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Astronomy - Astronomy, Observations and Techniques | Stellar Structure and Evolution

Stellar Structure and Evolution

Kippenhahn, Rudolf, Weigert, Alfred

1st ed. 1990. Corr. 3rd printing 1994, XVI, 468 pp. 192 figs.

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The attempt to understand the physics of the structure of stars and their change in time - their evolution - has been bothering many physicists and astronomers ever since the last century. This long chain of successful research is well documented not only by numerous papers in the corresponding journals but also by a series of books. Some of them are so excellently written that despite their age they can still be recommended, and not only as documents of the state of the art at that time. A few outstanding examples are the books of R. Emden (1907), A. S. Eddington (1926), S. Chandrasekhar (1939), and M. Schwarzschild (1958). But our science has rapidly expanded in the last few decades, and new aspects have emerged which could not even be anticipated, say, 30 years ago and which today have to be carefully explored. This does not mean, however, that our ambition is to present a complete account of the latest and most refined numerical results. This can well be left to the large and growing number of excellent review articles. The present book is intended rather to be a textbook that will help students and teachers to understand these results as far as possible and present them in a simple and clear manner. We know how difficult this is since we ourselves have tried for the largest part of our scientific career to understand "how the stars work" - and then to make others believe it.

Content Level » Lower undergraduate

Keywords » Sonne - Sternaufbau - Sterne - Sternentwicklung - astrophysics - stars - stellar - stellar models - sun

Related subjects » Astronomy, Observations and Techniques - Astrophysics and Astroparticles

