Evolution of Stars and Stellar Populations
Evolution of Stars and Stellar Populations Maurizio Salaris and Santi Cassisi © 2005 John Wiley & Sons, Ltd ISBN: 0-470-09219-X
Evolution of Stars and Stellar Populations Maurizio Salaris Astrophysics Research Institute, Liverpool John Moores University, UK
Santi Cassisi INAF-Astronomical Observatory of Collurania, Teramo, Italy
Copyright © 2005
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To Suzanne and my parents To all the people who really loved me
Contents
Preface
xi
1 Stars and the Universe 1.1 Setting the stage 1.2 Cosmic kinematics 1.2.1 Cosmological redshifts and distances 1.3 Cosmic dynamics 1.3.1 Histories of Rt 1.4 Particle- and nucleosynthesis 1.5 CMB fluctuations and structure formation 1.6 Cosmological parameters 1.7 The inflationary paradigm 1.8 The role of stellar evolution
1 1 5 8 13 14 17 24 25 26 28
2 Equation of State of the Stellar Matter 2.1 Physical conditions of the stellar matter 2.1.1 Fully ionized perfect gas 2.1.2 Electron degeneracy 2.1.3 Ionization 2.1.4 Additional effects
31 31 35 38 41 44
3 Equations of Stellar Structure 3.1 Basic assumptions 3.1.1 Continuity of mass 3.1.2 Hydrostatic equilibrium 3.1.3 Conservation of energy 3.1.4 Energy transport 3.1.5 The opacity of stellar matter 3.1.6 Energy generation coefficient 3.1.7 Evolution of chemical element abundances 3.1.8 Virial theorem 3.1.9 Virial theorem and electron degeneracy 3.2 Method of solution of the stellar structure equations 3.2.1 Sensitivity of the solution to the boundary conditions 3.2.2 More complicated cases
49 49 50 50 52 52 66 68 83 86 89 90 97 98
viii
CONTENTS
3.3 Non-standard physical processes 3.3.1 Atomic diffusion and radiative levitation 3.3.2 Rotation and rotational mixings 4 Star 4.1 4.2 4.3
Formation and Early Evolution Overall picture of stellar evolution Star formation Evolution along the Hayashi track 4.3.1 Basic properties of homogeneous, fully convective stars 4.3.2 Evolution until hydrogen burning ignition
99 100 102 105 105 106 110 110 114
5 The Hydrogen Burning Phase 5.1 Overview 5.2 The nuclear reactions 5.2.1 The p–p chain 5.2.2 The CNO cycle 5.2.3 The secondary elements: the case of 2 H and 3 He 5.3 The central H-burning phase in low main sequence (LMS) stars 5.3.1 The Sun 5.4 The central H-burning phase in upper main sequence (UMS) stars 5.5 The dependence of MS tracks on chemical composition and convection efficiency 5.6 Very low-mass stars 5.7 The mass–luminosity relation 5.8 The Schönberg–Chandrasekhar limit 5.9 Post-MS evolution 5.9.1 Intermediate-mass and massive stars 5.9.2 Low-mass stars 5.9.3 The helium flash 5.10 Dependence of the main RGB features on physical and chemical parameters 5.10.1 The location of the RGB in the H–R diagram 5.10.2 The RGB bump luminosity 5.10.3 The luminosity of the tip of the RGB 5.11 Evolutionary properties of very metal-poor stars
117 117 118 118 119 121 123 125 128
6 The 6.1 6.2 6.3
161 161 161 163 165 167 167
Helium Burning Phase Introduction The nuclear reactions The zero age horizontal branch (ZAHB) 6.3.1 The dependence of the ZAHB on various physical parameters 6.4 The core He-burning phase in low-mass stars 6.4.1 Mixing processes
133 136 138 140 141 141 142 148 149 150 151 152 155
CONTENTS
ix
6.5 The central He-burning phase in more massive stars 6.5.1 The dependence of the blue loop on various physical parameters 6.6 Pulsational properties of core He-burning stars 6.6.1 The RR Lyrae variables 6.6.2 The classical Cepheid variables
173 175 179 181 183
7 The Advanced Evolutionary Phases 7.1 Introduction 7.2 The asymptotic giant branch (AGB) 7.2.1 The thermally pulsing phase 7.2.2 On the production of s-elements 7.2.3 The termination of the AGB evolutionary phase 7.3 The Chandrasekhar limit and the evolution of stars with large CO cores 7.4 Carbon–oxygen white dwarfs 7.4.1 Crystallization 7.4.2 The envelope 7.4.3 Detailed WD cooling laws 7.4.4 WDs with other chemical stratifications 7.5 The advanced evolutionary stages of massive stars 7.5.1 The carbon-burning stage 7.5.2 The neon-burning stage 7.5.3 The oxygen-burning stage 7.5.4 The silicon-burning stage 7.5.5 The collapse of the core and the final explosion 7.6 Type Ia supernovae 7.6.1 The Type Ia supernova progenitors 7.6.2 The explosion mechanisms 7.6.3 The light curves of Type Ia supernovae and their use as distance indicators 7.7 Neutron stars 7.8 Black holes
187 187 187 189 194 195 198 199 206 210 212 213 214 217 219 220 221 222 224 225 229
8 From Theory to Observations 8.1 Spectroscopic notation of the stellar chemical composition 8.2 From stellar models to observed spectra and magnitudes 8.2.1 Theoretical versus empirical spectra 8.3 The effect of interstellar extinction 8.4 K-correction for high-redshift objects 8.5 Some general comments about colour–magnitude diagrams (CMDs)
239 239 241 248 250 253 254
9 Simple Stellar Populations 9.1 Theoretical isochrones 9.2 Old simple stellar populations (SSPs) 9.2.1 Properties of isochrones for old ages 9.2.2 Age estimates
259 259 264 264 268
230 233 236
CONTENTS
x
9.2.3 Metallicity and reddening estimates 9.2.4 Determination of the initial helium abundance 9.2.5 Determination of the initial lithium abundance 9.2.6 Distance determination techniques 9.2.7 Luminosity functions and estimates of the IMF 9.3 Young simple stellar populations 9.3.1 Age estimates 9.3.2 Metallicity and reddening estimates 9.3.3 Distance determination techniques
281 284 287 289 301 304 304 309 310
10 Composite Stellar Populations 10.1 Definition and problems 10.2 Determination of the star formation history (SFH) 10.3 Distance indicators 10.3.1 The planetary nebula luminosity function (PNLF)
315 315 320 327 329
11 Unresolved Stellar Populations 11.1 Simple stellar populations 11.1.1 Integrated colours 11.1.2 Absorption-feature indices 11.2 Composite stellar populations 11.3 Distance to unresolved stellar populations
