Molecular hydrogen in space

Molecular hydrogen is the most abundant molecule in the Universe. In recent years, advances in theory and laboratory experiments coupled with breakthrough observations with important new telescopes and satellites have revolutionized our understanding of molecular hydrogen in space. It is now possible to address the question of how molecular hydrogen formed in the early Universe and the role it played in the formation of primordial structures. This timely volume presents articles from a host of experts who reviewed this new understanding at an international conference in Paris. This book provides the first multi-disciplinary synthesis of our new understanding of molecular hydrogen. It covers the theory of the physical processes and laboratory experiments, as well as the latest observations. It will therefore be an invaluable reference for all students and researchers in astrophysics and cosmology.

CAMBRIDGE CONTEMPORARY ASTROPHYSICS

Molecular Hydrogen in Space

CAMBRIDGE CONTEMPORARY ASTROPHYSICS Series editors Jos6 Franco, Steven M. Kahn, Andrew R. King and Barry F. Madore Titles available in this series Gravitational Dynamics, edited by 0. Lahav, E. Terlevich and R. J. Terlevich (ISBN 0 52156327 5) High-sensitivity Radio Astronomy, edited by N. Jackson and R. J. Davis (ISBN 0 521 57350 5) Relativistic Astrophysics, edited by B. J. T. Jones and D. Markovi6 (ISBN 0 521 62113 5) Advances in Stellar Evolution, edited by R. T. Rood and A. Renzini (ISBN 0 521 59184 8) Relativistic Gravitation and Gravitational Radiation, edited by J.-A. Marck and J.-P. Lasota (ISBN 0 521 59065 5) Instrumentation for Large Telescopes, edited by J. M. Rodriguez Espinosa, A Herrero and F. Sanchez (ISBN 0 521 582911) Stellar Astrophysics for the Local Group, edited by A. Aparicio, A. Herrero and F. Sdnchez (ISBN 0 521 63255 2) Nuclear and Particle Astrophysics, edited by J. G. Hirsch and D. Page (ISBN 0 521 63010 X) Theory of Black Hole Accretion Discs, edited by M. A. Abramowicz, G. Bjornsson and J. E. Pringle (ISBN 0 521 62362 6) Interstellar Turbulence, edited by J. Franco and A. Carraminana (ISBN 0 521 65131 X) Globular Clusters, edited by C. Martinez Roger, I. Perez Fourn&n and F. Sdnchez (ISBN 0 521 77058 0) The Formation of Galactic Bulges, edited by C. M. Carollo, H. C. Ferguson and R. F. G. Wyse (ISBN 0 521 66334 2) Very Low-Mass Stars and Brown Dwarfs, edited by R. Rebolo and M. R. Zapatero-Osorio (ISBN 0 521 66335 0)

Molecular Hydrogen in Space Edited by F. COMBES Observatoire de Paris, DEMIRM

G. PINEAU DES FORETS DAEC, Observatoire de Meudon IAS, Universite de Paris-Sud, France

CAMBRIDGE UNIVERSITY PRESS

PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE

The Pitt Building, Trumpington Street, Cambridge CB2 1RP, United Kingdom CAMBRIDGE UNIVERSITY PRESS

The Edinburgh Building, Cambridge CB2 2RU, UK http://www.cup.cam.ac.uk 40 West 20th Street, New York, NY 10011-4211, USA http://www.cup.org 10 Stamford Road, Oakleigh, Melbourne 3166, Australia Ruiz de Alarcon 13, 28014 Madrid, Spain © Cambridge University Press 2000 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2000 Printed in the United States of America 10/12 pt. Typeset in I^TEX by the authors A catalog record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data is available

ISBN 0 521 78224 4 hardback

VII

Contents Preface Conference participants Conference photograph / poster

xi xiv xviii

1. Physics of H2 and HD Astrophysical Importance of H2

3

A. Da.lga.rno

Radiative and Electronic Excitation of Lyman and Werner Transitions in H2 E. Roueff, H. Abgra.ll, X. Liu and D. Shemansky The Cooling of Astrophysical Media by H2 and HD D. Flower, J. Le Bourlot, G. Pineau des Forets and E. Roueff Highly Excited Singlet Ungerade States of H2 and their Theoretical Description

13 23

31

Ch. Jungen and S. C. Ross Laboratory Studies of Long-range Excited States of H2 W. Ubachs A Model of Interstellar Dark Matter J. Schaefer Mass of H2 Dark Matter in the Galactic Halo

