Stellar structure and evolution [2nd ed] 9783642302558, 9783642303043, 3642302556, 3642303048

Table of contents :
Preface to the First Edition......Page 8
Preface to the Second Edition......Page 10
Contents......Page 12
Part I The Basic Equations......Page 20
1.1 Eulerian Description......Page 21
1.2 Lagrangian Description......Page 22
1.3 The Gravitational Field......Page 24
2.1 Hydrostatic Equilibrium......Page 26
2.2 The Role of Density and Simple Solutions......Page 27
2.3 Simple Estimates of Central Values Pc,Tc......Page 29
2.4 The Equation of Motion for Spherical Symmetry......Page 30
2.6 Hydrostatic Equilibrium in General Relativity......Page 32
2.7 The Piston Model......Page 34
3.1 Stars in Hydrostatic Equilibrium......Page 36
3.2 The Virial Theorem of the Piston Model......Page 38
3.3 The Kelvin–Helmholtz Timescale......Page 39
3.4 The Virial Theorem for Non-vanishing Surface Pressure......Page 40
4.1 Thermodynamic Relations......Page 41
4.2 The Perfect Gas and the Mean Molecular Weight......Page 44
4.3 Thermodynamic Quantities for the Perfect, Monatomic Gas......Page 46
4.4 Energy Conservation in Stars......Page 47
4.5 Global and Local Energy Conservation......Page 49
4.6 Timescales......Page 51
5.1.1 Basic Estimates......Page 53
5.1.2 Diffusion of Radiative Energy......Page 54
5.1.3 The Rosseland Mean for κν......Page 56
5.2 Conductive Transport of Energy......Page 58
5.3 The Thermal Adjustment Time of a Star......Page 59
5.4 Thermal Properties of the Piston Model......Page 61
6.1 Dynamical Instability......Page 63
6.2 Oscillation of a Displaced Element......Page 68
6.3 Vibrational Stability......Page 70
6.4 The Thermal Adjustment Time......Page 71
6.5 Secular Instability......Page 72
6.6 The Stability of the Piston Model......Page 74
Chapter7 Transport of Energy by Convection......Page 77
7.1 The Basic Picture......Page 78
7.2 Dimensionless Equations......Page 81
7.3 Limiting Cases, Solutions, Discussion......Page 82
7.4 Extensions of the Mixing-Length Theory......Page 86
8.1 Relative Mass Abundances......Page 88
8.2.1 Radiative Regions......Page 89
8.2.2 Diffusion......Page 91
8.2.3 Convective Regions......Page 95
Chapter9 Mass Loss......Page 97
Part II The Overall Problem......Page 100
10.1 The Full Set of Equations......Page 101
10.2 Timescales and Simplifications......Page 103
11.1 Central Conditions......Page 105
11.2 Surface Conditions......Page 107
11.3.1 Radiative Envelopes......Page 110
11.3.2 Convective Envelopes......Page 113
11.3.4 The T-r Stratification......Page 114
12.1 The Shooting Method......Page 116
12.2 The Henyey Method......Page 117
12.3 Treatment of the First- and Second-Order Time Derivatives......Page 124
12.4 Treatment of the Diffusion Equation......Page 126
12.5 Treatment of Mass Loss......Page 128
12.6 Existence and Uniqueness......Page 129
Part III Properties of Stellar Matter......Page 131
13.1 Radiation Pressure......Page 132
13.2 Thermodynamic Quantities......Page 133
14.1 The Boltzmann and Saha Formulae......Page 135
14.2 Ionization of Hydrogen......Page 138
14.3 Thermodynamical Quantities for a Pure Hydrogen Gas......Page 140
14.4 Hydrogen–Helium Mixtures......Page 141
14.5 The General Case......Page 143
14.6 Limitation of the Saha Formula......Page 145
15.1 Consequences of the Pauli Principle......Page 147
15.2 The Completely Degenerate Electron Gas......Page 148
15.3 Limiting Cases......Page 152
15.4 Partial Degeneracy of the Electron Gas......Page 153
16.1 The Ion Gas......Page 159
16.2 The Equation of State......Page 160
16.3 Thermodynamic Quantities......Page 162
16.4 Crystallization......Page 165
16.5 Neutronization......Page 166
16.6 Real Gas Effects......Page 167
17.1 Electron Scattering......Page 170
17.2 Absorption Due to Free–Free Transitions......Page 171
17.3 Bound–Free Transitions......Page 172
17.4 Bound–Bound Transitions......Page 173
