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Part I The Basic Equations |
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1 Coordinates, Mass Distribution, and Gravitational Field in Spherical Stars |
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3 | (6) |
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3 | (1) |
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1.2 Lagrangian Description |
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4 | (2) |
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1.3 The Gravitational Field |
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6 | (3) |
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2 Conservation of Momentum |
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9 | (10) |
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2.1 Hydrostatic Equilibrium |
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9 | (1) |
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2.2 The Role of Density and Simple Solutions |
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10 | (2) |
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2.3 Simple Estimates of Central Values Pc, Tc |
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12 | (1) |
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2.4 The Equation of Motion for Spherical Symmetry |
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13 | (2) |
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2.5 The Non-spherical Case |
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15 | (1) |
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2.6 Hydrostatic Equilibrium in General Relativity |
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15 | (2) |
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17 | (2) |
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19 | (6) |
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3.1 Stars in Hydrostatic Equilibrium |
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19 | (2) |
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3.2 The Virial Theorem of the Piston Model |
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21 | (1) |
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3.3 The Kelvin--Helmholtz Timescale |
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22 | (1) |
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3.4 The Virial Theorem for Non-vanishing Surface Pressure |
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23 | (2) |
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25 | (12) |
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4.1 Thermodynamic Relations |
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25 | (3) |
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4.2 The Perfect Gas and the Mean Molecular Weight |
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28 | (2) |
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4.3 Thermodynamic Quantities for the Perfect, Monatomic Gas |
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30 | (1) |
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4.4 Energy Conservation in Stars |
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31 | (2) |
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4.5 Global and Local Energy Conservation |
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33 | (2) |
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35 | (2) |
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5 Transport of Energy by Radiation and Conduction |
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37 | (10) |
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5.1 Radiative Transport of Energy |
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37 | (5) |
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37 | (1) |
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5.1.2 Diffusion of Radiative Energy |
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38 | (2) |
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5.1.3 The Rosseland Mean for kv |
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40 | (2) |
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5.2 Conductive Transport of Energy |
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42 | (1) |
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5.3 The Thermal Adjustment Time of a Star |
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43 | (2) |
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5.4 Thermal Properties of the Piston Model |
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45 | (2) |
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6 Stability Against Local, Non-spherical Perturbations |
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47 | (14) |
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6.1 Dynamical Instability |
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47 | (5) |
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6.2 Oscillation of a Displaced Element |
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52 | (2) |
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6.3 Vibrational Stability |
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54 | (1) |
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6.4 The Thermal Adjustment Time |
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55 | (1) |
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56 | (2) |
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6.6 The Stability of the Piston Model |
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58 | (3) |
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7 Transport of Energy by Convection |
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61 | (12) |
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62 | (3) |
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7.2 Dimensionless Equations |
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65 | (1) |
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7.3 Limiting Cases, Solutions, Discussion |
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66 | (4) |
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7.4 Extensions of the Mixing-Length Theory |
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70 | (3) |
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8 The Chemical Composition |
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73 | (10) |
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8.1 Relative Mass Abundances |
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73 | (1) |
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8.2 Variation of Composition with Time |
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74 | (9) |
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74 | (2) |
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76 | (4) |
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80 | (3) |
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83 | (6) |
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Part II The Overall Problem |
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10 The Differential Equations of Stellar Evolution |
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89 | (4) |
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10.1 The Full Set of Equations |
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89 | (2) |
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10.2 Timescales and Simplifications |
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91 | (2) |
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93 | (12) |
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93 | (2) |
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95 | (3) |
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11.3 Influence of the Surface Conditions and Properties of Envelope Solutions |
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98 | (7) |
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11.3.1 Radiative Envelopes |
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98 | (3) |
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11.3.2 Convective Envelopes |
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101 | (1) |
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102 | (1) |
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11.3.4 The T---r Stratification |
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102 | (3) |
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105 | (18) |
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105 | (1) |
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106 | (7) |
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12.3 Treatment of the First- and Second-Order Time Derivatives |
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113 | (2) |
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12.4 Treatment of the Diffusion Equation |
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115 | (2) |
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12.5 Treatment of Mass Loss |
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117 | (1) |
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12.6 Existence and Uniqueness |
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118 | (5) |
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Part III Properties of Stellar Matter |
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13 The Perfect Gas with Radiation |
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123 | (4) |
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123 | (1) |