39 47 57

Y. Shchekinov, R. J. Dettmar and P. M. W. Kalberla

2. Formation - Destruction Experiments with Trapped Ions and Nanoparticles

63

D. Gerlich, J. IHemann, and S. Schlemmer Laboratory Studies of Molecular Hydrogen Formation on Surfaces of Astrophysical Interest V. Pirronello, O. Biham, G. Manico, J. E. Roser and G. Vidali The Formation of H2 and Other Simple Molecules on Interstellar Grains E. Herbst

71

85

viii

Contents

The Interaction of H Atoms with Interstellar Dust Particles: Models V. Sidis, L. Jeloaica, A . G. Borisov and S. A . Deutscher The Energetics and Efficiency of H2 Formation on the Surface of Simulated Interstellar Grains

89

99

D. A. Williams, D. E. Williams, D. Clary, A. Farebrother, A. Fisher, J. Gingell, R. Jackman, N. Mason, A. Meijer, J. Perry, S. Price and J. Rawlings Probing the Connection between PAHs and Hydrogen (H, H2) in the Laboratory and in the Interstellar Medium 107 C. Joblin, J. P. Maillard, I. Vaughn, C. Pech and P. Boissel

3. Observations and Models N o n S t a t i o n a r y C-shocks: H 2 Emission i nMolecular Outflows

...

117

G. Pineau des Forets and D. Flower The Ortho/Para Ratio in C and J-type Shocks

123

D.Wilgenbus, S. Cabrit, G. Pineau des Forets and D. Flower Theoretical Models of Photodissociation Fronts

131

B. Draine and F. Bertoldi ISO Spectroscopy of H2 in Star Forming Regions 139 M. Van den Ancker, P. R. Wesselius and A. G. G. M. Tielens Observations of the H2 Ortho-Para Ratio in Photodissociation Regions 143 S. Ramsay, A. Chrysostomou, P. Brand, M. Burton and P. Puxley 151 H2 Emission from CRL618 F. Herpin, J. Cernicharo and A. Heras Hydrogen in Photodissociation Regions: NGC2023 and NGC7023 . 155 D. Field, J. L. Lemaire, J. P. Maillard, S. Leach, G. Pineau des Forets, E. Falgarone, F. P. Pijpers, M. Gerin, F. Rostas, D. Rouan and L. Vannier 161 A Pre-FUSE View of H2 M. Jura H2 Absorption Line Measurements with ORFEUS P. Richter, H. Bluhm, O. Marggraf and K. S, de Boer Ultraviolet Observations of Molecular Hydrogen in Interstellar Space T. Snow FUSE and Deuterated Molecular Hydrogen R. Ferlet, M. Andre, G. Hebrard, A. Lecavelier, M. Lemoine, G. Pineau des Forets, E. Roueff and A. Vidal-Madjar

165 171 179

Contents

ix

ISO-SWS Observations of H2 in Galactic Sources

189

C. Wright H2 in Molecular Supernova Remnants

193

W. Reach and J. Rho 3D Integral Field H2 Spectroscopy in Outflows

197

J. Tedds, P. Brand and M. Burton Near-Infrared Imaging and [01] Spectroscopy of IC443 using 2MASS and ISO J. Rho, S. Van Dyk, T. Jarrett, R. M. Cutri, and W. T. Reach

201

I S O C A M S p e c t r o - i m a g i n g of the S u p e r n o v a R e m n a n t I C 4 4 3 . . . . 2 0 5 P. Cox, D. Cesarsky and G. Pineau des Forets S p a t i a l S t r u c t u r e of a P h o t o - D i s s o c i a t i o n R e g i o n in O p h i u c u s . . . . 2 1 1 F. Boulanger, E. Habart, A. Abergel, E. Falgarone, G. Pineau des Forets and L. Verstraete Tracing H2 Via Infrared Dust Extinction 217 J. Alves, C. Lada and E. Lada The Small Scale Structure of H2 Clouds

221

P. Boisse, S. Thoraval, J. C. Cuillandre, G. Duvert, and L. Pagani Hot Chemistry in the Cold Diffuse Medium: Spectral Signature in the H2 Rotational Lines

225

E. Falgarone, L. Verstraete, P. Hily-Blant and G. Pineau des Forets H2 Observations of the OMC-1 Outflow with the ISO-SWS D. Rosenthal, F. Bertoldi and S. Dra.pa.tz

231

4. Extragalactic and Cosmology The Role of H2 Molecules in Cosmological Structure Formation T. Abel and Z. Haiman The Role of H2 Molecules in Primordial Star Formation

. .

