector holder and the other holder which read the position of the sample putted on the sample holder. We see also the Pb walls which divides the X-ray environment from the console room.

3. Main components of the X-ray facility A detailed description of the Ferrara X-ray facility has already been recently reported [9]. Here we summarize the main components. 3.1. X-ray sources Two X-ray tubes, with different operational voltage, are mounted onto an optical table and powered by independent high voltage supplies. One of the tubes, supplied by Philips (2001), is equipped with a Molybdenum anode, with its voltage which can be varied from 20 to 60 kV and the circulating current from 10 to 60 mA. The spot size is 5 × 5 mm2 . The other tube, supplied by Siemens (1990), is equipped with a Tungsten anode, with its voltage which can be set in the range from 40 to 140 kV and its current from 0.1 to 5 mA. The spot size is 5 × 5 mm2 . The X-ray output window of the first tube is equivalent to a 0.3 mm thick Beryllium foil, while that of the second tube is equivalent to a 1.5 mm thick aluminium foil. The window thickness fixes the low energy threshold of the X-ray beam: about 6 keV with the first tube, 15 keV with the second. By means of manipulators both tubes can be moved up and down and translated along a direction perpendicular to the X-ray beam. Every movement is directed by remote control. 3.2. Monochromator The continuum spectrum provided by either X-ray tube is monochromatized with a double crystal diffractometer [10]. Its main feature is that it provides a fixed-exit beam independently of the photon energy selected. Figure 5 shows the diffractometer scheme: the first crystal (B) has the role of selecting the desired wavelength from the incident continuum beam, while the second crystal (D) re-directs the monochromatized radiation along a direction parallel to the incident beam [4]. Springer

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Fig. 5 Top of view of the Bragg-Bragg fixed exit configuration: A is the rotation axis, θin is the Bragg angle and h = 2 × p.

Fig. 6 Three dimensional view of the X-ray facility.

3.3. X-ray beam path environment The monochromator system is inside a sealed plexiglass box, where helium is pumped. The X-ray entrance and exit window of the helium box are made of polyethylene terephthalate (PET) 75 µm thick with a very high transparency at the operation energies. Outside the helium box, the X-ray beam travels in evacuated tubes (10−3 mbar) up to the position of the sample to be tested. 3.4. Sample and detector holders The sample holder can be accurately moved in three perpendicular directions (X, Y, Z) and rotated around vertical and the horizontal axes. An angular position accuracy of 3

can be achieved with a repeatability of 1

. The above movements are monitored with an external system of optical encoders. In this way the true position of the sample and the performances of the XYZ table can be accurately measured. The detector holder can be also accurately moved in three perpendicular directions (X, Y, Z) and is equipped with a rotation stage around the vertical. The resolution of this stage is 3.6

. Both the sample and the detector holders can translate on the 10 m long rails. Figure 6 shows a three dimensional view of the X-ray facility in the extended configuration. 3.5. Collimation of X-ray beam A set of collimators (see Fig. 6) limits the divergence of the X-ray beam. The divergence of the beam influences the energy width of the monochromatized beam. Generally the aperture Springer

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55 50

Energy (keV)

45 40 35 30 25 20 15 10 2

3

4

5 6 7 Bragg angle (deg)

8

9

10

Fig. 7 Energy measured of the X-ray beam as a function of the Bragg angle of the crystal No. 1 of the double–crystal monochromator. The expected energy, derived from the Bragg law, is also shown (reprinted from [4]).

of the collimators depends on the kind of experiment to be performed. For example, to radiate the entire cross section of our CZT detector, see below, which has an X-ray entrance window of 5 × 5 mm2 , when it is positioned to the end of long rails, the pinhole size of the second collimator needs to be at least 0.3 × 0.3 mm2 , otherwise the cross section of the beam is lower than the detector’s window. The first collimator does not significantly influence the size of the beam but influences the beam intensity. The second collimator is crucial to get the size of the spot needed for the specific applications. 3.6. Detectors A set of detectors is available for the X-ray facility. They include three NaI(Tl) scintillators, one of which is an imager, a Cadmium Zinc Telluride (CZT) detector, a high purity germanium detector (HPGe), and a large area imaging detector. The NaI(Tl) imager has a square shape with a side of 42 mm and a thickness of 3 mm. The crystal is viewed by a position sensitive PMT. An PC-based interface running LabView provides a user-friendly environment for using this X-ray imager for locating the X-ray beam and other user applications. Details on the detector configuration can be found elsewhere ([11], [5]). The CZT X-ray detector, Peltier–cooled to 250 K, is used to monitor the intensity and the spectrum of the pencil beam incident on the sample to be tested. It shows a very good energy resolution (0.94 keV at 60 keV). Its cross section is 5 × 5 mm2 , its thickness 2 mm, while its X-ray entrance window is made of a 0.25 mm thickness beryllium layer. The high purity germanium detector (HPGe), cooled with liquid nitrogen, has a surface area of about 78.5 cm2 , a thickness of 13 mm and an X-ray entrance window of 0.254 mm Beryllium thickness. This configuration gives an high detection efficiency to the X-rays provided by the facility. The energy resolution is about 0.44% at 122 keV. The large area imaging detector is an X-ray Image Intensifier equipped with a CCD camera with 1000 × 1000 pixels and a digital video output. The X-ray entrance window has a 215 mm diameter. The X-ray detection efficiency is about 65% at 59.5 keV and the position resolution is 0.2 mm. In the present configuration the X-ray Image Intensifier and the high Springer