Table of contents 

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 Time-scale.- 3.4. The Virial Theorem for Non-vanishing Surface Pressure.- 4. Conservation of Energy.- 4.1 Thermodynamic Relations.- 4.2 Energy Conservation in Stars.- 4.3 Global and Local Energy Conservation.- 4.4 Time-scales.- 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.- 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.- II The Overall Problem.- 9. The Differential Equations of Stellar Evolution.- 9.1 The Full Set of Equations.- 9.2 Time-scales and Simplifications.- 10. Boundary Conditions.- 10.1 Central Conditions.- 10.2 Surface Conditions.- 10.3 Influence of the Surface Conditions and Properties of Envelope Solutions.- 10.3.1 Radiative Envelopes.- 10.3.2 Convective Envelopes.- 10.3.3 Summary.- 10.3.4 The T-r Stratification.- 11. Numerical Procedure.- 11.1 The Shooting Method.- 11.2 The Henyey Method.- 11.3 Treatment of the First- and Second-Order Time Derivatives.- 12. Existence and Uniqueness of Solutions.- 12.1 Notation and Outline of the Procedure.- 12.2 Models in Complete Equilibrium.- 12.2.1 Fitting Conditions in the Pc — Tc Plane.- 12.2.2 Local Uniqueness.- 12.2.3 Variation of Parameters.- 12.3 Hydrostatic Models without Thermal Equilibrium.- 12.3.1 Degrees of Freedom and Fitting Conditions.- 12.3.2 Local Uniqueness.- 12.3.3 Variation of Parameters.- 12.4 Connection with Stability Problems.- 12.5 Non-local Properties of Equilibrium Models.- III Properties of Stellar Matter.- 13. The Ideal Gas with Radiation.- 13.1 Mean Molecular Weight and 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-Helium Mixtures.- 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.- 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 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 Burnings.- 18.5.1 Hydrogen Burning.- 18.5.2 Helium Burning.- 18.5.3 Carbon Burning etc..- 18.6 Neutrinos.- 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 = 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 ? = ? = ? = 1, a = b = 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 Main Sequence.- 22.1 Surface Values.- 22.2 Interior Solutions.- 22.3 Convective Regions.- 22.4 Extreme Values of M.- 23. Other Main Sequences.- 23.1 The Helium Main Sequence.- 23.2 The Carbon Main Sequence.- 23.3 Main Sequences as Linear Series of Stellar Models.- 23.4 Generalized Main Sequences.- 24. The Hayashi Line.- 24.1 Luminosity of Fully Convective Models.- 24.2 A Simple Description of the Hayashi Line.- 24.3 The Neighbourhood of the Hayashi Line and the Forbidden Region.- 24.4 Numerical Results.- 24.5 Limitations for Fully Convective Models.- 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.- 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 Choosing the Initial Model.- 29.2 Solar Neutrinos.- 30. Chemical Evolution on the Main Sequence.- 30.1 Change in the Hydrogen Content.- 30.2 Evolution in the Hertzsprung-Russell Diagram.- 30.3 Time-scales for Central Hydrogen Burning.- 30.4 Complications Connected with Convection.- 30.4.1 Convective Overshooting.- 30.4.2 Semiconvection.- 30.5 The Schönberg-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.- VI Post-Main-Sequence Evolution.- 31. Evolution Through Helium Burning — Massive 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 — Low-Mass Stars.- 32.1 Post-Main-Sequence Evolution.- 32.2 Shell-Source Homology.- 32.3 Evolution to the Helium Flash.- 32.4 The Helium Flash.- 32.5 Numerical Results for the Helium Flash.- 32.6 Evolution after the Helium Flash.- 32.7 Evolution from the Zero-Age Horizontal Branch.- 32.8 Equilibrium Models with Helium Cores — Continued.- 33. Later Phases.- 33.1 Nuclear Cycles.- 33.2 Shell Sources and Their Stability.- 33.3 Thermal Pulses of a Shell Source.- 33.4 Evolution of the Central Region.- 33.5 The Core-Mass-Luminosity Relation for Large Core Masses.- 34. Final Explosions and Collapse.- 34.1 The Evolution of the C-O Core.- 34.2 Carbon Burning in Degenerate Cores.- 34.2.1 The Carbon Flash.- 34.2.2 Nuclear Statistical Equilibrium.- 34.2.3 Hydrostatic and Convective Adjustment.- 34.2.4 Combustion Fronts.- 34.2.5 Numerical Solutions.- 34.2.6 Carbon Burning in Accreting White Dwarfs.- 34.3 Collapse of Cores of Massive Stars.- 34.3.1 Simple Collapse Solutions.- 34.3.2 The Reflection of the Infall.- 34.3.3 Effects of Neutrinos.- 34.3.4 Numerical Results.- 34.3.5 Pair-Creation Instability.- VII Compact Objects.- 35. White Dwarfs.- 35.1 Chandrasekhar’s Theory.- 35.2 The Corrected Mechanical Structure.- 35.3 Thermal Properties and Evolution of White Dwarfs.- 36. Neutron Stars.- 36.1 Cold Matter Beyond Neutron Drip.- 36.2 Models of Neutron Stars.- 37. Black Holes.- VIII Pulsating Stars.- 38. Adiabatic Spherical Pulsations.- 38.1 The Eigenvalue Problem.- 38.2 The Homogeneous Sphere.- 38.3 Pulsating Polytropes.- 39. Non-adiabatic Spherical Pulsations.- 39.1 Vibrational Instability of the Piston Model.- 39.2 The Quasi-adiabatic Approximation.- 39.3 The Energy Integral.- 39.3.1 The ? Mechanism.- 39.3.2 The ? Mechanism.- 39.4 Stars Driven by the ? Mechanism — The Instability Strip.- 39.5 Stars Driven by the ? Mechanism.- 40. Non-radial Stellar Oscillations.- 40.1 Perturbations of the Equilibrium Model.- 40.2 Normal Modes and Dimensionless Variables.- 40.3 The Eigenspectra.- 40.4 Stars Showing Non-radial Oscillations.- IX Stellar Rotation.- 41. The Mechanics of Rotating Stellar Models.- 41.1 Uniformly Rotating Liquid Bodies.- 41.2 The Roche Model.- 41.3 Slowly Rotating Polytropes.- 42. The Thermodynamics of Rotating Stellar Models.- 42.1 Conservative Rotation 4.- 42.2 Von Zeipel’s Theorem.- 42.3 Meridional Circulation.- 42.4 The Non-conservative Case.- 42.5 The Eddington-Sweet Time-scale.- 42.6 Meridional Circulation in Inhomogeneous Stars.- 43. The Angular-Velocity Distribution in Stars.- 43.1 Viscosity.- 43.2 Dynamical Stability.- 43.3 Secular Stability.- References.

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