Stellar Interiors

, by Hansen, Carl J.; Kawaler, Steven D.; Trimble, Virginia

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ISBN: 9780387200897 | 0387200894
Cover: Hardcover
Copyright: 2/26/2004

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This text, designed for beginning students of stellar physics, introduces the fundamentals of stellar structure and evolution. In emphasizing the general picture of the life cycles of stars and the physics responsible, it also allows prospective specialists a taste of many of the detailed aspects of this mature discipline. The authors develop a solid foundation in important theory that is often overlooked in typical courses, yet steer clear of extraneous intensive mathematics and physics. Topics include nuclear physics and stellar energy sources, the equation of state of stellar material, phenomenological approaches to convection, and modern numerical techniques for computation of stellar evolution. Keeping pace with recent developments, the authors incorporate important elements such as asteroseismology, and the effects of rotation and magnetic fields.The text contains the source code for two useful programs, ZAMS (for constructing chemically homogeneous zero-age main sequence models) and PULS (to study the seismological properties of the ZAMS models). Some chapters include exercises. The diskette can be used on any computer with a FORTRAN compiler.

1 Preliminaries

(42)

1.1 Hydrostatic Equilibrium

(1)

1.2 An Energy Principle

(4)

1.3 The Vinal Theorem and Its Applications

(9)

1.3.1 Application: Global Energetics

(1)

1.3.2 Application: The Kelvin-Helmholtz Time Scale

(2)

1.3.3 Application: A Dynamic Time Scale

(1)

1.3.4 Application: Estimates of Stellar Temperatures

(1)

1.3.5 Application: Another Dynamic Time Scale

(2)

1.4 The Constant-Density Model

(5)

1.4.1 Calculation of Molecular Weights

(4)

1.4.2 The Temperature Distribution

(1)

1.5 Energy Generation and Transport

(3)

1.6 Stellar Dimensional Analysis

(6)

1.7 Evolutionary Lifetimes on the Main Sequence

(1)

1.8 The Hertzsprung-Russell Diagram

(2)

1.9 Summary Remarks

(1)

1.10 Exercises

(5)

1.11 References and Suggested Readings

(5)

2 An Overview of Stellar Evolution

(102)

2.1 Young Stellar Objects (YSOs)

(3)

2.2 The Zero-Age Main Sequence (ZAMS)

(4)

2.2.1 Life on the Main Sequence

(2)

2.2.2 Brown Dwarfs

(1)

2.3 Leaving the Main Sequence

(9)

2.3.1 Cluster HR Diagrams

(3)

Cluster and Galactics Ages

(1)

2.3.2 Mass Loss From Massive Stars

(3)

2.4 Red Giants and Supergiants

(2)

2.5 Hellum Flash or Fizzle

(8)

2.5.1 Hellum Core Burning

(2)

Hellum Core Exhaustion

(1)

2.5.2 Asymptotic Giant Branch

(3)

2.6 Later Phases, Initial Masses M less than 6-10 Mo 69

2.6.1 A Bit About White Dwarfs

(3)

2.7 Advanced Phases, Initial Masses M >6-10 Mo

(2)

2.8 Core Collapse and Nucleosynthesis

(8)

2.8.1 Abundances and Nucleosynthesis

(5)

2.9 Variable Stars: A Brief Overview

(106)

2.9.1 Eclipsing and Ellipsoidal Variables

(1)

2.9.2 Spotted, Rotating Stars

(1)

2.9.3 T Tauri Stars, FU Orionis Stars (FUORs), and Luminous Blue Variables

(1)

2.9.4 Last Helium Flash and Formation of Atmospheric Dust

(1)

2.10 Pulsational Variables

(4)

2.11 Explosive Variables

(14)

2.11.1 Novae

(4)

2.11.2 Supernovae

(3)

SN1987A

(3)

SN Type I

100

(2)

SN Remnants

102

(1)

2.12 White Dwarfs, Neutron Stars, and Black Holes

103

(2)

2.13 Binary Stars

105

(11)

2.13.1 Types of Binaries

105

(2)

2.13.2 The Roche Geometry

107

(2)

2.13.3 Formation and Early Evolution

109

(1)

2.13.4 The First Mass Transfer Phase and its Consequences

110

(3)

2.13.5 Systems With One Compact Component

113

(1)

2.13.6 The Second Phase of Mass Transfer

113

(1)

2.13.7 Binaries With Two Compact Components

114

(2)

2.14 Star Formation

116

(4)

