Stellar Physics (eBook)

Stellar Physics 1
Preface to the Second English Edition 7
Preface to the First English Edition 9
Preface to the Russian Edition 11
Contents of Volume 1 13
Contents of Volume 2 17
7 Star Formation 23
7.1 Observations of the Regions of Star Formation 23
7.1.1 Introduction 23
7.1.2 Observational Data 24
7.2 Spherically Symmetric Collapseof Interstellar Clouds 27
7.2.1 Heat Balance of an Optically Thin Cloud 27
7.2.2 Equations for Cloud Collapse 29
7.2.3 Calculational Results 32
7.3 Collapse of Rotating Clouds 36
7.3.1 Set of Equations and Difference Scheme Properties 37
7.3.2 Calculational Results 40
8 Pre-Main Sequence Evolution 46
8.1 Hayashi Phase 46
8.1.1 Nuclear Reactions 46
8.1.2 Non-Ideality of Matter 49
8.1.3 Evolution of Low-Mass Stars, Minimum Mass of a Star on the Main Sequence, Role of Various Factors 50
8.1.4 Evolutionary Role of the Mass Loss 52
8.2 Evolution of Rapidly Rotating Stars on Gravitational Contraction Stages 53
8.2.1 On the Distribution of Angular Velocity of Rotation 55
8.2.2 Method for Evolutionary Calculations 57
8.2.3 Calculation Results 60
8.3 Models for the Matter Outflow from Young Stars 62
8.3.1 Outflowing Bipolytropic Models 66
8.3.2 Outflowing Models for Isentropic Hydrogen Stars 70
8.3.3 Models for Outflowing Coronae of Young Stars 75
8.3.4 On the Phenomenon of Fuor 79
9 Nuclear Evolution of Stars 82
9.1 Sources of Uncertainty in Evolutionary Calculations 83
9.1.1 Convection 83
9.1.2 Semiconvection 83
9.1.3 Convective Non-Locality and Overshooting 85
9.1.4 Opacity and Nuclear Reactions 85
9.1.5 Methods for Calculating Envelope 86
9.1.6 Other Factors 86
9.2 Evolution of Stars in Quiescent Burning Phases 87
9.2.1 Iben's Calculations 88
9.2.2 Paczynski's Calculations 94
9.2.3 Evolution of Massive Stars 96
9.2.4 Evolution of Massive Stars with Mass Loss 104
9.2.5 CAK Theory 115
9.2.6 Line-Driven Winds in the Presence of Strong Gravitational Fields 120
9.2.7 Calculations with New Opacity Tables 125
9.3 Evolution with Degeneracy, Thermal Flashes 133
9.3.1 Core Helium Flash 134
9.3.2 Horizontal Branch 135
9.3.3 Asymptotic Giant Branch 137
9.3.4 Thermal Flashes in Helium-Burning Shell 142
9.3.5 The Mass Loss in AGB Stars 145
9.3.6 Evolution with Mass Loss: From AGB to White Dwarf State 147
9.3.7 On Mixing on the AGB and in Neighbourhoods 153
9.3.8 Thermal Instability in Degenerate Carbon Core 156
9.3.9 Convective ²URCA Shells² 157
9.3.9.1 Energy Equation in Presence of the Convective URCA Shell 161
9.3.9.2 Convective Flux 162
10 Collapse and Supernovae 165
10.1 Presupernova Models 167
10.1.1 Stellar Cores at Threshold of Hydrodynamical Stability: Energetic Method 167
10.1.2 Stellar Cores at Thermal Instability Threshold 175
10.2 Explosions Resulting from the Thermal Instability Development in Degenerate Carbon Cores 180
10.2.1 Basic Equations 180
10.2.2 Detonation 181
10.2.3 Deflagration 181
10.2.4 Spontaneous Burning and Detonation 183
10.2.5 Instabilities of Nuclear Flames 184
10.3 Collapse of Low-Mass Stellar Cores 187
10.4 Hydrodynamical Collapse of Stellar Cores 191
10.4.1 Low-Energy Window for Neutrinos 194
10.4.2 Asymmetric Neutrino Emission During Collapse of a Star with a Strong Magnetic Field 195
10.4.3 Neutrino Oscillations in Matter 198
10.4.4 Convective Instability in Collapsing Stellar Cores 199
10.4.5 Two-Dimensional and Three-Dimensional Calculations of Neutrino Convection 200
10.4.6 Explosion of Rapidly Rotating Star 204
10.4.7 Standing Accretion Induced Instability 205
10.4.8 Acoustic Explosion Model 206
10.5 Magnetorotational Model of Supernova Explosion 207
10.5.1 Mechanism of Magnetorotational Explosion 207
10.5.2 Basic Equations 208
10.5.3 Cylindrical Approximation 210
10.5.4 Calculational Results 212
10.5.5 Two-Dimensional Numerical Method in MHD 216
10.5.6 Magnetorotational Explosion of the Initially Uniform Cloud 219
10.5.7 Magnetorotational Supernova: Quadruple and Dipole Magnetic Configurations 221
10.5.8 Development of the Magnetorotational Instability in 2D Simulations 231
10.5.9 Symmetry Breaking Of the Magnetic Field, Anisotropic Neutrino Emission and High Velocity Neutron Star Formation 233
10.5.10 A Kick Due to Hydrodynamic Instabilities 239
11 Final Stages of Stellar Evolution 241
11.1 White Dwarfs 242
11.1.1 Case T=0 242
11.1.2 Account for a Finite Value of T and Cooling 247