237 247

F. Palla and D. Galli E v o l u t i o n of P r i m o r d i a l H2 for Different C o s m o l o g i c a l M o d e l s . . . . 2 5 9 D. Puy Dynamics of H2 Cool Fronts in the Primordial Gas M. Ibanez, and M. Bessega

263

x

C'o/i ten ts

Is Reionization Regulated by H2 in the Early Universe ?

269

A. Ferrara, B. Ciardi and P. Todini H2 in Galaxies

275

F. Combes Transformation of Galaxies within the Hubble Sequence

285

D. Pfenniger Extragalactic H2 and its Variable Relation to CO

293

F. Israel

The Galactic Dark Matter Halo: Is it H 2 ? P. Kalberla, J. Kerp and U. Haud

297

Observations of H2 in Quasar Absorbers J. Bechtold H2 Emission as a Diagnostic of Physical Processes in Starforming Galaxies

301

307

P. van der Werf

5. Outlook H2 in the Universe: Perspectives

317

J. Black-

Author index

325

Preface

xi

Preface This book gathers all contributions to the International Conference on H2 in Space held in Paris, France, on September 28- October 1st, 1999. The attendance was 106 participants from 16 countries. The goal was to gather together representatives of three communities: experts in the physics of the molecule, including experimentalists, observers of the interstellar medium, in particular of the warm H2 detected in infrared lines, and theoreticians studying H2 formation and cooling in astrophysical objects, from the early universe to the present galaxies. The electronic structure of the H2 molecule has been well studied in the past, but it was shown that recent progress has been made on the theory of highly excited and long-range Rydberg states, both from calculations of line-strengths and comparison with experiments. New and more accurate data are now available for the rates of collisional excitation of rovibrational transitions by neutrals, as well as protons or electrons. It has been known for several decades that interstellar H2 is formed on dust grains, but, until now, the efficiency of this process was poorly known. Recent experiments have reproduced this formation process on silicates and amorphous carbon and shown that the efficiency is strongly dependent on temperature. In particular, the mobility of H atoms on grains is much lower than previously thought. Laboratory experiments with trapped ions and nanoparticles have opened new avenues of investigation. The relationship of H2 with PAHs is being addressed both in the laboratory and by means of astronomical observations. H2 infrared emission is produced in photodissociation regions (PDRs) and shocks. An impressive harvest of data has been gathered by ISO, and the comparisons with models have considerably increased our knowledge of the physics and chemistry of star-forming regions. The rovibrational lines can help to distinguish the nature of the shocks (C-type, J-type, dissociative or not) and their age. The orthorpara ratio is an indicator of the state in which H2 is formed, the conditions of excitation in the shocks, or the history of molecular clouds. H2 emission has been observed and interpreted in sources as diverse as Herbig-Haro objects, star-forming molecular clouds and the associated PDRs, planetary nebulae, supernovae remnants, and Xray excited gas. Most observations of the H 2 molecule are of warm gas and pertain to only

xii

Preface

1% or less of the molecular mass. The bulk of the material is cold H2 that will be traced by FUSE, through H2 UV absorption, or has been traced by CO millimetric emission (but with a highly uncertain ratio for conversion to H2), by infrared measurements of dust extinction, or by thermal dust emission. These tracers are strongly dependent on metallicity, and there exists the tantalizing possibility that we are missing large amounts of cold H2 in the outer parts of galaxies. This is suggested by ISO mapping of pure rotational lines of H2 in galaxies, by the excess gamma-ray emission, and by the detection of small-scale (10 AU) structure in the ISM. In the primordial gas, H2 formed in the gas phase, in the absence of grains; H2 and HD cooling then triggered the collapse of the first structures. The re-ionization of large regions of the Universe is then necessary to avoid a "cooling catastrophe". The observation of the HD/H2 ratio at various redshifts is a crucial test of the baryonic fraction of the Universe, and our hopes rest with FUSE to resolve recent controversies. The conference confirmed that progress is currently being made in a number of crucial areas, including laboratory simulations of H2 formation on grains and cosmological scenarios. There is already a wealth of observational data, and their on-going interpretation will lead to further advances. A big step will be made in the near future, when results begin to flow from FUSE. Essential to the undoubted success of the meeting was the interaction between the three communities, which do not usually attend the same conferences: laboratory experts learned about the astrophysical applications, whilst astronomers were provided with more information on the basic physics of the molecule. We are grateful to the members of the Scientific Organizing Committee for their help in the choice of speakers and participants: F. Bertoldi (MPIfRBonn, Germany), J. Black (OnsalaSpace Observatory, Sweden), F. Boulanger (I.A.S., France), F. Combes (Obs. de Paris, France), P. Cox (I.A.S., France), B. Draine (Princeton, USA), D. Field (Univ. Aarhus, Denmark), D. Flower (Durham, UK), J-L. Lemaire (Univ. Cergy-Pontoise, France), G. Pineau des Forets (Obs. de Meudon, France), A. Vidal-Madjar (IAP, France). The conference was sponsored by Programme National Chimie du Milieu Interstellaire (PCMI-CNRS), Collaborative Computational Project Number 7 (CCP7, UK), Observatoire de Paris (MEN), Ministere des Affaires Etrangeres (MAE), University Cergy-Pontoise, University Paris XI (IAS), and Institut d'Astrophysique de Paris (IAP).

