stellar astrophysics, two questions.
An Introduction to the Theory of Stellar Structure and Evolution An Introduction to the Theory of Stellar Structure and Evolution Second Edition Using fundamental physics, the theory of stellar structure and evolution can predict how stars are born, how their complex internal structure changes, what nuclear fuel they burn, and their ultimate fate. This textbook is a stimulating introduction for students of astronomy, physics and applied mathematics, taking a course on the physics of stars. It uniquely emphasizes the basic physical principles governing stellar structure and evolution. This second edition contains two new chapters on mass loss from stars and interacting binary stars, and new exercises. Clear and methodical, it explains the processes in simple terms, while maintaining mathematical rigour. Starting from general principles, this textbook leads students step-by-step to a global, comprehensive understanding of the subject. Fifty exercises and full solutions allow students to test their understanding. No prior knowledge of astronomy is required, and only a basic background in undergraduate physics and mathematics is necessary. Dina Prialnik is a Professor of Planetary Physics at Tel Aviv University. Her research interests lie in stellar evolution; the structure and evolution of cataclysmic variables; comet nuclei and other small solar system bodies; and the evolution of planets. An Introduction to the Theory of Stellar Structure and Evolution Second Edition Dina Prialnik Tel Aviv University University Printing House, Cambridge CB2 8BS, United Kingdom Published in the United States of America by Cambridge University Press, New York Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org http://www.cambridge.org Information on this title: www.cambridge.org/9780521866040 First edition © Cambridge University Press 2000 Second edition © D. Prialnik 2010 This publication 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 D. Prialnik. First published 2000 Reprinted 2004, 2005, 2006, 2007, 2008 Second edition printed 2010 Reprinted 2010 (with corrections) 5th printing 2013 Printed by CPI Group (UK) Ltd, Croydon CR0 4YY A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Prialnik, Dina. An introduction to the theory of stellar structure and evolution / Dina Prialnik. – 2nd ed. p. cm. ISBN 978-0-521-86604-0 (hardback) 1. Stars – Structure. 2. Stars – Evolution. I. Title. QB808.P75 2009 523.8′8 – dc22 2009034267 ISBN 978 0 521 86604 0 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party Internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To my son Contents Preface to the second edition Preface to the first edition http://www.cambridge.org/9780521866040 1 Observational background and basic assumptions 1.1 What is a star? 1.2 What can we learn from observations? 1.3 Basic assumptions 1.4 The H–R diagram: a tool for testing stellar evolution 2 The equations of stellar evolution 2.1 Local thermodynamic equilibrium 2.2 The energy equation 2.3 The equation of motion 2.4 The virial theorem 2.5 The total energy of a star 2.6 The equations governing composition changes 2.7 The set of evolution equations 2.8 The characteristic timescales of stellar evolution 3 Elementary physics of gas and radiation in stellar interiors 3.1 The equation of state 3.2 The ion pressure 3.3 The electron pressure 3.4 The radiation pressure 3.5 The internal energy of gas and radiation 3.6 The adiabatic exponent 3.7 Radiative transfer 4 Nuclear processes that take place in stars 4.1 The binding energy of the atomic nucleus 4.2 Nuclear reaction rates 4.3 Hydrogen burning I: the p − p chain 4.4 Hydrogen burning II: the CNO bi-cycle 4.5 Helium burning: the triple-α reaction 4.6 Carbon and oxygen burning 4.7 Silicon burning: nuclear statistical equilibrium 4.8 Creation of heavy elements: the s- and r-processes 4.9 Pair production 4.10 Iron photodisintegration 5 Equilibrium stellar configurations – simple models 5.1 The stellar structure equations 5.2 What is a simple stellar model? 5.3 Polytropic models 5.4 The Chandrasekhar mass 5.5 The Eddington luminosity 5.6 The standard model 5.7 The point-source model 6 The stability of stars 6.1 Secular thermal stability 6.2 Cases of thermal instability 6.3 Dynamical stability 6.4 Cases of dynamical instability 6.5 Convection 6.6 Cases of convective instability 6.7 Conclusion 7 The evolution of stars – a schematic picture 7.1 Characterization of the (log T, log ρ) plane 7.2 The evolutionary path of the central point of a star in the (log T, log ρ) plane 7.3 The evolution of a star, as viewed from its centre 7.4 The theory of the main sequence 7.5 Outline of the structure of stars in late evolutionary stages 7.6 Shortcomings of the simple stellar evolution picture 8 Mass loss from stars 8.1 Observational evidence of mass loss 8.2 The mass loss equations 8.3 Solutions to the wind equations – the isothermal case 8.4 Mass loss estimates 8.5 Empirical solutions 9 The evolution of stars – a detailed picture 9.1 The Hayashi zone and the pre-main-sequence phase 9.2 The main-sequence phase 9.3 Solar neutrinos 9.4 The red giant phase 9.5 Helium burning in the core 9.6 Thermal pulses and the asymptotic giant branch 9.7 The superwind and the planetary nebula phase 9.8 White dwarfs: the final state of nonmassive stars 9.9 The evolution of massive stars 9.10 The H–R diagram – Epilogue 10 Exotic stars: supernovae, pulsars and black holes 10.1 What is a supernova? 