Structure and Evolution of Stars

✍ Scribed by Martin Schwarzschild

• Publisher: Princeton University Press
• Year: 2015
• Tongue: English
• Leaves: 316
• Series: Princeton Legacy Library; 2379
• Category: Library

✦ Synopsis

With the development of nuclear physics the theory of the stellar interior entered a new phase. Many new investigations have been conducted and the results published in a variety of specialized media. This book brings these results together in a single volume and summarizes the present status of the theory of stellar evolution.

Originally published in 1958.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

✦ Table of Contents

PREFACE
CONTENTS
INTRODUCTION
CHAPTER I. OBSERVATIONAL BASIS
§1. Luminosities and Radii
The Hertzsprung-Russell Diagram
Transformation to Luminosities and Radii
Subdwarfs and White Dwarfs
§2. Masses
Spectroscopic Binaries
Visual Binaries
Mass-Luminosity Relation
Masses of Giants and White Dwarfs
§3. Stellar Populations
Brightest Stars in Stellar Systems
Kinematical Behavior
Spectroscopic Differences
Sequence of Stellar Populations
§4. Abundances of the Elements
Composition of the Sun
Composition Differences between Populations
Composition Anomalies
CHAPTER II. PHYSICAL STATE OF THE STELLAR INTERIOR
§5. Hydrostatic and Thermal Equilibrium
Condition of Hydrostatic Equilibrium
The Energy Stores of a Star
Condition of Thermal Equilibrium
§6. Radiative Energy Transport
The General Radiation Transfer Equation
Radiative Equilibrium in the Stellar Interior
The Magnitude of Stellar Luminosities and the Mass-Luminosity Relation
Stability of Thermal Equilibrium
§7. Convective Energy Transport
Stability Condition for Radiative Equilibrium
Convective Equilibrium
Energy Transport by Convection
Adiabatie Approximation for Temperature Gradient
Character of Convection in Stellar Interior
§8. Equation of State
Ideal Gas
Radiation Pressure
Degeneracy
Complete Degeneracy
Degeneracy Limits
Partial Degeneracy
Semi-relativistic Degeneracy
Summary
§9. Opacity
Atomic Absorption Coefficients
The Over-all Absorption Coefficient
The Rosseland Mean
Kramers’ Law for Bound-Free Transitions
Kramers’ Law for Free-Free Transitions
Electron Scattering
Temperature-Density Diagram for the Opacity
Mixed Opacities
§10. Nuclear Reactions
Nuclear Processes at Stellar Temperatures
The Proton-Proton Reaction
The Carbon Cycle
Nuclear Reaction Rates
Mean Reaction Times and Equilibrium Abundances
Rate of Energy Generation by Proton-Proton Reaction and Carbon Cycle
The Triple-Alpha Process
Rate of Change of Hydrogen and Helium Abundances
Transmutations of the Heavier Elements
Summary
§11. Surface Layers
The Zero Boundary Conditions
The Physical Boundary Conditions
The Pressure-Temperature Relation in Stellar Envelopes
The Ionization Zone of Hydrogen and Helium
The Practical Boundary Conditions
CHAPTER III. MATHEMATICAL TECHNIQUES
§12. The Over-all Problem
Uniqueness of the Solution
lnhomogeneities in Composition and Evolutionary Model Sequences
The Over-all Problem for Fast Evolutionary Phases
§13. Transformations and Invariants
Integrations from Center and from Surface; Fitting Conditions
Standard Transformation
Reduction in the Numerical Work by the Standard Transformation
Supplementary Transformation for Integrations from the Center
The Invariants and the UV Plane
The Fitting Procedure in the UV Plane
§14. Numerical Integrations
Developments at the Center
Developments at the Surface
Logarithmic Variables
Procedures for Step-by-Step Integrations
CHAPTER IV. INITIAL STELLAR STRUCTURE
§15. The Upper Main Sequence
Choice of Gas Characteristics Relations
Equations for the Envelope
Equations for the Core
Choice of Mass and Composition
Fitting Procedure and Computation of Model Characteristics
Theoretical Results and Comparison With Observations
Dependence of Results on Composition
§16. The Lower Main Sequence
