Astrophysics Decoding the Stars

This is a balanced textbook presenting the theory and observations of stars and their evolution—a cornerstone of Astrophysics.

Astrophysics: Decoding the Stars is a companion volume to Astrophysics: Decoding the Cosmos from astrophysics teacher and researcher, Professor Judith Irwin. The text presents an accessible, student-friendly guide to the key theories and principles of stars, emphasizing the close connection between observation and theory.

To aid in reader comprehension, the text includes online resources and problems at the end of each chapter. Many highlighted boxes summarize key concepts or point to example stars that can be seen with the naked eye. The text focuses on physical concepts, but it also refers to the results of numerical models using online resources.

Sample topics covered in Astrophysics: Decoding the Stars include:

• The Sun, gaseous and radiative processes
• Stellar interiors, energy transport mechanisms, stellar cores and nuclear energy generation, the global energy budget, timescales, and stability
• Observational constraints, variable stars, and star formation from molecular clouds to the ZAMS
• Evolutionary tracks on the HR diagram for stars of different masses, and how stars end their lives
• Stellar remnants — white dwarfs, neutron stars and pulsars, and black holes

Astrophysics: Decoding the Stars is a highly useful textbook resource for second- to fourth-year undergraduate students pursuing an Astrophysics program, along with Physics undergraduates who have opted to take stellar structure and evolution as part of their program. It will also be useful for new graduate students who want a solid grounding in stellar astrophysics.

Professor Judith Irwin teaches undergraduate and graduate physics, astrophysics, and astronomy in the Department of Physics, Engineering Physics and Astronomy at Queen’s University, Canada. Her research focuses on gaseous halos of spiral galaxies.

