The Fundamentals of Stellar Astrophysics

The Fundamentals of Stellar Astrophysics

George W. Collins, II
Published in: W H Freeman & Co
Release Year: 1989
ISBN: 978-0716-7-1993-9
Pages: 525
Edition: First Edition
File Size: 9 MB
File Type: pdf
Language: English

Description of The Fundamentals of Stellar Astrophysics

One may justifiability wonder why anyone would take the time to put a decade-old book on astrophysics on the WEB. Several events of the past few months have led me to believe that may well be some who wish to learn about the basics of stellar structure. Since the fundamentals of stellar astrophysics have changed little in the past decade and as The Fundamentals of Stellar Astrophysics book has been out of print for nearly that long, I felt that some may still find it useful for learning the basics. 
The task was somewhat facilitated by my discovery of some old machine-readable disks that contained a version of the book including some of the corrections to the published version. With considerable help from Charles Knox, I was able to retrieve the information from the out-dated format and transfer the text to a contemporary word processor. However, the equations were lost in the process so that their inclusion in The Fundamentals of Stellar Astrophysics edition had to take another form. 
This was accomplished by scanning the originals from the book and correcting those with errors in a variety of ways. This accounts for the fonts of the equations being somewhat at variance with that of the text. However, I believe that difference does not detract significantly from the understandability of the material. The most common form of correction was to simply re-set them with an equation editor embedded in the WORD processor. Equations look somewhat different from the others. 
However, the ability to correct errors that arose in the published edition seemed to outweigh any visual inconvenience.
The reader will notice that all the recommended reading is to books published prior to 1987. Some of this is a result of a predilection of mine to cite initial references, but most of it is a result of my failure to update the references to contemporary times. There have been a number of books and many articles during the past decade or so which would greatly enlighten the reader, but to include them would be a major part of a new book and lies beyond the scope of this effort.

Content of The Fundamentals of Stellar Astrophysics

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
References and Supplemental Reading

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
2.3 Homology Transformations
2.4 Polytropes
a Polytropic Change and the Lane-Emden
b Mass-Radius Relationship for Polytropes
c Homology Invariants
d Isothermal Sphere
e Fitting Polytropes Together
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
References and Supplemental Reading

Chapter 4
Flow of Energy through the Star and Construction of Stellar
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
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 Boundary Conditions
b Schwarzschild Variables and Method
c Henyey Relaxation Method for Construction of
Stellar Models
References and Supplemental Reading

Chapter 5
Theory of Stellar Evolution
5.1 The Ranges of Stellar Masses, Radii, and
5.2 Evolution onto the Main Sequence
a Problems concerning the Formation of
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
b Calculated Evolution of a 5 M⊙ star
References and Supplemental Reading

Chapter 6
Relativistic Stellar Structure
6.1 Field Equations of the General Theory of Relativity
6.2 Oppenheimer-Volkoff Equation of Hydrostatic
a Schwarzschild Metric
b Gravitational Potential and Hydrostatic
6.3 Equations of Relativistic Stellar Structure and
Their Solutions
a A Comparison of Structure Equations
b A Simple Model
c Neutron Star Structure
6.4 Relativistic Polytrope of Index 3
a Virial Theorem for Relativistic Stars
b Minimum Radius for White Dwarfs
c Minimum Radius for Super-massive Stars
6.5 Fate of Super-massive Stars
a Eddington Luminosity
b Equilibrium Mass-Radius Relation
c Limiting Masses for Super-massive Stars
References and Supplemental Reading

Chapter 7
Structure of Distorted Stars
7.1 Classical Distortion: The Structure Equations
a A Comparison of Structure Equations
b Structure Equations for Cylindrical Symmetry
7.2 Solution of Structure Equations for a Perturbing
a Perturbed Equation of Hydrostatic Equilibrium
b Number of Perturbative Equations versus Number
of Unknowns
7.3 Von Zeipel's Theorem and Eddington-Sweet
Circulation Currents
a Von Zeipel's Theorem
b Eddington-Sweet Circulation Currents
7.4 Rotational Stability and Mixing
a Shear Instabilities
b Chemical Composition Gradient and Suppression
of Mixing
c Additional Types of Instabilities
References and Supplemental Reading