331 331 334 341 347 347
Appendix I: Constants
351
Appendix II: Selected Web Sites
353
References
357
Index
369
Preface
The theory of stellar evolution is by now well established, after more than half a century of continuous development, and its main predictions confirmed by various empirical tests. As a consequence, we can now use its results with some confidence, and obtain vital information about the structure and evolution of the universe from the analysis of the stellar components of local and high redshift galaxies. A wide range of techniques developed in the last decades make use of stellar evolution models, and are routinely used to estimate distances, ages, star formation histories and the chemical evolution of galaxies; obtaining this kind of information is, in turn, a necessary first step to address fundamental cosmological problems like the dynamical status and structure of the universe, the galaxy formation and evolution mechanisms. Due to their relevance, these methods rooted in stellar evolution should be part of the scientific background of any graduate and undergraduate astronomy and astrophysics student, as well as researchers interested not only in stellar modeling, but also in galaxy and cosmology studies. In this respect, we believe there is a gap in the existing literature at the level of senior undergraduate and graduate textbooks that needs to be filled. A number of good books devoted to the theory of stellar evolution do exist, and a few discussions about the application of stellar models to cosmological problems are scattered in the literature (especially the methods to determine distances and ages of globular clusters). However, an organic and self-contained presentation of both topics, that is also able to highlight their intimate connections, is still lacking. As an example, the so-called ‘stellar population synthesis techniques’ – a fundamental tool for studying the properties of galaxies – are hardly discussed in any existing stellar evolution textbook. The main aim of this book is to fill this gap. It is based on the experience of one of us (MS) in developing and teaching a third year undergraduate course in advanced stellar astrophysics and on our joint scientific research of the last 15 years. We present, in a homogeneous and self-contained way, first the theory of stellar evolution, and then the related techniques that are widely applied by researchers to estimate cosmological parameters and study the evolution of galaxies. The first chapter introduces the standard Big Bang cosmology and highlights the role played by stars within the framework of our currently accepted cosmology. The two following chapters introduce the basic physics needed to understand how stars
xii
PREFACE
work, the set of differential equations that describes the structure and evolution of stars, and the numerical techniques to solve them. Chapters 4 to 7 present both a qualitative and quantitative picture of the life cycle of single stars (although we give some basic information about the evolution of interacting binary systems when dealing with Type Ia supernovae progenitors) from their formation to the final stages. The emphasis in our presentation is placed on those properties that are needed to understand and apply the methods discussed in the rest of the book, that is, the evolution with time of the photometric and chemical properties (i.e. evolution of effective temperatures, luminosities, surface chemical abundances) of stars, as a function of their initial mass and chemical composition. The next chapter describes the steps (often missing in stellar evolution books) necessary to transform the results from theoretical models into observable properties. Finally, Chapters 9 to 11 present an extended range of methods that can be applied to different types of stellar populations – both resolved and unresolved – to estimate their distances, ages, star formation histories and chemical evolution with time, building on the theory of stellar evolution we have presented in the previous chapters. We have included a number of references which are not meant to be a totally comprehensive list, but should be intended only as a first guide through the vast array of publications on the subject. This book has greatly benefited from the help of a large number of friends and colleagues. First of all, special thanks go to David Hyder (Liverpool John Moores University) and Lucio Primo Pacinelli (Astronomical Observatory of Collurania) for their invaluable help in producing many of the figures for this book. Katrina Exter is warmly thanked for her careful editing of many chapters; Antonio Aparicio, Giuseppe Bono, Daniel Brown, Vittorio Castellani, Carme Gallart, Alan Irwin, Marco Limongi, Marcella Marconi and Adriano Pietrinferni are acknowledged for many discussions, for having read and commented on various chapters of this book and helped with some of the figures. We are also indebted to Leo Girardi, Phil James, Kevin Krisciunas, Bruno Leibundgut, Luciano Piersanti and Oscar Straniero for additional figures included in the book. Sue Percival and Phil James are warmly acknowledged for their encouragement during the preparation of the manuscript, Suzanne Amin and Anna Piersimoni for their endless patience during all these months. We are also deeply indebted to Achim Weiss and the Max Planck Institut für Astrophysik (MS), Antonio Aparicio and the Instituto de Astrofisica de Canarias (SC) for their invitation and hospitality. During our stays at those institutes a substantial part of the manuscript was prepared. Finally, we wish to send a heartfelt thank-you to all colleagues with whom we have worked in the course of these wonderful years of fruitful scientific research. Liverpool Teramo March 2005
Maurizio Salaris Santi Cassisi