10.2 Iron-disintegration supernovae: Type II – the fate of massive stars 10.3 Nucleosynthesis during Type II supernova explosions 10.4 Supernova progenies: neutron stars – pulsars 10.5 Carbon-detonation supernovae: Type Ia 10.6 Pair-production supernovae and black holes – the fate of very massive stars 11 Interacting binary stars 11.1 What is a binary star? 11.2 The general effects of stellar binarity 11.3 The mechanics of mass transfer between stars 11.4 Conservative mass transfer 11.5 Accretion discs 11.6 Cataclysmic phenomena: Nova outbursts 12 The stellar life cycle 12.1 The interstellar medium 12.2 Star formation 12.3 Stars, brown dwarfs and planets 12.4 The initial mass function 12.5 The global stellar evolution cycle Appendix A – The equation of radiative transfer Appendix B – The equation of state for degenerate electrons Appendix C – Solutions to all the exercises Appendix D – Physical and astronomical constants and conversion factors Bibliography Index Preface to the second edition It is now a decade since the publication of the first edition of this book. Despite the large number of research papers devoted to the subject during this period of time, the basic principles and their applications that are addressed in the book remain valid and hence the original text has been mostly left unchanged. And yet a major development did occur soon after the book first appeared in print: the ‘solar neutrino problem’ that had puzzled physicists and astrophysicists for almost four decades finally found its solution, which indeed necessitated new physics. However, the new physics belongs to the theory of elementary particles, which must now account for neutrino masses, rather than to the theory of stars. Also worth mentioning is a major recent discovery that finally provides support to the theory proposed about four decades ago regarding the end of very massive stars in powerful supernova explosions triggered by pair-production instability: SN2006gy, the first observed candidate for such a mechanism. Thus the section on solar neutrinos is now complete and that on supernovae expanded. Stellar evolution calculations have made great progress in recent years, following the rapid development of computational means: increasingly faster CPUs and greater memory volumes. Nevertheless, I have made use of new results only when they provide better illustration for points raised in text. For the most part, old results are still valid and this long-term validity is worth emphasizing; the theory of stellar structure and evolution, with all its complexity, is a well-established physical theory. The text was expanded to include two new chapters on topics that were not addressed in the first edition: mass loss and interacting binary stars. Both are complicated subjects, some aspects of which are still not well understood, similarly to star formation. Although this may justify their exclusion from a basic textbook on stellar structure and evolution theory, an exposition of the theory would not be complete without some reference to them. Each one deserves a full textbook by itself, and in fact books have been devoted to each in the last decade, not to mention older texts dealing with these subjects. In the new chapters I have touched upon them briefly enough to adapt the treatment to the general level and scope of this book, but also in sufficient detail to arouse interest and enable a basic understanding of where the problems lie. I have also added an appendix that explains and develops more rigorously the concept of degeneracy pressure in an attempt to dispel some confusion related to the applicability of complete degeneracy, which was the only form developed in the early edition: is the omission of temperature an assumption or a justified result? Another, minor, addition is a concise discussion of the mixing-length treatment of convection. Finally, I have included a few more exercises, which are mostly of the same nature and serve the same purpose as the older ones: to elucidate points made in the text or provide additional information. While I am still grateful to those who have helped, supported and encouraged me during the writing of the original version of this book, it is with new pleasure and gratitude that I thank those who have commented on it since, who have used the book in their classes and have helped to improve it. Among them are Nuria Calvet, Aparna Venkatesan, Allan Walstad, Werner Däppen, Nicolay Samus, Bill Herbst, Phil Armitage, Silvia Rossi and Barry Davids, and my long-time friends Mike Shara, Mario Livio and Oded Regev. Special thanks are due to Robert Smith for pointing out a number of inaccuracies and for making important suggestions. Preface