Chapter 8
Stellar Pulsation and Oscillation
8.1 Linear Adiabatic Radial Oscillations
a Stellar Oscillations and the Variational Virial
b Effect of Magnetic Fields and Rotation on Radial
c Stability and the Variational Virial Theorem
d Linear Adiabatic Wave Equation
8.2 Linear Nonadiabatic Radial Oscillations
a Adiabatic Exponents
b Nonadiabatic Effects and Pulsational Stability
c Constructing Pulsational Models
d Pulsational Behavior of Stars
8.3 Nonradial Oscillations
a Nature and Form of Oscillations
b Homogeneous Model and Classification of Modes
c Toroidal Oscillations
d Nonradial Oscillations and Stellar Structure
References and Supplemental Reading
Epilogue to Part I: Stellar Interiors
Part II Stellar Atmospheres

Chapter 9
The Flow of Radiation Through the Atmosphere
9.1 Basic Assumptions for the Stellar Atmosphere
a Breakdown of Strict Thermodynamic
Equilibrium 228
b Assumption of Local Thermodynamic
Equilibrium 229
c Continuum and Spectral Lines 230
d Additional Assumptions of Normal Stellar
Atmospheres 231
9.2 Equation of Radiative Transfer 233
a Specific Intensity and Its Relation to the Density
of Photons in Phase Space 233
b General Equation of Radiative Transfer
c "Creation" Rate and the Source Function
d Physical Meaning of the Source Function 240
e Special Forms of the Redistribution Function 241
9.3 Moments of the Radiation Field 243
a Mean Intensity 244
b Flux 244
c Radiation Pressure 245
9.4 Moments of the Equation of Radiative Transfer
a Radiative Equilibrium and Zeroth Moment of the
Equation of Radiative Transfer
b First Moment of the Equation of Radiative
Transfer and the Diffusion Approximation
c Eddington Approximation 249
Problems 251
Supplemental Reading 252

Chapter 10
Solution of the Equation of Radiative Transfer 253
10.1 Classical Solution to the Equation of Radiative Transfer
and Integral Equations for the Source Function 254
a Classical Solution of the Equation of Transfer for
the Plane-Parallel Atmosphere 254
b Schwarzschild-Milne Integral Equations 257
c Limb-darkening in a Stellar Atmosphere 260
10.2 Gray Atmosphere 263
a Solution of Schwarzschild-Milne Equations for
the Gray Atmosphere 265
b Solutions for the Gray Atmosphere Utilizing the
Eddington Approximation 266
c Solution by Discrete Ordinates: Wick-
Chandrasekhar Method 268
10.3 Nongray Radiative Transfer 274
a Solutions of the Nongray Integral Equation for the
Source Function 275
b Differential Equation Approach: The Feautrier
Method 276
10.4 Radiative Transport in a Spherical Atmosphere 279
a Equation of Radiative Transport in Spherical
b An Approach to Solution of the Spherical Radiative
Transfer Problem 283
Problems 287
References and Supplemental Reading 289

Chapter 11
Environment of the Radiation Field 291
11.1 Statistics of the Gas and the Equation of State 292
a Boltzmann Excitation Formula 292
b Saha Ionization Equilibrium Equation 293
11.2 Continuous Opacity 296
a Hydrogenlike Opacity 296
b Neutral Helium 297
c Quasi-atomic and Molecular States 297
d Important Sources of Continuous Opacity for
Main Sequence Stars 299
11.3 Einstein Coefficients and Stimulated Emission 300
a Relations among Einstein Coefficients 301
b Correction of the Mass Absorption Coefficient for
Stimulated Emission 302
11.4 Definitions and Origins of Mean Opacities 303
a Flux-Weighted (Chandrasekhar) Mean Opacity 304
b Rosseland Mean Opacity 304
c Planck Mean Opacity 306
11.5 Hydrostatic Equilibrium and the Stellar Atmosphere 307
Problems 308
References 309