Preface

xiii

This meeting could not have gone smoothly without the active collaboration of all LOC members and the graduate students Pierre Hily-Blant and David Wilgenbus. We want also to thank Lionel Provost, for his web registration software, and Jean Mouette, for his technical expertise and for taking photographs. The participants greatly appreciated being invited by Senator Loridant to the Palais du Luxembourg, where the conference dinner was held. Paris, December, 1999 The Editors, Frangoise COMBES (Observatoire de Paris) Guillaume PINEA U des FORETS (Observatoire de Meudon)

xiv

Participant List

Participant List Abel Tom, Center for Astrophysics Cambridge- USA [email protected] Abergel Alain, IAS Orsay - FRANCE [email protected] Abgrall Herve, Observatoire de Paris, Meudon -FRANCE [email protected] Allard Nicole, Observatoire de Meudon - FRANCE [email protected] Alves Joao, ESO Garching - GERMANY [email protected] Bertoldi Frank, MPIfR Bonn, Bonn - GERMANY [email protected] Black John, Onsala Space Observatory Onsala-SWEDEN [email protected] Boisse Patrick, Lab. de radioastronomie Paris-FRANCE [email protected] Boucard Stephane, DIAM, Univ. Paris 6, Paris - FRANCE [email protected] Boulanger Francois, IAS Orsay - FRANCE [email protected] Brechignac Philippe, LPPM, Univ. Paris-Sud, Orsay - France [email protected]

Cabrit Sylvie, Observatoire de Paris - FRANCE [email protected] Cernicharo Jose, CSIC. IEM Madrid - SPAIN [email protected] Combes Franchise, Observatoire de Paris - [email protected] Cox Pierre, IAS Orsay -FRANCE [email protected] Dalgarno Alexander, Center for Astrophysics Cambridge - USA adalgarno@cfa. harvard, edu

Dowek Danielle, LCAM Orsay - FRANCE [email protected] Draine Bruce, Princeton University Princeton - USA [email protected] Dubernet-Tuckey Marie-Lise, Obs. de Besancon, Besancon -FRANCE [email protected]

Dulieu Fran$ois, Universite Cergy Pontoise, Cergy Pontoise - FRANCE francois. dulieu@lamap. u-cergy.fr

Ellinger Yves, ENS Paris - FRANCE [email protected] Falgarone Edith, ENS Paris - FRANCE [email protected] Feautrier Nicole, Observatoire de Meudon - FRANCE [email protected] Ferlet Roger, 1AP Paris - FRANCE [email protected] Ferrara Andrea, Osservatorio Astrofisico Arcetri Firenze - ITALY ferrara@arcetri. astro, it

Field David, University of Aarhus Aarhus -DENMARK [email protected] Fillion Jean-Hugues, Observatoire De Meudon, Meudon -FRANCE [email protected] Flower David, University of Durham, Durham -UK [email protected] Gee Christelle, Universite de Cergy-Pontoise, Cergy-Pontoise - FRANCE gee@paris. u-cergy.fr

