The Fundamentals Of Stellar Astrophysics - Collins G. W eBook download

The Fundamentals Of Stellar Astrophysics - Collins G. W

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• Book title                    :The Fundamentals Of Stellar Astrophysics
• Author                         : Collins G. W

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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
• Problems
• 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
• Pressure
• 2.3 Homology Transformations
• 2.4 Polytropes
• a Polytropic Change and the Lane-Emden
• Equation
• 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
• Chapter 4
• Flow of Energy through the Star and Construction of Stellar Models

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 Boundary Conditions
• b Schwarzschild Variables and Method
• c Henyey Relaxation Method for Construction of Stellar Models
• Problems
• References and Supplemental Reading

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

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
• 6.3 Equations of Relativistic Stellar Structure and Their Solutions
• a A Comparison of Structure Equations
• b A Simple Model
• c Neutron Star Structure6.4 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
• Problems
• 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
• Force
• 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
• Problems
• References and Supplemental Reading

Chapter 8
Stellar Pulsation and Oscillation

• 8.1 Linear Adiabatic Radial Oscillations
• a Stellar Oscillations and the Variational Virial theoremb Effect of Magnetic Fields and Rotation on Radial Oscillations
• 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
• Problems
• 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 Functiond 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 279a Equation of Radiative Transport in Spherical Coordinates 280
• 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 Helium297
• 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 314b 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 351b 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 426b 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 Win 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. 495