Maser Sources in Astrophysics Malcolm Gray Frontmatter More Information

Cambridge University Press 978-0-521-87980-4 - Maser Sources in Astrophysics Malcolm Gray Frontmatter More information

MASER SOURCES IN ASTROPHYSICS

Masers are observed at a range of scales – from comets to star-forming clouds and galactic nuclei – and have many astrophysical applications, for example, measuring cosmological distances. Written for postgraduate students and for professional researchers in molecular astrophysics, this volume is an up-to-date survey of the theory and observations of astrophysical maser sources and their use as astronomical tools. The book summarizes the history of the discovery of various maser molecules and lines, and discusses maser observations on various scales. The theory is discussed in detail, including the quantum-mechanical response of the molecules, before being linked to more general radiation transfer. A discussion of spectral-line radio astronomy techniques shows how maser observations can be applied more generally to radio astronomy. The book introduces new and projected instruments, including ALMA and SKA. Additional topics address the radiation statistics of astrophysical masers and numerical methods of analysis.

Malcolm Gray is a Senior Lecturer at the Jodrell Bank Centre for Astrophysics at the University of Manchester. Astrophysical masers have been a major theme in Dr Gray’s research career, but he has also worked in the ﬁelds of astrophysical dust, the calculation of collision cross-sections for astrophysical molecules and radiation transfer.

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MASER SOURCES IN ASTROPHYSICS

MALCOLM GRAY Jodrell Bank Centre for Astrophysics, the University of Manchester

cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao˜ Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York

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C M. Gray 2012

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First published 2012

Printed in the United Kingdom at the University Press, Cambridge

A catalogue record for this publication is available from the British Library

Library of Congress Cataloguing in Publication data Gray, Malcolm, 1962– Maser sources in astrophysics / Malcolm Gray, Jodrell Bank Centre for Astrophysics, the University of Manchester. pages cm. – (Cambridge astrophysics series ; 50) Includes bibliographical references and index. ISBN 978-0-521-87980-4 (hardback) 1. Astronomical masers. 2. Radio astronomy. 3. Microwave measurements. I. Title. QB479.4.G73 2012 523.01875344 – dc23 2012007505

ISBN 978-0-521-87980-4 Hardback

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Contents

Preface page ix

1 Introduction 1 1.1 Masers and lasers 1 1.2 Atoms and molecules 2 1.3 Electromagnetic radiation 5 1.4 Light and molecules interacting 17 1.5 Concepts of equilibrium 28

2 Discovery 33 2.1 Mysterium 33 2.2 Raining in Orion 36 2.3 Searching for X-ogen: SiO masers 41 2.4 Methanol 50 2.5 Formaldehyde 53 2.6 Ammonia 56 2.7 Hydrogen cyanide (HCN) 57 2.8 Other masers 58 2.9 A case study: W3(OH) 62

3 Basic theory 76 3.1 Non-LTE physics 76 3.2 Inversions 83 3.3 Formal integration of the source function 84 3.4 Radiation transfer 85 3.5 Geometry 89 3.6 Standard maser equations 91 3.7 Beaming and geometry 102 3.8 An introduction to polarization 108

4 Observations of masers 113 4.1 Introduction 113 4.2 Criteria of merit for radio telescopes 117 v

vi Contents

4.3 Single-dish observations 126 4.4 Interferometry 142 4.5 Polarimetry issues 153

5 Maser molecules 156 5.1 Molecular spectroscopy 156 5.2 Collisional rate coefﬁcients 157 5.3 Silicon monoxide (SiO) 158 5.4 Other simple rotors 165 5.5 Hydroxyl (OH) 165 5.6 Hydrogen cyanide (HCN) 170 5.7 Ammonia (NH3) 173 5.8 Water (H2O) 178 5.9 Formaldehyde (H2CO) 182 5.10 Methanol (CH3OH) 182 5.11 Other maser species 185

6 Environments of masers 186 6.1 Galactic star-forming regions 186 6.2 Evolved stars 218 6.3 Planetary nebulae and pPN 230 6.4 Megamasers 232 6.5 Supernova remnants 235 6.6 Comets 236 6.7 Hot stars 238 6.8 Planetary atmospheres 239

7 Advanced theory 241 7.1 Introduction to semi-classical theory 241 7.2 Multi-level systems 267 7.3 Polarization 270 7.4 Beaming 281 7.5 Moving media 286 7.6 Free-electron masers 289

8 Computer modelling 294 8.1 Large velocity gradient approximation 294 8.2 Accelerated lambda iteration 297 8.3 Direct non-linear methods 310 8.4 Semi-classical maser saturation 316 8.5 Convergence accelerators 321 8.6 Population tracing 325

9 Masers as diagnostics 327 9.1 Magnetic ﬁelds 327 9.2 Dynamics: measuring masses 329

Contents vii

9.3 Measuring distances with masers 332 9.4 Masers have their day in cosmology 336 9.5 Variation of ‘constants’? 340 9.6 Masers as probes of turbulence 347 9.7 The inverse problem 351