Participant List

xv

Gerbaldi Michele, Institut d'Astrophysique PARIS - FRANCE [email protected] Gerlich Dieter, Institut fur Physik Chemnitz -GERMANY [email protected] Gingell Jon, University College London -UK [email protected] Giraud Edmond, Observatoire, Marseille- FRANCE [email protected] Glownia James, IBM Research Division Yorktown Heights - USA [email protected] Gry Cecile, ESA Vilspa Madrid - SPAIN [email protected] Habart Emilie, I.A.S Orsay - FRANCE [email protected] Hennebelle Patrick, Demirm, ENS Paris - FRANCE [email protected] Herbst Eric, Ohio State University Columbus Ohio - USA [email protected] Herpin Fabrice, CSIC Madrid -SPAIN [email protected] Hily-Blant Pierre, Demirm, ENS Paris - FRANCE [email protected] Humbert Eric, DIAM, Univ. Paris 6, Paris - FRANCE [email protected] Ibanez Miguel, Universidad de los Andes Merida- VENEZUELA [email protected] Israel Frank, Leiden Observatory Leiden - NETHERLANDS [email protected] Joblin Christine, CESR-CNRS Toulouse Cdx 04 - FRANCE [email protected] Jolicard George, Observatoire de Besancon, Besancon - FRANCE [email protected] Jungen Christian, Univ. Orsay, Orsay - FRANCE jungl @sslO. lac. u-psud.fr Jura Michael, UCLA Los Angeles - USA [email protected] Kalberla Peter, Radioastronomical Inst. Bonn, Bonn - GERMANY [email protected] Kawamura Akiko, University of Tokyo, Tokyo - JAPAN [email protected] Kulesa Craig, University of Arizona Tucson - USA [email protected] Lakhlifi Azzedine, Observatoire De Besancon, Besancon - FRANCE [email protected] Leach Sydney, Observatoire de Paris Meudon - FRANCE [email protected] Le Bourlot Jacques, Observatoire de Meudon - FRANCE [email protected] Le Page Valery, Paris - FRANCE [email protected] Lee Jung-Kyu, Univ. of New South Wales Sydney - AUSTRALIA jklee@phys. unsw. edu. au Lemaire Jean Louis, Universite de Cergy-Pontoise, Cergy - FRANCE [email protected] Liszt Harvey, NRAO Charlottesville - USA [email protected] Mccarroll Ronald, Univ. P et M Curie Paris- FRANCE [email protected]

xvi

Participant List

Minh Young Choi, Korea Astron. Observatory Taejon - SOUTH-KOREA minh@hanul. issa. re. kr Miville-Deschenes Marc-Antoine, I.A.S. Orsay - FRANCE [email protected] Noriega-Crespo Alberto, IPAC Pasadena- USA [email protected] Oosato Takahiro, Ibaraki University Mito-JAPAN [email protected] Omont Alain, IAP, Paris, FRANCE [email protected] Palla Francesco, Osservatorio Di Arcetri Firenze - ITALY [email protected] Parneix Pascal, LPPM, Univ. Paris-Sud, Orsay - France [email protected]. u-psud.fr Pauzat Francoise, ENS Paris - FRANCE [email protected] Perault Michel, ENS Paris - FRANCE [email protected] Perry James, University College London London - UK [email protected] Pfenniger Daniel, Univ. of Geneva Sauverny -SWITZERLAND daniel.pfenniger@obs. unige.ch Philippe Laurent, DIAM, Univ. Paris 6, Paris-FRANCE [email protected] Pineau Des Forets Guillaume, Observatoire de Meudon, FRANCE [email protected] Pirronello Valerio, Universita' di Catania Catania - ITALY [email protected] Puy Denis, Institute of Theoretical Physics Zurich -SWITZERLAND [email protected] Ramsay Howat Suzanne, Royal Observatory Edinburgh - UK [email protected] Reach William, Caltech Pasadena - USA [email protected] Rho Jeonghee, Caltech Pasadena - USA [email protected] Richter Philipp, Sternwarte, Bonn - GERMANY [email protected] Rosenthal Dirk, Max-Planck-Institut Garching- GERMANY [email protected] Rostas Frangois, Observatoire de Paris-Meudon, Meudon - FRANCE [email protected] Roueff Evelyne, Observatoire de Paris Meudon - FRANCE [email protected] Schaefer Joachim, MPI Garching- GERMANY [email protected] Schermann Catherine, DIAM, Paris 6, Paris - FRANCE [email protected] Shchekinov Yuri, Rostov State University Rostov on Don - RUSSIA yus@rsussl. rnd. runnet. ru Sidis Victor, LCAM Orsay - FRANCE [email protected] Snow Theodore, University of Colorado Boulder, CO - USA [email protected] Sorokin Peter, IBM Research Division Yorktown Heights - USA [email protected] Spielfledel Annie, Observatoire de Meudon - FRANCE [email protected] Szczerba Ryszard, N. Copernicus Astr. Center Torun - POLAND