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Fig. 8 Reflectivity curve of a Cu (111) mosaic crystal sample in transmission configuration (Laue geometry) at about 90 keV. The best fit curve and parameters of the model function to the data are also shown: θ0 is the Bragg angle, FWHM is the full width half maximum of the reflectivity curve and t0 is the average thickness of the microcrystals of the mosaic crystal (reprinted from [4]).

Fig. 9 Experimental setup in determining the optical axis of the copper tiles. In (a) the incident beam is diffracted with the angle α1 = θ + δ rispect to the normal n. By rotating of π the crystal around n, (b), the angle becames α2 = θ − δ.

purity germanium detector (HPGe) are positioned on the detector holder and can be translated and rotated simultaneously. An example of facility calibration with the CZT detector is shown in Fig. 7.

4. Some example of recent applications of the X-ray facility After the ground calibration of the JEM-X detectors, as mentioned before [4], the facility in the current configuration has been used for reflectivity measurements of crystal samples of Cu (111) in Laue configuration within the development project of a hard X-ray focusing optics [5]. The centroid energy of the monochromatized photons measured with the CZT detector is compared with the energy expected from the Bragg law (see Fig. 7). An example of reflectivity measurement of a mosaic crystal sample of Cu (111) expected to be used as reflecting material in a Laue lens [5] under development is shown in Fig. 8. In the context of the development project of a Laue lens, a key task is the measurement of the optical axis of mosaic crystals tiles of Cu (111) used for the lens and provided by Springer

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Fig. 10 Set up for the crystal axis determination. The X-ray Imager Intensifier is able to resolve the distance x which is quite 2δL

the Institute Laue Langevin of Grenoble. The optical axis of the Cu (111) tiles is required to be determined with an accuracy better than 10 arcsec. As figs. 9 show the angle between the normal to the crystal’s surface, n, to the average orientation of the crystal’s plane is δ and the angle between the diffracted beam to n is α. If δ = 0 then α = θ where θ is the angle between n and the incident beam. By rotating of π the crystal around n, the geometry shows two angles between n and the diffracted beam: α1 = θ + δ, Fig. 9(a), and α2 = θ − δ, Fig. 9(b). As Fig. 10 shows, if the distance from the crystal to the X-ray Image Intensifier is L, we can measure the distance x between the focal spot of the beam diffracted with the angle α1 from that diffracted with the angle α2 . Immediately we can see: x ≈ δ. 2L

(1)

The X-ray Image Intensifier permit us to achieve 0.2 mm of spatial resolution and the rails to change the distance from the cryslal up to the X-ray detector. The maximum distance L from the crystal up to the X-ray Image Intensifier is 6 m and it permit us to achieve δ ≈ 4 arcsec. References 1. Pareschi, G., et al.: Astronomical soft X-ray mirrors reflectivity enhancement by multilayer coatings with carbon overcoating, SPIE, 5488 (2004) 2. Pisa, A., et al.: Development status of a Laue lens for high energy X-rays (≥ 60 keV), Proc. SPIE 5900, 350–359 (2005) 3. von Ballmoos, P., et al.: The MAX mission: focusing on high sensitivity gamma-ray spectroscopy, Proceedings of the 5th INTEGRAL Workshop, Munich 16–20 February 2004, ESA SP-552 (2004) 4. Loffredo, G., et al.: X-ray facility for the ground calibration of the X-ray monitor JEM-X on board INTEGRAL, A&A 411, L239 (2003) 5. Pellicciotta, D., et al.: Laue Lens Development for Hard X-rays (>60 keV), IEEE Trans. on Nucl. Sci., (2006) (in press) 6. Frontera, F., et al.: Hard x-ray (>15 keV) facility for calibration of Space Astronomy Experiments, IEEE TNS 40, 874 (1993) 7. Frontera, F., et al.: Hard X-ray imaging via crystal diffraction: first results of reflectivity measurements, Proc. SPIE 1549, 113–119 (1991) 8. Zavattini, G., et al.: Linearity discontinuities in Xe–filled X-ray microstrip detectors, Nucl. Instr. & Meth. A401, 206 (1997) 9. Loffredo, G., et al.: The X-ray facility of the Physics Department of the Ferrara University, Experimental Astronomy 18, 1–11 (2004) 10. Mills, D.M. & King, M.T. A tunable, fixed–exit, monolithic X-ray monochromator for synchrotron radiation sources, Nucl. Inst. and Meth. 208, 341 (1983) 11. Poulsen, J.M., Verbeni, R., and Frontera, F. Position–sensitive scintillator detector for hard X-rays, Nucl Instr. & Meth. A310, 398–402 (1991) Springer