10 Future prospects 352 10.1 EVLA 352 10.2 e-MERLIN 353 10.3 ALMA 356 10.4 SKA 358 10.5 VERA 360 10.6 Other new/upgraded telescopes 360

Appendix A: Boltzmann’s formula 362 Appendix B: Vector identities 365 Appendix C: Dirac delta-function 368 Appendix D: Change of variables in integration 369 Appendix E: Coordinate systems 371 Appendix F: Lagrange inversion theorem 376 Appendix G: Local standard of rest 377 Appendix H: Stochastic processes 378 Appendix I: Fourier transforms 382 Appendix J: Matrices 385 Appendix K: The centre of mass frame 387 Appendix L: Quantum-mechanical operators 389

References 392 Index 415

Preface

The study of astrophysical masers is a very young branch of science, with a history extending back no further than the mid 1960s. Even so, the subject has advanced rapidly to the point where masers can be used as tools to investigate problems as diverse as the chemistry of comets and the measurement of the Hubble constant. A recent (2007) international conference on astrophysical masers had over 120 delegates: hopefully this shows that the subject is as attractive to young astronomers today as it was to the pioneers who ﬁrst detected these incredibly bright, and at the time mysterious, radio sources just 45 years ago. The observational side of astrophysical maser research has always been a branch of radio astronomy, and developments in radio techniques continue to govern advances in the knowledge of masers. The inclusion of Chapter 4 is intended to provide the reader with sufﬁcient knowledge of radio techniques to understand modern observing procedures. As most astrophysical masers originate from molecules, there is also a chapter (Chapter 5) devoted to molecular spectroscopy.

Intended readership The book is aimed at senior undergraduates, postgraduate students and research workers in astronomy, but the ﬁrst two chapters can be easily read by the non-specialist, as they contain little mathematics and technical detail. The same is true of Chapter 6, which takes a modern view of the main astrophysical environments in which masers form. Chapters 9 and 10, though more specialized, are also accessible to the reader who does not wish to delve into too much mathematical detail. Chapter 3 provides sufﬁcient information to understand astrophysical masers at a fairly basic level, whilst Chapter 7 offers a more accurate description, and both these theory-based chapters unavoidably contain a good deal of mathematics.

Previous works This is certainly not the ﬁrst book on astrophysical masers. There are two previous works: one dates from the early days of maser research, little more than a decade after the discovery of astrophysical masers (Cook, 1977); the other was written when the ﬁeld was considerably more mature (Elitzur, 1992a). Several shorter review articles on the subject have also appeared, for example Cohen (1989), Elitzur (1992b) and Gray (1999).

x Preface

Three international conferences on astrophysical masers have also taken place, all with published proceedings. These were, in chronological order, the Arlington, Virginia, conference of 1992 (Clegg and Nedoluha, 1993), the Rio de Janeiro conference of 2001 (Migenes and Reid, 2002) and the Alice Springs conference of 2007 (Chapman and Baan, 2007). A fourth conference (IAU 287) was held in Stellenbosch, South Africa, in January 2012.

Major developments since 1992 Since the last major textbook on astrophysical masers was written, a number of developments, particularly in observational hardware, have made it timely to write a new book. A new generation of single-dish telescopes has led to the discovery of many new maser lines in the millimetre and sub-millimetre wavelength range. Several important maser surveys have also been completed, giving us improved knowledge of large-scale maser distributions. There has been a signiﬁcant improvement in the capabilities of interferometers. For example, the Very Long Baseline Array (VLBA), comissioned after 1992, is a dedicated interferometer network, operated by the National Radio Astronomy Observatory (NRAO) of the United States. The VLBA has made high-resolution time-series imaging, in full polarization, almost routine. Another important development in interferometry is external phase-referencing, allowing precision astrometry to milliarcsecond scales, and the precise alignment of images taken at different frequencies and different times. Advances in computer technology have supported the observational developments, and have also made possible computational mod- els that are far larger and more complex than at the time the last book went to press. At the time of writing, several existing telescopes worldwide are being signiﬁcantly upgraded, whilst other new instruments are being built. The new developments will generally expand observing bandwidth, increase sensitivity and extend high-resolution interferometer capability to maser lines at higher frequencies.

Acknowledgements The author would like to thank the Manchester Universities Gilbert and Sullivan Society (MUGSS) for preserving his sanity while writing this book. He would like to express his appreciation of the help and advice given by his contacts at Cambridge University Press, Claire Poole, Laura Clark and Megan Waddington, and also to Simon Mitton for the original invitation to write the book. Some of the computations were carried out on the Legion supercomputer at the HiPerSPACE Computing Centre, University College London, which is funded by the UK Science and Technology Facilities Council (STFC).