2.15 Supplemental Material

120

(2)

2.16 Exercises

122

(16)

2.17 References and Suggested Readings

138

(7)

3 Equations of State

145

(48)

3.1 Distribution Functions

146

(4)

3.2 Blackbody Radiation

150

(2)

3.3 Ideal Monatomic Gas

152

(3)

3.4 The Saha Equation

155

(4)

3.5 Fermi-Dirac Equations of State

159

(12)

3.5.1 The Completely Degenerate Gas

160

(3)

3.5.2 Application to White Dwarfs

163

(3)

3.5.3 Effects of Temperature on Degeneracy

166

(5)

3.6 "Almost Perfect" Equations of State

171

(2)

3.7 Adiabatic Exponents and Other Derivatives

173

(11)

3.7.1 Keeping the Composition Fixed

174

(6)

Specific Heats

174

(1)

Adiabatic Exponents

175

(1)

Mixtures of Ideal Gases and Radiation

176

(2)

Mixtures of Degenerate and Ideal Gases

178

(2)

3.7.2 Allowing for Chemical Reactions

180

(4)

3.8 Exercises

184

(5)

3.9 References and Suggested Readings

189

(4)

4 Radiative and Conductive Heat Transfer

193

(48)

4.1 Radiative Transfer

193

(6)

4.2 The Diffusion Equation

199

(3)

4.2.1 A Brief Diversion into "Vs"

201

(1)

4.3 A Simple Atmosphere

202

(5)

4.4 Radiative Opacity Sources

207

(7)

4.4.1 Electron Scattering

208

(1)

4.4.2 Free-Free Absorption

209

(3)

4.4.3 Bound-Free and Bound-Bound Absorption

212

(1)

4.4.4 H- Opacity and Others

213

(1)

4.5 Heat Transfer by Conduction

214

(2)

4.6 Tabulated Opacities

216

(7)

4.7 Some Observed Spectra

223

(3)

4.8 Line Profiles and the Curve of Growth

226

(6)

4.8.1 The Lorentz Profile

226

(2)

4.8.2 Doppler Broadening

228

(2)

4.8.3 Curve of Growth

230

(2)

4.9 Exercises

232

(4)

4.10 References and Suggested Readings

236

(5)

5 Heat Transfer by Convection

241

(30)

5.1 The Mixing Length Theory

241

(17)

5.1.1 Criteria for Convection

242

(5)

5.1.2 Radiative Leakage

247

(2)

5.1.3 The Equation of Motion

249

(1)

5.1.4 Convective Efficiencies and Time Scales

250

(3)

5.1.5 Convective Fluxes

253

(1)

5.1.6 Calculations in the MLT

254

(1)

5.1.7 Numeric Examples

255

(3)

5.2 Variations on the MLT

258

(5)

5.2.1 Beyond the MLT

261

(1)

5.2.2 Semiconvection

261

(2)

5.3 Hydrodynamic Calculations

263

(3)

5.4 Exercises

266

(1)

5.5 References and Suggested Readings

267

(4)

6 Stellar Energy Sources

271

(58)

6.1 Gravitational Energy Sources

271

(2)

6.2 Thermonuclear Energy Sources

273

(26)

6.2.1 Preliminaries

274

(2)

6.2.2 Nuclear Energetics

276

(3)

6.2.3 Astrophysical Thermonuclear Cross Sections and Reaction Rates

279

(3)

6.2.4 Nonresonant Reaction Rates

282

(7)

Example: The 12C (p,γ) 13N Reaction

286

(3)

6.2.5 Resonant Reaction Rates

289

(2)

6.2.6 Other Forms of Reaction Rates

291

(6)

Neutron Capture and the S-Process

292

(2)

Weak Interactions

294

(2)

The Proton-Proton Reaction

296

(1)

6.2.7 Special Effects

297

(2)

6.3 The Proton-Proton Chains

299

(4)

6.3.1 Deuterium and Lithium Burning

303

(1)

6.4 The Carbon-Nitrogen-Oxygen Cycles

303

(4)

6.5 Helium-Burning Reactions

307

(4)

6.6 Carbon, Neon, and Oxygen Burning

311

(2)

6.7 Silicon "Burning"

313

(1)

6.8 Neutrino Emission Mechanisms

314

(4)

Pair Annihilation Neutrinos

315

(1)

Photoneutrinos and Bremsstrahlung Neutrinos

316

(1)

Plasma Neutrinos

317

(1)

6.9 Exercises

318

(4)

