The Fundamentals Of Stellar Astrophysics - Collins G. W.pdf

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1 Introduction and Fundamental Principles
The Fundamentals of
StellarAstrophysics
George W. Collins, II
 Copyright 2003: All sections of this book may be reproduced as
long as proper attribution is given.
Contents
. . .
Page
Preface to the Internet Edition
Preface to the W. H. Freeman Edition
xiv
xv
Part I Stellar Interiors
Chapter 1
Introduction and Fundamental Principles
1.1 Stationary or “Steady” Properties of matter
a Phase Space and Phase Density
b Macrostates and Microstates .
c Probability and Statistical Equilibrium
d Quantum Statistics
e Statistical Equilibrium for a Gas
f Thermodynamic Equilibrium – Strict and
Local
1.2 Transport Phenomena
a. Boltzmann Transport Equation
b. Homogeneous Boltzmann Transport Equation
and Liouville’s Theorem
c. Moments of the Boltzmann Transport Equation
and Conservation Laws
1.3 Equation of State for the Ideal Gas and Degenerate
Matter
3
5
5
6
6
9
11
15
15
15
17
18
26
Problems
References and Supplemental Reading
32
33
ii
Chapter 2
Basic Assumptions, Theorems, and Polytropes
2.1 Basic Assumptions
2.2 Integral Theorems from Hydrostatic Equilibrium
a Limits of State Variables
b β * Theorem and Effects of Radiation
Pressure
2.3 Homology Transformations
2.4 Polytropes
a Polytropic Change and the Lane-Emden
Equation
34
34
36
36
38
40
42
43
46
47
49
51
53
54
b
Mass-Radius Relationship for Polytropes
c
Homology Invariants
d
Isothermal Sphere
e
Fitting Polytropes Together
Problems
References and Supplemental Reading
Chapter 3
Sources and Sinks of Energy
3.1 "Energies" of Stars
a Gravitational Energy
b Rotational Energy
c Nuclear Energy
3.2 Time Scales
a Dynamical Time Scale
b Kelvin-Helmholtz (Thermal) Time Scale
c Nuclear (Evolutionary) Time Scale
3.3 Generation of Nuclear Energy
a General Properties of the Nucleus
b The Bohr Picture of Nuclear Reactions
c Nuclear Reaction Cross Sections
d Nuclear Reaction Rates
e Specific Nuclear Reactions
Problems
References and Supplemental Reading
56
57
57
59
60
61
61
62
63
64
65
66
68
70
72
75
75
iii
Chapter 4
Flow of Energy through the Star and Construction of Stellar
Models
77
4.1 The Ionization, Abundances, and Opacity of
Stellar Material
a Ionization and the Mean Molecular Weight
b Opacity
4.2 Radiative Transport and the Radiative Temperature
Gradient
a Radiative Equilibrium
b Thermodynamic Equilibrium and Net Flux
c Photon Transport and the Radiative Gradient
d Conservation of Energy and the Luminosity
4.3 Convective Energy Transport
a Adiabatic Temperature Gradient
b Energy Carried by Convection
4.4 Energy Transport by Conduction
a Mean Free Path
b Heat Flow
4.5 Convective Stability
a Efficiency of Transport Mechanisms
b Schwarzschild Stability Criterion
4.6 Equations of Stellar Structure
4.7 Construction of a Model Stellar Interior
a
78
78
80
Boundary Conditions
86
86
86
87
89
90
90
91
94
94
95
96
96
97
100
101
102
102
b
Schwarzschild Variables and Method
c
Henyey Relaxation Method for Construction of
Stellar Models
105
109
110
Problems
References and Supplemental Reading
iv
Chapter 5
Theory of Stellar Evolution
5.1 The Ranges of Stellar Masses, Radii, and
Luminosity
5.2 Evolution onto the Main Sequence
a Problems concerning the Formation of
Stars
b Contraction out of the Interstellar Medium
c Contraction onto the Main Sequence
5.3 The Structure and Evolution of Main Sequence Stars
a Lower Main Sequence Stars
b Upper Main Sequence Stars
5.4 Post Main Sequence Evolution
a Evolution off the Lower Main Sequence
b Evolution away from the Upper Main Sequence
c The Effect of Mass-loss on the Evolution of Stars
5.5 Summary and Recapitulation
a Core Contraction - Envelope Expansion: Simple
Reasons
b Calculated Evolution of a 5 M ⊙ star
Problems
References and Supplemental Reading
112
113
114
114
116
119
125
126
128
129
129
136
138
139
140
143
144
145
Chapter 6
Relativistic Stellar Structure
6.1 Field Equations of the General Theory of Relativity
6.2 Oppenheimer-Volkoff Equation of Hydrostatic
Equilibrium
a Schwarzschild Metric
b Gravitational Potential and Hydrostatic
Equilibrium
149
150
152
152
154
6.3 Equations of Relativistic Stellar Structure and
Their Solutions
154
155
156
158
a
A Comparison of Structure Equations
b
A Simple Model
c
Neutron Star Structure
v

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