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13.2 Thermodynamic Quantities |
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124 | (3) |
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127 | (12) |
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14.1 The Boltzmann and Saha Formulae |
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127 | (3) |
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14.2 Ionization of Hydrogen |
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130 | (2) |
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14.3 Thermodynamical Quantities for a Pure Hydrogen Gas |
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132 | (1) |
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14.4 Hydrogen--Helium Mixtures |
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133 | (2) |
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135 | (2) |
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14.6 Limitation of the Saha Formula |
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137 | (2) |
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15 The Degenerate Electron Gas |
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139 | (12) |
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15.1 Consequences of the Pauli Principle |
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139 | (1) |
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15.2 The Completely Degenerate Electron Gas |
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140 | (4) |
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144 | (1) |
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15.4 Partial Degeneracy of the Electron Gas |
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145 | (6) |
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16 The Equation of State of Stellar Matter |
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151 | (12) |
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151 | (1) |
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16.2 The Equation of State |
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152 | (2) |
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16.3 Thermodynamic Quantities |
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154 | (3) |
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157 | (1) |
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158 | (1) |
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159 | (4) |
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163 | (12) |
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163 | (1) |
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17.2 Absorption Due to Free--Free Transitions |
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164 | (1) |
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17.3 Bound--Free Transitions |
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165 | (1) |
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17.4 Bound--Bound Transitions |
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166 | (2) |
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17.5 The Negative Hydrogen Ion |
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168 | (1) |
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169 | (1) |
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170 | (2) |
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172 | (3) |
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18 Nuclear Energy Production |
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175 | (38) |
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18.1 Basic Considerations |
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175 | (4) |
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18.2 Nuclear Cross Sections |
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179 | (3) |
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18.3 Thermonuclear Reaction Rates |
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182 | (6) |
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188 | (4) |
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18.5 The Major Nuclear Burning Stages |
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192 | (9) |
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193 | (4) |
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197 | (2) |
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18.5.3 Carbon Burning and Beyond |
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199 | (2) |
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18.6 Neutron-Capture Nucleosynthesis |
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201 | (4) |
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205 | (8) |
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Part IV Simple Stellar Models |
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19 Polytropic Gaseous Spheres |
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213 | (20) |
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19.1 Polytropic Relations |
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213 | (2) |
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19.2 Polytropic Stellar Models |
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215 | (1) |
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19.3 Properties of the Solutions |
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216 | (2) |
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19.4 Application to Stars |
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218 | (1) |
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19.5 Radiation Pressure and the Polytrope n = 3 |
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219 | (1) |
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19.6 Polytropic Stellar Models with Fixed K |
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220 | (1) |
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19.7 Chandrasekhar's Limiting Mass |
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221 | (1) |
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19.8 Isothermal Spheres of an Ideal Gas |
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222 | (2) |
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19.9 Gravitational and Total Energy for Polytropes |
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224 | (2) |
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226 | (1) |
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19.11 A Collapsing Polytrope |
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227 | (6) |
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233 | (10) |
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20.1 Definitions and Basic Relations |
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233 | (4) |
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20.2 Applications to Simple Material Functions |
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237 | (4) |
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237 | (1) |
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20.2.2 The Case α = δ = φ = 1, a = b = 0 |
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237 | (2) |
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20.2.3 The Role of the Equation of State |
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239 | (2) |
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20.3 Homologous Contraction |
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241 | (2) |
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21 Simple Models in the U--V Plane |
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243 | (8) |
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243 | (3) |
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21.2 Radiative Envelope Solutions |
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246 | (2) |
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21.3 Fitting of a Convective Core |
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248 | (2) |
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21.4 Fitting of an Isothermal Core |
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250 | (1) |
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22 The Zero-Age Main Sequence |
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251 | (12) |
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251 | (3) |
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254 | (4) |
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258 | (2) |
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260 | (1) |
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22.5 The Eddington Luminosity |
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261 | (2) |
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263 | (8) |
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23.1 The Helium Main Sequence |
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263 | (3) |
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23.2 The Carbon Main Sequence |
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266 | (1) |
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23.3 Generalized Main Sequences |
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267 | (4) |
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271 | (12) |
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24.1 Luminosity of Fully Convective Models |
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272 | (1) |
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24.2 A Simple Description of the Hayashi Line |
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273 | (3) |