6.10 References and Suggested Readings

322

(7)

7 Stellar Modeling

329

(50)

7.1 The Equations of Stellar Structure

329

(2)

7.2 Polytropes Equations of State and Polytropes

331

(31)

7.2.1 General Properties of Polytropes

332

(5)

7.2.2 Numerical Calculation of the Lane-Emden Functions

337

(6)

Shooting for a Solution

338

(2)

The Fitting Method

340

(3)

7.2.3 The U-V Plane

343

(2)

7.2.4 Newton-Raphson or "Henyey" Methods

345

(4)

7.2.5 Eigenvalue Problems and the Henyey Method

349

(2)

7.2.6 Dynamic Problems

351

(6)

7.2.7 The Eddington Standard Model

357

(4)

7.2.8 Applications to Zero-Temperature White Dwarfs

361

(1)

7.3 The Approach to Real Models

362

(12)

7.3.1 Central Expansions

362

(1)

7.3.2 The Radiative Stellar Envelope

363

(4)

The Structure of the Envelope

363

(3)

The Radiative Temperature Structure

366

(1)

7.3.3 Completely Convective Stars

367

(13)

A Question of Entropy

370

(3)

Application to Pre-Main Sequence Evolution

373

(1)

7.4 Exercises

374

(2)

7.5 References and Suggested Readings

376

(3)

8 Asteroseismology

379

(52)

8.1 Adiabatic Radial Pulsations

380

(11)

8.1.1 The Linear Adiabatic Wave Equation

384

(1)

8.1.2 Some Examples

385

(3)

8.1.3 Asymptotic Analysis

388

(3)

8.2 Nonadiabatic Radial Motions

391

(13)

8.2.1 The Quasi-Adiabatic Approximation

394

(3)

8.2.2 The κ- and γ-Mechanisms

397

(3)

The Epstein Weight Function and Cepheids

399

(1)

8.2.3 Nonadiabaticity and the Cepheid Strip

400

(4)

A Footnote on Nonlinear Modeling

403

(1)

8.3 An Introduction to Nonradial Oscillations

404

(20)

8.3.1 Linearization of the Hydrodynamic Equations

404

(4)

8.3.2 Separation of the Pulsation Equations

408

(4)

8.3.3 Properties of the Solutions

412

(7)

Mode Classification

415

(3)

The Eigenfunctions

418

(1)

8.3.4 The Inverse Problem and Rotation

419

(15)

Probing for Internal Rotation

421

(2)

Solid Stars?!

423

(1)

8.4 Exercises

424

(3)

8.5 References and Suggested Readings

427

(4)

9 Structure and Evolution of the Sun

431

(36)

9.1 Vital Statistics of the Sun

432

(2)

9.2 From the ZAMS to the Present

434

(8)

9.2.1 The Sun on the ZAMS

434

(3)

9.2.2 Evolution From the ZAMS

437

(2)

9.2.3 The Present-Day Sun

439

(3)

9.3 The Solar Neutrino "Problem"

442

(6)

9.4 The Role of Rotation in Evolution

448

(6)

9.4.1 von Zeipel's Paradox

450

(2)

9.4.2 Rotational Mixing of Stellar Interiors

452

(2)

9.5 Helioseismology

454

(6)

9.5.1 Observed and Predicted Pulsation Frequencies

455

(1)

9.5.2 Helioseismology and the Solar Interior

456

(13)

Structural Inversions

457

(2)

Rotational Inversions

459

(1)

9.6 References and Suggested Readings

460

(7)

10 Structure and Evolution of White Dwarfs

467

(1)

10.1 Observed Properties of White Dwarfs

467

(2)

10.2 White Dwarf Evolution

469

10.2.1 Cooling of White Dwarfs

470

(2)

10.2.2 Realistic Evolutionary Calculations

472

(5)

10.3 The Magnetic White Dwarfs

477

(2)

10.3.1 Magnetic Field Decay

479

(2)

10.4 The Variable White Dwarfs

481

(1)

10.4.1 The Observed Variables

482

(1)

10.4.2 White Dwarf Seismology

482

(3)

White Dwarfs and the Whole Earth Telescope

485

(5)

10.5 Exercises

490

(1)

10.6 References and Suggested Readings

490

(7)

A Mini Stellar Glossary

497

(6)

B Table of Symbols and Physical Constants

503

(10)

C List of Journal Abbreviations

513

(2)

Index

515

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Stellar Interiors

Summary

Author Biography

Table of Contents

Supplemental Materials