Choice of Gas Characteristics Relations
Equations for the Envelope
Equations for the Core
Fitting Procedure and Computation of Model Characteristics
Relation of Model Characteristics to Observed L, M, and R Values
Checks and Results
§17. The Subdwarfs
Effects of Low Abundance of the Heavier Elements
Gas Characteristics Relations and Boundary Conditions
Construction of Radiative Model
Effects of Possible Convective Envelopes
Problem of Helium Abundance in Subdwarfs
§18. The Apsidal-Motion Test
Observation of Apsidal Motion
Simplifying Approximations
Hydrostatic Equilibrium Conditions
Transformation of the Poisson Equation
Differential Equation for the Distortion Function C2
The Surface Conditions
The Perturbing Potential and the Rate of Apsidal Motion
Theoretical Results and Comparison With Observations
§19. Pre-main-sequence Contraction
Homologous Contraction
Construction of Contraction Model
Results for the Contraction Model
Rate of Contraction
CHAPTER V. EARLY EVOLUTIONARY PHASES
§20. Simplified Example of Evolution
Simplifying Circumstances and Basic Equations
Fitting Conditions With Discontinuity of Composition
Construction of Models
Evolutionary Track in Hertzsprung-Russell Diagram
Comparison of Inhomogeneous and Homogeneous Evolutions
§21. Rotational Mixing
Hydrostatic Equilibrium in a Rotating Star
Deficiency of Radiation Flux and Meridional Circulation
Determination of Rotational Distortion
Determination of the Divergence of the Radiation Flux
Speed of the Meridional Circulation
Numerical Results
Effects of Inhomogeneities in Composition
§22. Evolution of Upper Main-Sequence Stars
Occurrence of Inhomogeneous Zone
Basic Equations and Definitions
Construction of the “First Model”
Construction of the Subsequent Models
Results for Hydrogen Depletion
Later Phases With Hydrogen Burning in the Intermediate Zone
Evolutionary Tracks in Hertzsprung-Russell Diagram
Time Scale of Evolution
Apsidal-Motion Test for Evolutionary Models
§23. Evolution of the Sun
Depletion of Hydrogen in the Sun
Construction of Inhomogeneous Solar Model
Results for the Present State of the Sun
Changes in the Solar Luminosity and Radius in the Past
CHAPTER VI. ADVANCED EVOLUTIONARY PHASES
§24. Growth of Isothermal Core
Stars With Cores Exhausted of Hydrogen
Dilemma of Massive Stars With Isothermal Cores
Stars of Moderate Mass With Partially Degenerate Cores
Stars with Large Partially Degenerate Cores
The Surface Layers of Stars With Isothermal Cores
Results for Stars of Various Compositions
Onset of Fast Core Contraction
§25. Heating of Core by Contraction
Contracting Cores in Massive Stars
Gravitational Energy Release in a Contracting Core
Evolution of Massive Stars During Core Contraction
Core Contraction in Stars of Moderate Mass
CHAPTER VII. FINAL STELLAR STRUCTURE
§26. Structure of White Dwarfs
Models for Completely Degenerate Stars
Corrections to the Degenerate Equation of State
Mass-Radius Relation and Mass Limit
Location of Degenerate Stars in Hertzsprung-Russell Diagram
§27. Thermodynamics of White Dwarfs
The Internal Temperatures
Extent of Non-Degenerate Layers
Proton-Proton Reaction and the Interior Hydrogen Content
Secular Instability Caused By Nuclear Reactions
Pulsational Instability Caused by Nuclear Reactions
Residual Thermal Energy and Cooling Time
CHAPTER VIII. SUMMARY AND REVIEW
§28. Physical State of the Stellar Interior
Temperatures and Densities
Equation of State and Opacity
Nuclear Energy Sources
Density Distribution
§29. Evolutionary Tracks in the Hertzsprung-Russell Diagram
Evolutionary Tracks of Massive Stars
Evolutionary Tracks of Medium-Weight Stars
Mass Ejection
Time Lines in the Hertzsprung-Russell Diagram
Age and Composition of Clusters
§30. Vital Statistics of the Stars
Galactic Densities and Luminosity Functions
Birth-Rate Function
Death Rate
Irreversible Developments
REFERENCES
INDEX