Participant List

xvii

szczerba@ncac. torun.pl Talbi Dahbia, ENS Paris - FRANCE [email protected] Tappe Achim, Onsala Space Observatory Onsala-SWEDEN [email protected] Tchang-Brillet Lydia, Observatoire Meudon - FRANCE [email protected] Tedds Jonathan, University of Leeds,Leeds - UK [email protected] Tine Stefano, Observatoire Meudon - FRANCE [email protected] Ubachs Wim, Vrije Universiteit Amsterdam - NETHERLANDS [email protected] Usuda Tomonori, Subaru Telescope, NAOJ Hilo -USA [email protected] Van Den Ancker Mario, Astronomical Inst. Amsterdam NETHERLANDS [email protected] Van Der Werf Paul, Leiden Observatory Leiden - NETHERLANDS pvdwerf@strw. leidenuniv. nl Vannier Laurence, Observatoire de Meudon, Meudon - FRANCE laurence. [email protected] Verstraete Laurent, I.A.S. Orsay - FRANCE [email protected] Vidal-Madjar Alfred, IAP Paris - FRANCE [email protected] Vidali Gianfranco, Syracuse University Syracuse - USA [email protected] Wesselius Paul, SRON, Groningen - NETHERLANDS [email protected] Wilgenbus David, Observatoire de Paris - FRANCE [email protected] Williams David, University College London - UK [email protected] Wright Christopher, Univ. College, ADFA, UNSW Canberra AUSTRALIA [email protected]

XVU1

Conference Photograph

Conference Photograph

Conference Poster

xix

\\i in Space l \ l \ Paris, I'tancv, 28 Sep. - I Oct. IW9

Scientific Organizing ('oinwittcc I'. l!titi>ltlt

/•.

1 and J = 2 —> 0. The much larger values of the rate coefficients for HD imply less sensitivity to the remaining uncertainties in the interaction potential and to the form of the vibrational eigenfunctions. Flower and Roueff (1999c) have extended the collision calculations for the systems HD - H and HD - H2 to excited vibrational states of HD, including levels v < 2, J < 9. Roueff and Zeippen (1999b) have studied HD - He, including levels of HD up to (v, J) — (3, 3). Thus, the data relating to the collisional excitation of HD are approaching a level of completeness similar to those of H2.

3. Cooling functions For convenience in applications, we have fitted the dependence of the rate coefficients, q(T), on the kinetic temperature, T, to the functional form log [q(T) cm3 s"1] = a + b/t + c/t2 3 where t = 10~ T (K) + St and a, 6, c are transition- dependent constants; St is also a constant, which prevents divergence of the fit at low temperatures. St depends on the collision system (e.g. HD - H) but is independent of the transition. Knowing the rate coefficients, spontaneous radiative transition probabilities, and the spectroscopic values of the energy levels, the level populations (of H2 and HD) may be computed, in steady state, for given values of the total density, nn = n(H) + 2n(H2), kinetic temperature, T (K), atomic to molecular hydrogen density ratio, n(H)/n(H 2 ), and ortho:para density ratio, n(ortho-H2)/n(para-H2). The rate of cooling per H2 or HD molecule, the cooling function, is then given by w{x) =

7Jx~) ^{Ei" Ej)niA(i ~> j)

D. Flower et al.: The cooling of astwphysical media

27

60

o

log(T(K)) 1. The cooling function, W(E2) (in units of 10~7 W), calculated for 1 < nH < 10* cm" 3 , an ortho:para-H2 density ratio of 1, and a H/H2 abundance ratio of 1.

FIGURE

where X = H2 or HD, E{ is the energy of level i, relative to the ground state, n,- is the density of population in this level, and A(i —> j) is a spontaneous radiative transition probability; W(X) is expressed in units of erg s" 1 (10~ 7 W). The H2 cooling function, W(H2), has been calculated (Le Bourlot et al. 1999) for values of riH, T, n(H)/n(H2), and n(ortho-H 2 )/n(para-H2), within the ranges 1 < nH < 108 c m " 3 100 < T < 104 K 8 10- < 7i(H)/n(H 2 ) < 106 0.1 < n(ortho)/n(para) < 3 and taking n(He)/tiH = 0.10. W(H2) is obtained by numerical interpolation within a data set, le-cube; together with this data set, the interpolation program, interp.f, is provided on the website (http://ccp7.dur.ac.uk). In the case of HD, the cooling function, W(HD), has been computed (Flower et al. 2000) for the following ranges of the parameters l