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24.3 The Neighbourhood of the Hayashi Line and the Forbidden Region |
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276 | (3) |
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279 | (2) |
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24.5 Limitations for Fully Convective Models |
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281 | (2) |
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25 Stability Considerations |
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283 | (16) |
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283 | (2) |
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25.2 Stability of the Piston Model |
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285 | (3) |
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25.2.1 Dynamical Stability |
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285 | (1) |
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25.2.2 Inclusion of Non-adiabatic Effects |
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286 | (2) |
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288 | (11) |
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25.3.1 Perturbation Equations |
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289 | (1) |
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25.3.2 Dynamical Stability |
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290 | (2) |
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25.3.3 Non-adiabatic Effects |
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292 | (1) |
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25.3.4 The Gravothermal Specific Heat |
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293 | (1) |
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25.3.5 Secular Stability Behaviour of Nuclear Burning |
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294 | (5) |
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Part V Early Stellar Evolution |
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26 The Onset of Star Formation |
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299 | (12) |
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299 | (4) |
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26.1.1 An Infinite Homogeneous Medium |
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299 | (3) |
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26.1.2 A Plane-Parallel Layer in Hydrostatic Equilibrium |
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302 | (1) |
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26.2 Instability in the Spherical Case |
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303 | (4) |
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307 | (4) |
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27 The Formation of Protostars |
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311 | (12) |
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27.1 Free-Fail Collapse of a Homogeneous Sphere |
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311 | (2) |
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27.2 Collapse onto a Condensed Object |
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313 | (1) |
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27.3 A Collapse Calculation |
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314 | (1) |
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27.4 The Optically Thin Phase and the Formation of a Hydrostatic Core |
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315 | (2) |
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317 | (3) |
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27.6 Evolution in the Hertzsprung-Russell Diagram |
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320 | (3) |
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28 Pre-Main-Sequence Contraction |
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323 | (6) |
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28.1 Homologous Contraction of a Gaseous Sphere |
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323 | (3) |
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28.2 Approach to the Zero-Age Main Sequence |
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326 | (3) |
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29 From the Initial to the Present Sun |
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329 | (14) |
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329 | (2) |
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29.2 Choosing the Initial Model |
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331 | (2) |
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29.3 A Standard Solar Model |
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333 | (3) |
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29.4 Results of Helioseismology |
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336 | (2) |
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338 | (5) |
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30 Evolution on the Main Sequence |
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343 | (24) |
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30.1 Change in the Hydrogen Content |
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343 | (3) |
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30.2 Evolution in the Hertzsprung-Russell Diagram |
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346 | (1) |
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30.3 Timescales for Central Hydrogen Burning |
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347 | (1) |
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30.4 Complications Connected with Convection |
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348 | (8) |
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30.4.1 Convective Overshooting |
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349 | (5) |
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354 | (2) |
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30.5 The Schonberg-Chandrasekhar Limit |
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356 | (11) |
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30.5.1 A Simple Approach: The Virial Theorem and Homology |
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358 | (2) |
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30.5.2 Integrations for Core and Envelope |
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360 | (1) |
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30.5.3 Complete Solutions for Stars with Isothermal Cores |
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361 | (6) |
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Part VI Post-Main-Sequence Evolution |
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31 Evolution Through Helium Burning: Intermediate-Mass Stars |
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367 | (18) |
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31.1 Crossing the Hertzsprung Gap |
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367 | (4) |
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31.2 Central Helium Burning |
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371 | (4) |
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375 | (3) |
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31.4 To Loop or Not to Loop |
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378 | (6) |
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31.5 After Central Helium Burning |
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384 | (1) |
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32 Evolution Through Helium Burning: Massive Stars |
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385 | (6) |
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385 | (2) |
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387 | (2) |
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389 | (2) |
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33 Evolution Through Helium Burning: Low-Mass Stars |
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391 | (26) |
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33.1 Post-Main-Sequence Evolution |
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391 | (1) |
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33.2 Shell-Source Homology |
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392 | (5) |
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33.3 Evolution Along the Red Giant Branch |
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397 | (4) |
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401 | (1) |
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33.5 Numerical Results for the Helium Flash |
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402 | (5) |
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33.6 Evolution After the Helium Flash |
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407 | (3) |
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33.7 Evolution from the Zero-Age Horizontal Branch |
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410 | (7) |
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Part VII Late Phases of Stellar Evolution |
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34 Evolution on the Asymptotic Giant Branch |
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417 | (22) |
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34.1 Nuclear Shells on the Asymptotic Giant Branch |