SIMBOL-X: An hard X-ray formation flying mission Rodolphe Clédassou · Philippe Ferrando

Received: 20 January 2006 / Accepted: 13 July 2006 C Springer Science + Business Media B.V. 2006

Abstract In 2004 and 2005 CNES decided to perform phase 0 studies on 4 scientific missions: ASPICS (Solar physics), MAX (γ -rays Laue lens), PEGASE (hot Jupiter study by an interferometer in the 2 µm to 4.5 µm range) and SIMBOL-X (hard X-rays telescope). This last mission had already undergone a feasibility study in 2003 (ref. [4]), however a complementary study was necessary to take into account the possibilities of increasing the payload mass allowance, as well as the developments in the payload design and science goals (see ref. [1]). The output of this new detailed study is described hereafter.

1. SIMBOL-X scientific mission The SIMBOL-X project is a high energy new generation telescope covering by a single instrument a continuous energy range starting at classical X-rays and extending to hard X-rays ie from 0.5 to 80 keV. It is using in this field a focalizing payload which until now was only used at energy below 10 keV, via the construction of a telescope distributed on two satellites flying in formation. SIMBOL-X permits a gain of two orders of magnitude in sensibility and spatial resolution in comparison to state of the art hard X-rays instruments. The energy range targeted by SIMBOL-X is the one where thermal emissions leave place to harder emissions which are due to particles acceleration or which are due to accretion phenomena on a massive central object. The study of these phenomena is the heart of SIMBOL-X scientific objectives.

R. Clédassou () Centre National d’Etudes Spatiales, 18 Avenue Edouard Belin, 31041 Toulouse Cedex, France P. Ferrando UMR 7164, APC & DSM/DAPNIA/Service d’Astrophysique, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France Springer

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1.1. Why hard-X rays? Non thermal emissions in X and γ rays are unique signatures needed to answer fundamental questions in modem astrophysics: – How works the dynamics of the universe at all scales? From star formation to cosmological large structure formation, this is driven by accretion power, particularly on Black Holes, and violent non thermal phenomena (as jets) – How good are our physics laws in extreme conditions, of gravity, pressure, magnetic field? Do we need new physics? – How and where are accelerated the cosmic rays at the highest energies?

2. SIMBOL-X mission SIMBOL-X orbit has been revisited during the 2005 study. It has permitted to define an orbit giving more mass allowance at launch, as well as a very good flexibility in the mission scheduling. In particular the mass impact linked to the major drivers (redundancy, collimator) revisit have been absorbed and left intact a comfortable system margin (>30%). This mission should allow for observations during 2 years (cumulated observations). It means that the total space system life duration would be about 3 years (taking into account some months for “In flight formation acquisition, reacquisition and checking” and a provision for servicing operations and accidental safe mode). Scientific observations have to be performed outside the Van Allen belts (no instrument background noise): that is to say an altitude greater than 73 000 km. Nevertheless it has been accepted to pass very high in these belts once every week. The telescope is implemented with a “mirror spacecraft” and “detector spacecraft” in formation flying. Optimizing the global resources of both spacecrafts led then to select a scientific orbit with a 44 000 km perigee altitude/a 253 000 km apogee altitude/a 7 sidereal days period /Low initial inclination. This orbit is subject to significant luni solar effect. It has been chosen to give 90% time above 73 000 km which maximizes the science return. The satellites V is around 500 m/s and can be achieved with a classical and robust hydrazine system. The daily visibility are ∼12 hours per station with a maximum of 2 hours gap. At perigee the visibility is permanent (24 hours) for the chosen station. Springer

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During mission there is no need to maintain exactly the orbit parameters. The important point is to keep the correct orbit period and the phasing with the ground segment to facilitate the operations with the Ground at perigee pass (maximization of telemetry rate). In that perspective roughly one manoeuvre per month is expected to maintain the semi-major axis. The result is that orbit parameters evolution are constrained by luni-solar effects and the perigee will increase to ∼70 000 km after 2 years due to lunar effects combined to semi major axis conservation (see below).

Typical operations on such an orbit consists in performing science during 6 days (out of perigee) and to use permanent perigee visibility to download the bigger part of the telemetry. Outside perigee a daily contact of one to two hours is sufficient for Status of Health and/or monitoring of the formation repointing to a new target.

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The distributed instrument (“mirror spacecraft” and “detector spacecraft”) would be able to observe a great variety of astrophysical sources. Depending on them the observation time varies a lot. As an example a bright source like the “Crab” one needs an observation time in the range of an hour, on the contrary a faint source or a deep field observation could need several days of continuous observation. In the satellite design 500 observations per year have been taken into account. The following schemes are giving examples of operation for different sources.

Example 1. Several bright sources on one day (22 ks each; >1m Crab)

Example 2. One weak source (79 ks;

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