11.1.3 Cooling of White Dwarfs Near the Stability Limit with the Inclusion of Heating by Non-Equilibrium -Processes [34] 251
11.1.4 On the Evolution of Magnetic Fields in White Dwarfs 255
11.1.5 Nova Outbursts 258
11.2 Neutron Stars 260
11.2.1 Cold Neutron Stars 262
11.2.2 Hot Neutron Stars 265
11.2.3 Cooling of Neutron Stars 269
11.2.4 Magnetic Field Decay in Neutron Stars 273
11.2.5 Stars with Neutron Cores 274
11.2.6 Quark stars 274
11.2.6.1 Strange Quark Matter 279
11.2.6.2 Strange Stars 280
11.2.6.3 The Surface: Bare or Crusted Strange Stars? 282
11.3 Black Holes and Accretion 283
11.3.1 Spherically Symmetric Accretion 284
11.3.2 Accretion at an Ordered Magnetic Field 288
11.3.3 Conical Accretion on to a Rapidly Moving Black Hole 291
11.3.4 Disk Accretion in Binaries 294
11.3.5 Accretion Disc Structure with Optically Thin/Thick Transition 298
11.3.6 Black Hole Advective Accretion Disks with Optical Depth Transition 300
11.3.6.1 Basic Equations 303
11.3.6.2 Singular Points and Uniqueness of Solutions 304
11.3.6.3 Method of Solution 306
11.3.6.4 Numerical Results and Physical Effects 306
11.3.7 Large-Scale Magnetic Fields Dragging in Accretion Disks 312
11.3.7.1 Turbulent Disk with Radiative Outer Zones 314
11.3.8 Battery Effect in Accretion Disks 316
11.3.8.1 Radiatively Induced Current and Toroidal Magnetic Field Production in Accretion Disks 317
11.3.8.2 Production of a Poloidal Magnetic Field in Optically Thin Accretion Flows by Poynting--Robertson Effect 320
11.3.9 Screening of the Magnetic Field of Disk Accreting Stars 321
11.3.10 Jet Confinement by Magneto-Torsional Oscillations 324
11.3.10.1 Profiling in Axially Symmetric MHD Equations 326
11.3.10.2 Further Simplification: Reducing the Problem to an Ordinary Differential Equation 327
11.3.10.3 Numerical Solution 330
11.3.10.4 Restrictions of the Model 330
11.4 Cosmic Gamma Ray Bursts: Observations and Modeling 334
11.4.1 Central Engine of Cosmic Gamma-Ray Bursts 337
11.4.2 Optical Afterglows 340
11.4.3 Short GRB and Giant SGR Bursts 343
11.4.4 High Energy Afterglows (30--10,000MeV) 345
12 Dynamic Stability 369
12.1 Hierarchy of Time Scales 369
12.2 Variational Principle and Small Perturbations 371
12.2.1 Variational Principle in General Relativity 371
12.2.2 Newtonian and Post-Newtonian Limits 373
12.2.3 Method of Small Perturbations in Newtonian Theory 377
12.3 Static Criteria for Stability 381
12.3.1 Non-Rotating Stars 381
12.3.2 Criteria for Rotating Stars 383
12.3.3 Removal of Degeneracy of Neutral Oscillatory Modes in Rotating Isentropic Stars 384
12.3.4 Numerical Examples 386
12.4 Star Stability in the Presence of a Phase Transition 387
12.4.1 Evaluation of Variations and 2 388
12.4.2 Other Forms of Stability Criterion 392
12.4.3 Rough Test for Stability 393
12.4.4 Derivation of Stability Condition for a Phase Transition in the Center of Star 396
12.5 Dynamic Stabilization of NonSpherical Bodies Against Unlimited Collapse 397
12.5.1 Equations of Motion 398
12.5.2 Dimensionless Equations 399
12.5.3 Numerical Results for the Case H=0 402
12.5.4 Poincaré Section 404
12.5.4.1 The Bounding Curve 406
12.6 General Picture 407
13 Thermal Stability 410
13.1 Evolutionary Phases Exhibiting Thermal Instabilities 410
13.1.1 Instability in Degenerate Regions 410
13.1.2 Instabilities in the Absence of Degeneracy 414
13.2 Thermal Instability Development in Non-Degenerate Shells 415
13.2.1 Stability of a Burning Shell with Constant Thickness 415
13.2.2 Calculations of Density Perturbations 417
13.2.3 A Strict Criterion for Thermal Stability 420
14 Stellar Pulsations and Stability 421
14.1 Eigenmodes 421
14.1.1 Equations for Small Oscillations 421
14.1.2 Boundary Conditions 425
14.1.3 p-, g- and f-Modes 427
14.1.4 Pulsational Instability 429
14.2 Pulsations in Stars with Phase Transition 431
14.2.1 Equations of Motion in the Presence of a Phase Transition 431
14.2.2 Physical Processes at the Phase Jump 434
14.2.3 Adiabatic Oscillations of Finite Amplitude 435
14.2.4 Decaying Finite-Amplitude Oscillations 436
14.3 Pulsational Stability of Massive Stars 438
14.3.1 The Linear Analysis 438
14.3.2 Non-Linear Oscillations 442
14.4 On Variable Stars and Stellar Seismology 443
References 446
List of Symbols and Abbreviations 489
Some Important Constants 502
Subject Index 504