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417 | (2) |
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34.2 Shell Sources and Their Stability |
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419 | (3) |
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34.3 Thermal Pulses of a Shell Source |
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422 | (2) |
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34.4 The Core-Mass-Luminosity Relation for Large Core Masses |
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424 | (2) |
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34.5 Nucleosynthesis on the AGB |
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426 | (4) |
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34.6 Mass Loss on the AGB |
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430 | (3) |
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34.7 A Sample AGB Evolution |
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433 | (3) |
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436 | (2) |
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438 | (1) |
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35 Later Phases of Core Evolution |
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439 | (10) |
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439 | (2) |
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35.2 Evolution of the Central Region |
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441 | (8) |
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36 Final Explosions and Collapse |
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449 | (26) |
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36.1 The Evolution of the CO-Core |
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450 | (4) |
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36.2 Carbon Ignition in Degenerate Cores |
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454 | (7) |
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454 | (1) |
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36.2.2 Nuclear Statistical Equilibrium |
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455 | (3) |
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36.2.3 Hydrostatic and Convective Adjustment |
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458 | (1) |
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459 | (2) |
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36.2.5 Carbon Burning in Accreting White Dwarfs |
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461 | (1) |
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36.3 Collapse of Cores of Massive Stars |
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461 | (10) |
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36.3.1 Simple Collapse Solutions |
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462 | (3) |
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36.3.2 The Reflection of the Infall |
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465 | (1) |
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36.3.3 Effects of Neutrinos |
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466 | (3) |
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36.3.4 Electron-Capture Supernovae |
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469 | (1) |
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36.3.5 Pair-Creation Instability |
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469 | (2) |
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36.4 The Supernova-Gamma-Ray-Burst Connection |
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471 | (4) |
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Part VIII Compact Objects |
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475 | (22) |
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37.1 Chandrasekhar's Theory |
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475 | (4) |
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37.2 The Corrected Mechanical Structure |
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479 | (8) |
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480 | (2) |
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37.2.2 Pycnonuclear Reactions |
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482 | (1) |
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483 | (1) |
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37.2.4 Nuclear Equilibrium |
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483 | (4) |
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37.3 Thermal Properties and Evolution of White Dwarfs |
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487 | (10) |
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497 | (12) |
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38.1 Cold Matter Beyond Neutron Drip |
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497 | (4) |
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38.2 Models of Neutron Stars |
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501 | (8) |
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509 | (10) |
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40 Adiabatic Spherical Pulsations |
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519 | (10) |
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40.1 The Eigenvalue Problem |
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519 | (4) |
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40.2 The Homogeneous Sphere |
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523 | (2) |
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40.3 Pulsating Polytropes |
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525 | (4) |
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41 Non-adiabatic Spherical Pulsations |
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529 | (14) |
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41.1 Vibrational Instability of the Piston Model |
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529 | (2) |
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41.2 The Quasi-adiabatic Approximation |
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531 | (1) |
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532 | (3) |
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534 | (1) |
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534 | (1) |
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41.4 Stars Driven by the κ Mechanism: The Instability Strip |
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535 | (6) |
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41.5 Stars Driven by the ε Mechanism |
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541 | (2) |
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42 Non-radial Stellar Oscillations |
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543 | (14) |
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42.1 Perturbations of the Equilibrium Model |
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543 | (2) |
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42.2 Normal Modes and Dimensionless Variables |
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545 | (3) |
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548 | (4) |
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42.4 Stars Showing Non-radial Oscillations |
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552 | (5) |
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43 The Mechanics of Rotating Stellar Models |
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557 | (8) |
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43.1 Uniformly Rotating Liquid Bodies |
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557 | (3) |
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560 | (2) |
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43.3 Slowly Rotating Polytropes |
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562 | (3) |
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44 The Thermodynamics of Rotating Stellar Models |
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565 | (10) |
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44.1 Conservative Rotation |
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565 | (1) |
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44.2 Von Zeipel's Theorem |
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566 | (1) |
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44.3 Meridional Circulation |
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567 | (2) |
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44.4 The Non-conservative Case |
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569 | (1) |
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44.5 The Eddington--Sweet Timescale |
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570 | (3) |
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44.6 Meridional Circulation in Inhomogeneous Stars |
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573 | (2) |
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45 The Angular-Velocity Distribution in Stars |
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575 | (12) |
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575 | (2) |
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577 | (5) |
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582 | (5) |
References |
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587 | (8) |
Index |
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595 | |