Preface xiii

Acknowledgments xv

Introduction xvii

I.1 The Simple Physical Star xix

I.2 The Dominance of Gravity for Stars xxi

I.3 The Numerical and Analytical Star xxvi

I.4 The Theoretical and Observational Star xxviii

Problems  xxxiv

1 The Closest Star 1

1.1 The Sun { First among Equals 1

1.2 The Solar Atmosphere 6

1.2.1 Physical Overview 6

1.2.2 The Photosphere 11

1.2.3 The Chromosphere 14

1.2.4 The Transition Region 17

1.2.5 The Corona 21

1.2.6 Energy Source for Heating the Solar Atmosphere 23

1.3 The Solar Interior 25

1.3.1 The Standard Solar Model (SSM) 25

1.3.2 Solar Rotation 28

1.4 The Magnetic Sun 31

Problems  38

2 The Gaseous and Radiative Star { the Basics 41

2.1 The Gaseous Star 41

vii

2.1.1 The Ideal Gas 41

2.1.2 Abundances and Metallicity 43

2.1.3 The Maxwell-Boltzmann Velocity Distribution and

Gas Temperature 46

2.1.4 The mean molecular Weight 49

2.1.5 Fractional Ionization 50

2.1.6 Pressure of a Partially Ionized Ideal Gas 54

2.1.7 Degrees of Freedom, Adiabatic Index and SpecicHeats 55

2.1.8 Adiabatic and Isothermal Gases 58

2.2.1 Gas motions and the Doppler Shift 62

2.2 The Radiative Star 64

2.3 Stellar Opacities 67

Problems  72

3 The Observed Star { Towards the Essential Parameters 77

3.1 Temperature and Spectral Type 78

3.2 Luminosity and Luminosity Class 84

3.3 Chemical Composition 88

3.4 Mass  91

3.4.1 Visual Binaries 95

3.4.2 Spectroscopic Binaries 98

3.5 Radius  101

3.5.1 Eclipsing Binaries 102

3.6 Rotation and Winds 107

Problems  113

4 The Shining Star | Interiors 115

4.1 Energy Transport in Stars 115

4.2 Radiative Transport 116

4.2.1 The Rosseland Mean Opacity 118

4.2.2 Analytical forms for the Mean Opacities 121

4.2.3 The Equation of Radiative Transport 125

4.3 Convective Transport 128

4.3.1 Condition for Convective Instability 129

4.3.2 Mixing Length Theory 134

4.4.1 Real Convection 140

4.4 Conductive Energy Transport in Dense Regions 144

Problems  148

5 The Burning Star | Cores 151

5.1 Classical and Quantum Approaches 151

5.2 Energy Generation Rate 155

5.3 Energy Release and Binding Energy 156

5.4 Main Sequence Reactions 162

5.4.1 The PP-chain 162

5.4.2 The CNO Cycle 165

5.5 Reactions after the Main Sequence 169

5.5.1 The Triple-
 Process { Helium Burning 169

5.5.2 Additional and Higher Temperature Reactions 171

Problems  175

6 The Modelled Star 177

6.1 The Equations of Stellar Structure 177

6.1.1 Conservation of Mass 179

6.1.2 Hydrostatic Equilibrium 179

6.1.3 Energy Conservation 180

6.1.4 Energy Transport 181

6.1.5 Constitutive Relations 181

6.1.6 Boundary Conditions 182

6.2 Solving the Equations of Stellar Structure 183

6.2.1 Numerical Solutions 184

6.2.2 Conceptual and Analytical Approaches 185

6.3 The Vogt-Russell Theorem, Mass-Luminosity Relation, and Mass-

Radius Relation 191

Problems  202

7 The Quasistatic Star | Energies, Timescales, and Limits 205

7.1 The Virial Theorem 206

7.2 Timescales 211

7.2.1 The Dymamical Timescale 211

7.2.2 The Thermal (Kelvin-Helmholtz) Timescale 212

7.2.3 The Nuclear Timescale 214

7.3 Stability  216

7.3.1 Stability against Perturbations 216

7.3.2 Secular Evolution of the Sun along the Main Sequence 217

7.4 The Minimum and Maximum Stable Star 219

7.4.1 The Lowest Mass Stars 219

7.4.2 The Highest Mass Stars 221

7.6 A Main Sequence Primer 226

Problems  231

8 The Forming and Ageing Star { Evolution to and from the

Main Sequence 233

8.1 The Forming Star 233

8.1.1 The Jeans Criterion and Free-Fall Timescale 234

8.1.2 Real Star Formation 237

8.1.3 Protostars 238

8.1.4 From Protostar to the ZAMS 243

8.2.1 Number, Mass, and Luminosity Functions 251

8.4 The Ageing Star 256

8.4.1 Post-main sequence Evolution of a 1 M
 Star 257

8.5.1 Post-main sequence Evolution of Stars of Di
erent

Mass 266

8.6.1 Connecting Theory with Observations 276

Problems  284

9 The Variable Star { Stellar Pulsation 287

9.1 Pulsation  291

9.2 Asteroseismology 296

9.4 Radial Pulsation 307

9.5 The Drivers | the Kappa Mechanism 311

9.7 Period-Luminosity Relations 314

Problems  321

10 The Dying Star, and its Remnant 323

10.1 Planetary Nebulae 324

10.2 White Dwarfs { Stellar Cinders 327

10.2.1 The Mass-Radius Relation for White Dwarfs 330

10.2.2 The Cooling Curve | A Cosmic Clock 336

10.3 Supernovae 339

10.3.1 Core Collapse Supernovae 344

10.3.2 Thermonuclear Supernovae 349

10.5 The Densest Remnants | Neutron Stars and Pulsars 353

10.5.1 The Mass-Radius Relation for Neutron Stars 355

10.5.2 Stellar Beacons | Pulsars 358

10.5.3 The P _P Relation and Characteristic Age 367

10.6 The Ultimate Stellar Remnant | Black Holes 371

10.6.1 Observational Evidence 374

Problems  378

11 A Stellar Invitational 381

A Physical and Astronomical Data 385

B The Solar Atmosphere 389

C The Standard Solar Model 395

D Taylor Expansions for the Center of a Star 401

E Chandrasekhar's Argument for a Declining Pressure Distribu-on i a Star 405

F Stellar Data 409

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.