Chapter 12
The Construction of a Model Stellar Atmosphere 310
12.1 Statement of the Basic Problem 310
12.2 Structure of the Atmosphere, Given the Radiation Field 312
a Choice of the Independent Variable of
Atmospheric Depth 314
b Assumption of Temperature Dependence with
Depth 314
c Solution of the Equation of Hydrostatic
Equilibrium 314
12.3 Calculation of the Radiation Field of the Atmosphere 316
12.4 Correction of the Temperature Distribution and Radiative
Equilibrium 318
a Lambda Iteration Scheme 318
b Avrett-Krook Temperature Correction Scheme 319
12.5 Recapitulation 325
Problems 326
References and Supplemental Reading 328

Chapter 13
Formation of Spectral Lines 330
13.1 Terms and Definitions Relating to Spectral Lines 331
a Residual Intensity, Residual Flux, and
Equivalent Width 331
b Selective (True) Absorption and Resonance
Scattering 333
c Equation of Radiative Transfer for Spectral
Line Radiation 335
13.2 Transfer of Line Radiation through the Atmosphere 336
a Schuster-Schwarzschild Model Atmosphere for
Scattering Lines 336
b Milne-Eddington Model Atmosphere for the
Formation of Spectral Lines 339
Problems 346
Supplemental Reading 347

Chapter 14
Shape of Spectral Lines 348
14.1 Relation between the Einstein, Mass Absorption, and
Atomic Absorption Coefficients 349
14.2 Natural or Radiation Broadening 350
a Classical Radiation Damping 351
b Quantum Mechanical Description of Radiation
Damping 354
c Ladenburg f-value 355
14.3 Doppler Broadening of Spectral Lines 357
a Microscopic Doppler Broadening 358
b Macroscopic Doppler Broadening 364
14.4 Collisional Broadening 369
a Impact Phase-Shift Theory 370
b Static (Statistical) Broadening Theory 378
14.5 Curve of Growth of the Equivalent Width 385
a Schuster-Schwarzschild Curve of Growth 385
b More Advanced Models for the Curve of Growth 389
c Uses of the Curve of Growth 390
Problems 392
References and Supplemental Reading 395

Chapter 15
Breakdown of Local Thermodynamic Equilibrium 398
15.1 Phenomena Which Produce Departures from Local
Thermodynamic Equilibrium 400
a Principle of Detailed Balancing 400
b Interlocking 401
c Collisional versus Photoionization 402
15.2 Rate Equations for Statistical Equilibrium 403
a Two-Level Atom 403
b Two-Level Atom plus Continuum 407
c Multilevel Atom 409
d Thermalization Length 410

15.3 Non-LTE Transfer of Radiation and the Redistribution
Function 411
a Complete Redistribution 412
b Hummer Redistribution Functions 413
15.4 Line Blanketing and Its Inclusion in the construction of
Model Stellar Atmospheres and Its Inclusion in the
Construction of Model Stellar Atmospheres 425
a Opacity Sampling 426
b Opacity Distribution Functions 427
Problems 429
References and Supplemental Reading 430

Chapter 16
Beyond the Normal Stellar Atmosphere 432
16.1 Illuminated Stellar Atmospheres 434
a Effects of Incident Radiation on the Atmospheric
Structure 434
b Effects of Incident Radiation on the Stellar Spectra 439
16.2 Transfer of Polarized Radiation 440
a Representation of a Beam of Polarized Light and
the Stokes Parameters 440
b Equations of Transfer for the Stokes 445
c Solution of the Equations of Radiative Transfer
for Polarized Light. 454
d Approximate Formulas for the Degree of
Emergent Polarization 457
e Implications of the Transfer of Polarization for
Stellar Atmospheres 465
16.3 Extended Atmospheres and the Formation of Stellar
Winds 469
a Interaction of the Radiation Field with the Stellar
Wind 470
b Flow of Radiation and the Stellar Wind 474
Problems 477
References and Supplemental Reading 478
Epilog 480
Index 483

Errata to the W. H. Freeman edition.
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