Evolution of stars and stellar populations

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

Evolution of Stars and

Stellar Populations

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 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester,

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Library of Congress Cataloging in Publication Data

Salaris, Maurizio.

Evolution of stars and stellar populations / Maurizio Salaris, Santi Cassisi.

p. cm.

Includes bibliographical references and index.

ISBN-13 978-0-470-09219-X (cloth : alk. paper) ISBN-10 0-470-09219-X (cloth : alk. paper)

ISBN-13 978-0-470-09220-3 (pbk. : alk. paper) ISBN-10 0-470-09220-3 (pbk. : alk. paper)

1. Stars—Evolution. 2. Stars—Populations. 3. Galaxies—Evolution. I. Cassisi, Santi. II. Title.

QB806.S25 2005

523.8

8—dc22

2005021402

British Library Cataloguing in Publication Data

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

ISBN-13 978-0-470-09219-X (HB) 978-0-470-09220-3 (PB)

ISBN-10 0-470-09219-X (HB) 0-470-09220-3 (PB)

Typeset in 10.5/12.5pt Times by Integra Software Services Pvt. Ltd, Pondicherry, India

Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire

This book is printed on acid-free paper responsibly manufactured from sustainable forestry

in which at least two trees are planted for each one used for paper production.

To Suzanne and my parents

To all the people who really loved me

Contents

Preface xi

1 Stars and the Universe 1

1.1 Setting the stage 1

1.2 Cosmic kinematics 5

1.2.1 Cosmological redshifts and distances 8

1.3 Cosmic dynamics 13

1.3.1 Histories of R
t 14

1.4 Particle- and nucleosynthesis 17

1.5 CMB fluctuations and structure formation 24

1.6 Cosmological parameters 25

1.7 The inflationary paradigm 26

1.8 The role of stellar evolution 28

2 Equation of State of the Stellar Matter 31

2.1 Physical conditions of the stellar matter 31

2.1.1 Fully ionized perfect gas 35

2.1.2 Electron degeneracy 38

2.1.3 Ionization 41

2.1.4 Additional effects 44

3 Equations of Stellar Structure 49

3.1 Basic assumptions 49

3.1.1 Continuity of mass 50

3.1.2 Hydrostatic equilibrium 50

3.1.3 Conservation of energy 52

3.1.4 Energy transport 52

3.1.5 The opacity of stellar matter 66

3.1.6 Energy generation coefficient 68

3.1.7 Evolution of chemical element abundances 83

3.1.8 Virial theorem 86

3.1.9 Virial theorem and electron degeneracy 89

3.2 Method of solution of the stellar structure equations 90

3.2.1 Sensitivity of the solution to the boundary conditions 97

3.2.2 More complicated cases 98

viii CONTENTS

3.3 Non-standard physical processes 99

3.3.1 Atomic diffusion and radiative levitation 100

3.3.2 Rotation and rotational mixings 102

4 Star Formation and Early Evolution 105

4.1 Overall picture of stellar evolution 105

4.2 Star formation 106

4.3 Evolution along the Hayashi track 110

4.3.1 Basic properties of homogeneous, fully convective stars 110

4.3.2 Evolution until hydrogen burning ignition 114

5 The Hydrogen Burning Phase 117

5.1 Overview 117

5.2 The nuclear reactions 118

5.2.1 The p–p chain 118

5.2.2 The CNO cycle 119

5.2.3 The secondary elements: the case of 2H and 3He 121

5.3 The central H-burning phase in low main sequence (LMS) stars 123

5.3.1 The Sun 125

5.4 The central H-burning phase in upper main sequence (UMS) stars 128

5.5 The dependence of MS tracks on chemical composition and

convection efficiency 133

5.6 Very low-mass stars 136

5.7 The mass–luminosity relation 138

5.8 The Schönberg–Chandrasekhar limit 140

5.9 Post-MS evolution 141

5.9.1 Intermediate-mass and massive stars 141

5.9.2 Low-mass stars 142

5.9.3 The helium flash 148

5.10 Dependence of the main RGB features on physical and chemical

parameters 149

5.10.1 The location of the RGB in the H–R diagram 150

5.10.2 The RGB bump luminosity 151

5.10.3 The luminosity of the tip of the RGB 152

5.11 Evolutionary properties of very metal-poor stars 155

6 The Helium Burning Phase 161

6.1 Introduction 161

6.2 The nuclear reactions 161

6.3 The zero age horizontal branch (ZAHB) 163

6.3.1 The dependence of the ZAHB on various physical parameters 165

6.4 The core He-burning phase in low-mass stars 167

6.4.1 Mixing processes 167

CONTENTS ix

6.5 The central He-burning phase in more massive stars 173

6.5.1 The dependence of the blue loop on various physical parameters 175

6.6 Pulsational properties of core He-burning stars 179

6.6.1 The RR Lyrae variables 181

6.6.2 The classical Cepheid variables 183

7 The Advanced Evolutionary Phases 187

7.1 Introduction 187

7.2 The asymptotic giant branch (AGB) 187

7.2.1 The thermally pulsing phase 189

7.2.2 On the production of s-elements 194

7.2.3 The termination of the AGB evolutionary phase 195

7.3 The Chandrasekhar limit and the evolution of stars with large CO cores 198

7.4 Carbon–oxygen white dwarfs 199

7.4.1 Crystallization 206

7.4.2 The envelope 210

7.4.3 Detailed WD cooling laws 212

7.4.4 WDs with other chemical stratifications 213

7.5 The advanced evolutionary stages of massive stars 214

7.5.1 The carbon-burning stage 217

7.5.2 The neon-burning stage 219

7.5.3 The oxygen-burning stage 220

7.5.4 The silicon-burning stage 221

7.5.5 The collapse of the core and the final explosion 222

7.6 Type Ia supernovae 224

7.6.1 The Type Ia supernova progenitors 225

7.6.2 The explosion mechanisms 229

7.6.3 The light curves of Type Ia supernovae and their use as distance

indicators 230

7.7 Neutron stars 233

7.8 Black holes 236

8 From Theory to Observations 239

8.1 Spectroscopic notation of the stellar chemical composition 239

8.2 From stellar models to observed spectra and magnitudes 241

8.2.1 Theoretical versus empirical spectra 248

8.3 The effect of interstellar extinction 250

8.4 K-correction for high-redshift objects 253

8.5 Some general comments about colour–magnitude diagrams (CMDs) 254

9 Simple Stellar Populations 259

9.1 Theoretical isochrones 259

9.2 Old simple stellar populations (SSPs) 264

9.2.1 Properties of isochrones for old ages 264

9.2.2 Age estimates 268

x CONTENTS

9.2.3 Metallicity and reddening estimates 281

9.2.4 Determination of the initial helium abundance 284

9.2.5 Determination of the initial lithium abundance 287

9.2.6 Distance determination techniques 289

9.2.7 Luminosity functions and estimates of the IMF 301

9.3 Young simple stellar populations 304

9.3.1 Age estimates 304

9.3.2 Metallicity and reddening estimates 309

9.3.3 Distance determination techniques 310

10 Composite Stellar Populations 315

10.1 Definition and problems 315

10.2 Determination of the star formation history (SFH) 320

10.3 Distance indicators 327

10.3.1 The planetary nebula luminosity function (PNLF) 329

11 Unresolved Stellar Populations 331

11.1 Simple stellar populations 331

11.1.1 Integrated colours 334

11.1.2 Absorption-feature indices 341

11.2 Composite stellar populations 347

11.3 Distance to unresolved stellar populations 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 Maurizio Salaris

Teramo Santi Cassisi

March 2005