17.5 The Negative Hydrogen Ion......Page 175
17.6 Conduction......Page 176
17.7 Molecular Opacities......Page 177
17.8 Opacity Tables......Page 179
18.1 Basic Considerations......Page 182
18.2 Nuclear Cross Sections......Page 186
18.3 Thermonuclear Reaction Rates......Page 189
18.4 Electron Shielding......Page 195
18.5 The Major Nuclear Burning Stages......Page 199
18.5.1 Hydrogen Burning......Page 200
18.5.2 Helium Burning......Page 204
18.5.3 Carbon Burning and Beyond......Page 206
18.6 Neutron-Capture Nucleosynthesis......Page 208
18.7 Neutrinos......Page 212
Part IV Simple Stellar Models......Page 217
19.1 Polytropic Relations......Page 218
19.2 Polytropic Stellar Models......Page 220
19.3 Properties of the Solutions......Page 221
19.4 Application to Stars......Page 223
19.5 Radiation Pressure and the Polytrope n = 3......Page 224
19.6 Polytropic Stellar Models with Fixed K......Page 225
19.7 Chandrasekhar's Limiting Mass......Page 226
19.8 Isothermal Spheres of an Ideal Gas......Page 227
19.9 Gravitational and Total Energy for Polytropes......Page 229
19.10 Supermassive Stars......Page 231
19.11 A Collapsing Polytrope......Page 232
20.1 Definitions and Basic Relations......Page 237
20.2.2 The Case α= δ= = 1,a = b = 0......Page 241
20.2.3 The Role of the Equation of State......Page 243
20.3 Homologous Contraction......Page 245
21.1 The U–V Plane......Page 247
21.2 Radiative Envelope Solutions......Page 250
21.3 Fitting of a Convective Core......Page 252
21.4 Fitting of an Isothermal Core......Page 254
22.1 Surface Values......Page 255
22.2 Interior Solutions......Page 258
22.3 Convective Regions......Page 262
22.4 Extreme Values of M......Page 264
22.5 The Eddington Luminosity......Page 265
23.1 The Helium Main Sequence......Page 267
23.2 The Carbon Main Sequence......Page 270
23.3 Generalized Main Sequences......Page 271
Chapter24 The Hayashi Line......Page 274
24.1 Luminosity of Fully Convective Models......Page 275
24.2 A Simple Description of the Hayashi Line......Page 276
24.3 The Neighbourhood of the Hayashi Line and the Forbidden Region......Page 279
24.4 Numerical Results......Page 282
24.5 Limitations for Fully Convective Models......Page 284
25.1 General Remarks......Page 286
25.2.1 Dynamical Stability......Page 288
25.2.2 Inclusion of Non-adiabatic Effects......Page 289
25.3 Stellar Stability......Page 291
25.3.1 Perturbation Equations......Page 292
25.3.2 Dynamical Stability......Page 293
25.3.3 Non-adiabatic Effects......Page 295
25.3.4 The Gravothermal Specific Heat......Page 296
25.3.5 Secular Stability Behaviour of Nuclear Burning......Page 297
Part V Early Stellar Evolution......Page 300
26.1.1 An Infinite Homogeneous Medium......Page 301
26.1.2 A Plane-Parallel Layer in Hydrostatic Equilibrium......Page 304
26.2 Instability in the Spherical Case......Page 305
26.3 Fragmentation......Page 309
27.1 Free-Fall Collapse of a Homogeneous Sphere......Page 312
27.2 Collapse onto a Condensed Object......Page 314
27.3 A Collapse Calculation......Page 315
27.4 The Optically Thin Phase and the Formation of a Hydrostatic Core......Page 316
27.5 Core Collapse......Page 318
27.6 Evolution in the Hertzsprung–Russell Diagram......Page 321
28.1 Homologous Contraction of a Gaseous Sphere......Page 324
28.2 Approach to the Zero-Age Main Sequence......Page 327
29.1 Known Solar Data......Page 330
29.2 Choosing the Initial Model......Page 332
29.3 A Standard Solar Model......Page 334
29.4 Results of Helioseismology......Page 337
29.5 Solar Neutrinos......Page 339
30.1 Change in the Hydrogen Content......Page 343
30.2 Evolution in the Hertzsprung–Russell Diagram......Page 346
30.3 Timescales for Central Hydrogen Burning......Page 347
30.4 Complications Connected with Convection......Page 348
30.4.1 Convective Overshooting......Page 349
30.4.2 Semiconvection......Page 354
30.5 The Schönberg–Chandrasekhar Limit......Page 356
