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Astrophysical Lasers This page intentionally left blank Astrophysical Lasers Vladilen LETOKHOV Institute of Spectroscopy Russian Academy of Sciences Sveneric JOHANSSON Institute of Astronomy Lund University 1 3 Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York c Vladilen Letokhov and Sveneric Johansson 2009 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First Published 2009 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn, Norfolk ISBN 978–0–19–954827–9 (Hbk) 10987654321 Bengt EDLEN´ We dedicate this volume to the late Professor Bengt Edl´en(1906–1993) to the memory of his 100th birthday. To the astronomical community Edl´enis best known for this explanation of the strong emission lines in the solar corona spectrum. Edl´enstarted his scientific career in Siegbahn’s spectroscopy laboratory in Uppsala. Siegbahn had received the Nobel Prize for physics in 1924 for his studies of X-ray spec- tra, and Edl´engot the task of bridging the wavelength gap between X-ray and optical vi Dedication spectroscopy. His first important results came as early as 1929, when he published experimental results for He-like ionic systems, i.e. Li+,Be2+,B3+ etc., which at that time had become a target for the application of quantum mechanics. Edl´en’sdoctoral thesis from 1934 contains extraordinarily extensive and careful analyses of the spectra and energy levels of various ions of the eight lightest elements (H to O). The famous astrophysicist H. N. Russel evaluated it as follows: “It is su- perb work and so complete that it should be the definitive treatise on the subject. I need not emphasize how great its astrophysical value has been and will continue to be”. Still today this thesis is the only source for experimental wavelengths for many fundamental resonance lines in astrophysically important ions. In fact, Edl´en pointed out a small difference between measured and calculated energies in hydrogen- like ions, and this was the first detection of the Lamb shift, later predicted by quantum electro dynamics. Edl´enhad a great interest in astronomy and astrophysics. His pioneering work on spectra of ionized carbon, nitrogen and oxygen led to extensive line identifications in spectra of Wolf–Rayet stars, and the early (1933) division of these stars into two parallel sequences: WC(C-rich) and WN (N-rich). The optical lines from these ionized spectra originated from higher quantum states, as the resonance lines appear in the far-UV region. From the low energy levels of Fe VII, which had been determined in an experimental analysis, Edl´enderived wavelengths for forbidden transitions, applying the same technique as Bowen had used for O2+ about 10 years earlier. Edl´enand Bowen published in 1939 a joint paper on the identification of forbidden Fe6+ lines in Nova Pictoris. This was at that time the highest ionization state found in any astrophysical object. Thus, the spectral lines from highly ionized atoms that could be detected in the optical region were either allowed transitions between high quantum states or forbid- den transitions between low quantum states. This fact came to be the solution behind Edl´en’sidentification of the strong emission lines, observed during a solar eclipse in 1969. The well-known astronomer Harlow Shapley stated in 1933 that “the coronal lines are our most conspicuous riddle in astronomical spectroscopy”. From extrapo- lations of his own laboratory measurements Edl´enconcluded in 1942 that the lines originated from forbidden transitions in very high ionization stages of Ar, Ca, Fe and Ni. The strongest line, the green coronal line at 5303 A,˚ is emitted by Fe13+. The impressive fact about the identifications of the coronal lines is that forbidden tran- sitions do not appear in laboratory sources, and that the conclusion was based on extrapolations from measurements in lighter elements. The intriguing fact was that the temperature in the solar corona must be about 2 million degrees, which seemed unlikely in comparison to the 6000 degrees on the solar surface. Edl´enwas a person of high integrity, free from tactical and political considerations about scientific matters. He was very accurate and had high demands on quality. Edl´en was a member of many academies and served on the Nobel Committee for Physics during 1961–1976. He received the Gold Medal of the Royal Astronomical Society in London, which at that time was regarded as the highest sign of recognition in astronomy. Dedication vii Edl´en’scontribution to astrophysics is to a great extent associated with identifica- tions of prominent lines in spectra of various astrophysical objects. Spectral lines are the outstanding source of detailed information about these objects. They also offer a great challenge. One of the authors (S. J.) had the privilege of being a PhD student in his group, and much material in this volume comes from a major research project on iron, suggested by Edl´en. This page intentionally left blank Preface This book is based on the early research by V. L. in 1972, which was continued after almost 30 years together with S. J., when V. L. was the Tage Erlander Professor at Lund University in 2000 and later through support by grants from the Royal Academy of Sciences, the Nobel Foundation and the Wenner-Gren Foundations. V. L. is grateful to the Lund Observatory for hospitality, and to the Russian Foundation for Basic Research for support. The research project on astrophysical lasers was also supported by a grant (S. J.) from the Swedish National Space Board. The Royal Physiographic Society, Lund, kindly supported the final preparation of this book. The Oxford University Press and particularly Dr S¨onke Adlung were so kind to sup- port the idea of publishing this book. We would like to thank Professor Vladimir Mino- gin for reading a few Chapters. Finally we would like to thank Mrs Ol’ga Tatyanchenko for her highly qualified and fast processing of our manuscript, Mrs Alla Makarova and Mrs Elena Nikolaeva, librarians at the Institute of Spectroscopy, for their valuable help and Mr Alexandr Korniushkin for graphic work. Lund, Sweden, 2008 Troitsk, Russia, 2008 This page intentionally left blank Contents 1 Introduction 1 1.1 Historical remark 2 1.2 From astrophysical masers to astrophysical lasers 4 1.3 Amplification conditions for an atomic ensemble 6 1.4 Structure of the book 10 2 Elements of radiative quantum transitions 12 2.1 Spontaneous and stimulated emission 12 2.1.1 Thermodynamical equilibrium – Einstein coefficients A and B 12 2.1.2 Semiclassical approach 16 2.1.3 Quantum theory 18 2.2 Broadening of spectral lines 22 2.2.1 Radiative (natural) broadening 22 2.2.2 Collisional broadening 23 2.2.3 Doppler (nonhomogeneous) broadening 25 2.3 Resonance scattering of radiation 27 2.3.1 Coherence of scattering in the atomic frame 27 2.3.2 Doppler redistribution of frequency 29 2.3.3 Number of resonance scattering events – escaping of photons 30 3 Elements of atomic spectroscopy 36 3.1 Basic concepts 36 3.1.1 Structure and interactions 36 3.1.2 LS coupling 37 3.1.3 Terms, levels, and transitions in LS coupling – equivalent electrons 37 3.1.4 Complex spectra 38 3.1.5 Metastable states, pseudo-metastable states – forbidden lines 39 3.2 One-electron systems 39 3.2.1 One-electron atoms and ions 39 3.2.2 Alkali and alkali-like spectra 40 3.3 Two-electron systems 42 3.3.1 Alkaline earth elements and iso-electronic spectra 42 3.3.2 Elements with two electrons or two holes in the p-shell 43 3.4 Complex spectra – with emphasis on Fe II 45 xii Contents 3.4.1 Definition and properties of complex spectra 45 3.4.2 Astrophysical importance of Fe II 45 3.4.3 The atomic structure of Fe II 46 4 Elementary excitation processes in rarefied plasmas 51 4.1 Photoionization of atoms 51 4.2 Recombination 53 4.3 Electron excitation and ionization 55 4.4 Total and local thermodynamic equilibrium (TE and LTE) in plasma 55 4.5 Non-LTE astrophysical media 58 4.6 Non-LTE: photoselective excitation 59 5 Astrophysical rarefied gas/plasma 62 5.1 Low-density gas nearby a hot star – Str¨omgrensphere