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Part I The Basic Equations

1 Coordinates, Mass Distribution, and Gravitational Field

in Spherical Stars

1.1 Eulerian Description

1.2 Lagrangian Description

1.3 The Gravitational Field

2 Conservation of Momentum

2.1 Hydrostatic Equilibrium

2.2 The Role of Density and Simple Solutions

2.3 Simple Estimates of Central Values Pc; Tc

2.4 The Equation of Motion for Spherical Symmetry

2.5 The Non-spherical Case

2.6 Hydrostatic Equilibrium in General Relativity

2.7 The Piston Model

3 The Virial Theorem

3.1 Stars in Hydrostatic Equilibrium

3.2 The Virial Theorem of the Piston Model

3.3 The Kelvin-Helmholtz Timescale

3.4 The Virial Theorem for Non-vanishing Surface Pressure

4 Conservation of Energy

4.1 Thermodynamic Relations

4.2 The Perfect Gas and the Mean MolecularWeight

4.3 Thermodynamic Quantities for the Perfect, Monatomic Gas

4.4 Energy Conservation in Stars

4.5 Global and Local Energy Conservation

4.6 Timescales

5 Transport of Energy by Radiation and Conduction

5.1 Radiative Transport of Energy

5.1.1 Basic Estimates

5.1.2 Diffusion of Radiative Energy

5.1.3 The Rosseland Mean for

5.2 Conductive Transport of Energy

5.3 The Thermal Adjustment Time of a Star

5.4 Thermal Properties of the Piston Model

6 Stability Against Local, Non-spherical Perturbations

6.1 Dynamical Instability

6.2 Oscillation of a Displaced Element

6.3 Vibrational Stability

6.4 The Thermal Adjustment Time

6.5 Secular Instability

6.6 The Stability of the Piston Model

7 Transport of Energy by Convection

7.1 The Basic Picture

7.2 Dimensionless Equations

7.3 Limiting Cases, Solutions, Discussion

7.4 Extensions of the Mixing-Length Theory

8 The Chemical Composition

8.1 Relative Mass Abundances

8.2 Variation of Composition with Time

8.2.1 Radiative Regions

8.2.2 Diffusion

8.2.3 Convective Regions

9 Mass Loss

Part II The Overall Problem

10 The Differential Equations of Stellar Evolution

10.1 The Full Set of Equations

10.2 Timescales and Simplifications

11 Boundary Conditions

11.1 Central Conditions

11.2 Surface Conditions

11.3 Influence of the Surface Conditions and Properties of

Envelope Solutions

11.3.1 Radiative Envelopes

11.3.2 Convective Envelopes

11.3.3 Summary

11.3.4 The T _r Stratification

12 Numerical Procedure

12.1 The ShootingMethod

12.2 The Henyey Method

12.3 Treatment of the First- and Second-Order Time Derivatives

12.4 Treatment of the Diffusion Equation

12.5 Treatment of Mass Loss

12.6 Existence and Uniqueness

Part III Properties of Stellar Matter

13 The Perfect Gas with Radiation

13.1 Radiation Pressure

13.2 Thermodynamic Quantities

14 Ionization

14.1 The Boltzmann and Saha Formulae

14.2 Ionization of Hydrogen

14.3 Thermodynamical Quantities for a Pure Hydrogen Gas

14.4 Hydrogen-HeliumMixture

14.5 The General Case

14.6 Limitation of the Saha Formula

15 The Degenerate Electron Gas

15.1 Consequences of the Pauli Principle

15.2 The Completely Degenerate Electron Gas

15.3 Limiting Cases

15.4 Partial Degeneracy of the Electron Gas

16 The Equation of State of Stellar Matter

16.1 The Ion Gas

16.2 The Equation of State

16.3 Thermodynamic Quantities

16.4 Crystallization

16.5 Neutronization

16.6 Real Gas Effects

17 Opacity

17.1 Electron Scattering

17.2 Absorption Due to Free-Free Transitions

17.3 Bound-Free Transitions

17.4 Bound-Bound Transitions

17.5 The Negative Hydrogen Ion

17.6 Conduction

17.7 Molecular Opacities

17.8 Opacity Tables

18 Nuclear Energy Production

18.1 Basic Considerations

18.2 Nuclear Cross Sections

18.3 Thermonuclear Reaction Rates

18.4 Electron Shielding

18.5 The Major Nuclear Burning Stages

18.5.1 Hydrogen Burning.

18.5.2 Helium Burning

18.5.3 Carbon Burning and Beyond

18.6 Neutron-Capture Nucleosynthesis

18.7 Neutrinos

Part IV Simple Stellar Models

19 Polytropic Gaseous Spheres

19.1 Polytropic Relations

19.2 Polytropic Stellar Models

19.3 Properties of the Solutions

19.4 Application to Stars

19.5 Radiation Pressure and the Polytrope n D 3.

19.6 Polytropic Stellar Models with Fixed K

19.7 Chandrasekhar's Limiting Mass

19.8 Isothermal Spheres of an Ideal Gas

19.9 Gravitational and Total Energy for Polytropes

19.10 Supermassive Stars

19.11 A Collapsing Polytrope

20 Homology Relations

20.1 Definitions and Basic Relations