30.5.1 A Simple Approach: The Virial Theorem and Homology......Page 358
30.5.2 Integrations for Core and Envelope......Page 360
30.5.3 Complete Solutions for Stars with Isothermal Cores......Page 361
Part VI Post-Main-Sequence Evolution......Page 364
31.1 Crossing the Hertzsprung Gap......Page 365
31.2 Central Helium Burning......Page 369
31.3 The Cepheid Phase......Page 373
31.4 To Loop or Not to Loop …......Page 376
31.5 After Central Helium Burning......Page 382
32.1 Semiconvection......Page 383
32.2 Overshooting......Page 385
32.3 Mass Loss......Page 387
33.1 Post-Main-Sequence Evolution......Page 389
33.2 Shell-Source Homology......Page 390
33.3 Evolution Along the Red Giant Branch......Page 395
33.4 The Helium Flash......Page 399
33.5 Numerical Results for the Helium Flash......Page 400
33.6 Evolution After the Helium Flash......Page 405
33.7 Evolution from the Zero-Age Horizontal Branch......Page 408
Part VII Late Phases of Stellar Evolution......Page 413
34.1 Nuclear Shells on the Asymptotic Giant Branch......Page 414
34.2 Shell Sources and Their Stability......Page 416
34.3 Thermal Pulses of a Shell Source......Page 419
34.4 The Core-Mass-Luminosity Relation for Large Core Masses......Page 421
34.5 Nucleosynthesis on the AGB......Page 423
34.6 Mass Loss on the AGB......Page 427
34.7 A Sample AGB Evolution......Page 430
34.8 Super-AGB Stars......Page 433
34.9 Post-AGB Evolution......Page 435
35.1 Nuclear Cycles......Page 436
35.2 Evolution of the Central Region......Page 438
Chapter36 Final Explosions and Collapse......Page 446
36.1 The Evolution of the CO-Core......Page 447
36.2.1 The Carbon Flash......Page 451
36.2.2 Nuclear Statistical Equilibrium......Page 452
36.2.3 Hydrostatic and Convective Adjustment......Page 455
36.2.4 Combustion Fronts......Page 456
36.3 Collapse of Cores of Massive Stars......Page 458
36.3.1 Simple Collapse Solutions......Page 459
36.3.2 The Reflection of the Infall......Page 462
36.3.3 Effects of Neutrinos......Page 463
36.3.5 Pair-Creation Instability......Page 466
36.4 The Supernova-Gamma-Ray-Burst Connection......Page 468
Part VIII Compact Objects......Page 470
37.1 Chandrasekhar's Theory......Page 472
37.2 The Corrected Mechanical Structure......Page 476
37.2.1 Crystallization......Page 477
37.2.2 Pycnonuclear Reactions......Page 479
37.2.4 Nuclear Equilibrium......Page 480
37.3 Thermal Properties and Evolution of White Dwarfs......Page 484
38.1 Cold Matter Beyond Neutron Drip......Page 494
38.2 Models of Neutron Stars......Page 498
Chapter39 Black Holes......Page 506
Part IX Pulsating Stars......Page 514
40.1 The Eigenvalue Problem......Page 515
40.2 The Homogeneous Sphere......Page 519
40.3 Pulsating Polytropes......Page 521
41.1 Vibrational Instability of the Piston Model......Page 525
41.2 The Quasi-adiabatic Approximation......Page 527
41.3 The Energy Integral......Page 528
41.3.2 The Mechanism......Page 530
41.4 Stars Driven by the κ Mechanism: The Instability Strip......Page 531
41.5 Stars Driven by the Mechanism......Page 537
42.1 Perturbations of the Equilibrium Model......Page 538
42.2 Normal Modes and Dimensionless Variables......Page 540
42.3 The Eigenspectra......Page 543
42.4 Stars Showing Non-radial Oscillations......Page 547
Part X Stellar Rotation......Page 549
43.1 Uniformly Rotating Liquid Bodies......Page 550
43.2 The Roche Model......Page 553
43.3 Slowly Rotating Polytropes......Page 555
44.1 Conservative Rotation......Page 558
44.2 Von Zeipel's Theorem......Page 559
44.3 Meridional Circulation......Page 560
44.4 The Non-conservative Case......Page 562
44.5 The Eddington–Sweet Timescale......Page 563
44.6 Meridional Circulation in Inhomogeneous Stars......Page 566
45.1 Viscosity......Page 568
45.2 Dynamical Stability......Page 570
45.3 Secular Stability......Page 575
References......Page 579
Index......Page 587