20.2 Applications to Simple Material Functions

20.2.1 The Case ? D 0

20.2.2 The Case ? D ? D ' D 1; a D b D 0

20.2.3 The Role of the Equation of State

20.3 Homologous Contraction

21 Simple Models in the U-V Plane

21.1 The U-V Plane

21.2 Radiative Envelope Solutions

21.3 Fitting of a Convective Core

21.4 Fitting of an Isothermal Core

22 The Zero-AgeMain Sequence

22.1 Surface Values

22.2 Interior Solutions

22.3 Convective Regions

22.4 Extreme Values of M

22.5 The Eddington Luminosity

23 Other Main Sequences

23.1 The Helium Main Sequence.

23.2 The Carbon Main Sequence.

23.3 Generalized Main Sequences

24 The Hayashi Line

24.1 Luminosity of Fully ConvectiveModels

24.2 A Simple Description of the Hayashi Line

24.3 The Neighbourhood of the Hayashi Lineand the Forbidden Region

24.4 Numerical Results

24.5 Limitations for Fully ConvectiveModels

25 Stability Considerations

25.1 General Remarks

25.2 Stability of the Piston Model

25.2.1 Dynamical Stability

25.2.2 Inclusion of Non-adiabatic Effects

25.3 Stellar Stability

25.3.1 Perturbation Equations

25.3.2 Dynamical Stability

25.3.3 Non-adiabatic Effects

25.3.4 The Gravothermal Specific Heat

25.3.5 Secular Stability Behaviour of Nuclear Burning

Part V Early Stellar Evolution

26 The Onset of Star Formation

26.1 The Jeans Criterion

26.1.1 An Infinite Homogeneous Medium.

26.1.2 A Plane-Parallel Layer in Hydrostatic Equilibrium

26.2 Instability in the Spherical Case

26.3 Fragmentation

27 The Formation of Protostars.

27.1 Free-Fall Collapse of a Homogeneous Sphere

27.2 Collapse onto a Condensed Object

27.3 A Collapse Calculation

27.4 The Optically Thin Phase and the Formation of a Hydrostatic Core

27.5 Core Collapse

27.6 Evolution in the Hertzsprung-Russell Diagram

28 Pre-Main-Sequence Contraction.

28.1 Homologous Contraction of a Gaseous Sphere

28.2 Approach to the Zero-Age Main Sequence

29 From the Initial to the Present Sun

29.1 Known Solar Data

29.2 Choosing the Initial Model

29.3 A Standard Solar Model

29.4 Results of Helioseismology.

29.5 Solar Neutrinos.

30 Evolution on the Main Sequence

30.1 Change in the Hydrogen Content

30.2 Evolution in the Hertzsprung-Russell Diagram

30.3 Timescales for Central Hydrogen Burning

30.4 Complications Connected with Convection

30.4.1 Convective Overshooting

30.4.2 Semiconvection

30.5 The Sch¨onberg-Chandrasekhar Limit

30.5.1 A Simple Approach: The Virial Theorem and Homology

30.5.2 Integrations for Core and Envelope.

30.5.3 Complete Solutions for Stars with Isothermal Cores

Part VI Post-Main-Sequence Evolution

31 Evolution Through Helium Burning: Intermediate-Mass Stars

31.1 Crossing the Hertzsprung Gap

31.2 Central Helium Burning

31.3 The Cepheid Phase.

31.4 To Loop or Not to Loop

31.5 After Central Helium Burning

32 Evolution Through Helium Burning: Massive Stars

32.1 Semiconvection

32.2 Overshooting

32.3 Mass Loss

33 Evolution Through Helium Burning: Low-Mass Stars

33.1 Post-Main-Sequence Evolution

33.2 Shell-Source Homology

33.3 Evolution Along the Red Giant Branch.

33.4 The Helium Flash

33.5 Numerical Results for the Helium Flash

33.6 Evolution After the Helium Flash.

33.7 Evolution from the Zero-Age Horizontal Branch

Part VII Late Phases of Stellar Evolution

34 Evolution on the Asymptotic Giant Branch

34.1 Nuclear Shells on the Asymptotic Giant Branch

34.2 Shell Sources and Their Stability.

34.3 Thermal Pulses of a Shell Source.

34.4 The Core-Mass-Luminosity Relation for Large Core Masses.

34.5 Nucleosynthesis on the AGB

34.6 Mass Loss on the AGB

34.7 A Sample AGB Evolution

34.8 Super-AGB Stars.

34.9 Post-AGB Evolution

35 Later Phases of Core Evolution

35.1 Nuclear Cycles

35.2 Evolution of the Central Region

36 Final Explosions and Collapse

36.1 The Evolution of the CO-Core

36.2 Carbon Ignition in Degenerate Cores

36.2.1 The Carbon Flash

36.2.2 Nuclear Statistical Equilibrium

36.2.3 Hydrostatic and Convective Adjustment

36.2.4 Combustion Fronts.

36.2.5 Carbon Burning in AccretingWhite Dwarfs

36.3 Collapse of Cores of Massive Stars

36.3.1 Simple Collapse Solutions

36.3.2 The Reflection of the Infall

36.3.3 Effects of Neutrinos

36.3.4 Electron-Capture Supernovae

36.3.5 Pair-Creation Instability

36.4 The Supernova-Gamma-Ray-Burst Connection

Part VIII Compact Objects

37 White Dwarfs

37.1 Chandrasekhar's Theory

37.2 The Corrected M<