Stellar Structure and Evolution

by Kippenhahn, Rudolf; Weigert, A.; Kippenhahn, R.

• ISBN13: 9780387580135
• ISBN10: 0387580131
• Edition: 1st
• Format: Paperback
• Copyright: 1994-08-01
• Publisher: Springer Verlag

Table of Contents

Part I The Basic Equations
Coordinates, Mass Distribution, and Gravitational Field in Spherical Stars	2	(4)
Eulerian Description	2	(1)
Lagrangian Description	3	(1)
The Gravitational Field	4	(2)
Conservation of Movement	6	(9)
Hydrostatic Equilibrium	6	(1)
The Role of Density and Simple Solutions	7	(1)
Simple Estimates of Central Values Pc, Tc	8	(1)
The Equation of Motion for Spherical Symmetry	9	(2)
The Non-spherical Case	11	(1)
Hydrostatic Equilibrium in General Relativity	12	(1)
The Position Model	13	(2)
The Virial Theorem	15	(4)
Stars in Hydrostatic Equilibrium	15	(2)
The Virial Theorem of the Piston Model	17	(1)
The Kelvin-Helmhotz Time-scale	18	(1)
The Virial Theorem for Non-vanishing surface Pressure	18	(1)
Conservation of Energy	19	(8)
Thermodynamic Relations	19	(2)
Energy Conservation in Stars	21	(2)
Global and Local Energy Conservation	23	(2)
Time-scales	25	(2)
Transport of Energy by Radiation and Conduction	27	(9)
Radiative Transport of Energy	27	(4)
Basic Estimates	27	(1)
Diffusion of Radiative Energy	28	(1)
The Rosseland Mean for κv	29	(2)
Conductive Transport of Energy	31	(2)
The Thermal Adjustment Time of a Star	33	(1)
Thermal Properties of the Piston Model	34	(2)
Stability Against Local, Non-spherical Perturbtions	36	(12)
Dynamical Instability	36	(5)
Oscillation of a Displaced Element	41	(1)
Vibrational Stability	42	(1)
The Thermal Adjustment Time	43	(1)
Secular Instability	44	(1)
The Stability of the Piston Model	45	(3)
Transport of Energy by Convection	48	(8)
The Basic Picture	49	(2)
Dimensionless, Equatioin	51	(1)
Limiting Cases, Solutions, Discussion	52	(4)
The Chemical Composition	56	(8)
Relative Mass Abundances	56	(1)
Variation of Composition with Time	57	(7)
Radiative Regions	57	(1)
Diffusion	58	(3)
Convective Regions	61	(3)
Part II The Overall Problem
The Differential Equations of Stellar Evolution	64	(4)
The Full Set of Equations	64	(2)
Time-scales and Simplificiations	66	(2)
Boundary Conditions	68	(9)
Central Conditions	68	(1)
Surface Conditions	69	(3)
Influence of the Surface Conditions and Properties of Envelope Solutions	72	(5)
Radiative Envelopes	72	(3)
Convective Envelopes	75	(1)
Summary	75	(1)
The T-r Stratification	76	(1)
Numerical Procedure	77	(8)
The Shooting Method	77	(1)
The Henyey Method	78	(5)
Treatment of the First- and Second-Order Time Derivatives	83	(2)
Existence and Uniqueness of Solutions	85	(17)
Notation and Outline of the Procedure	86	(1)
Models in Complete Equilibrium	87	(4)
Fitting Conditions in the Pc - Tc Plane	87	(1)
Local Uniqueness	88	(1)
Variation of Parameters	89	(2)
Hydrostatic Models without Thermal Equilibrium	91	(4)
Degrees of Freedom and Fitting Conditions	91	(2)
Local Uniqueness	93	(1)
Variatioin of Parameters	93	(2)
Connection with Stability Problems	95	(2)
Non-local Properties of Equilibrium Models	97	(5)
Part III Properties of Stellar Matter
The Ideal Gas with Radiation	102	(5)
Mean Molecular Weight and Radiation Pressure	102	(2)
Thermodynamic Quantities	104	(3)
Ionization	107	(11)
The Boltzmann and Saha Formulae	107	(3)
Ionization of Hydrogen	110	(1)
Thermodynamical Quantities for a Pure Hydrogen Gas	111	(1)
Hydrogen-Helium Mixtures	112	(2)
The General Case	114	(1)
Limitation of the Saha Formula	115	(3)
The Degenerate Electron Gas	118	(11)
Consequences of the Pauli Principle	118	(1)
The Completely Degenerate Electron Gas	119	(3)
Limiting Cases	122	(1)
Partial Degeneracy of the Electron Gas	123	(6)
The Equation of State of Stellar Matter	129	(8)
The Ion Gas	129	(1)
The Equation of State	130	(2)
Thermodynamic Quantities	132	(2)
Crystallization	134	(1)
Neutronization	135	(2)
Opacity	137	(9)
Electron Scattering	137	(1)
Absorption Due to Free-Free Transitions	138	(1)
Bound-Free Transitions	139	(1)
Bound-Bound Transitions	140	(1)
The Negative Hydrogen Ion	141	(1)
Conduction	142	(1)
Opacity Tables	143	(3)
Nuclear Energy Production	146	(28)
Basic Considerations	146	(4)
Nuclear Cross-sections	150	(2)
Thermonuclear Reaction Rates	152	(5)
Electron Shielding	157	(4)
The Major Nuclear Burnings	161	(8)
Hydrogen Burning	162	(3)
Helium Burning	165	(2)
Carbon Burning etc.	167	(2)
Neutrinos	169	(5)
Part IV Simple Stellar Models
Polytropic Gaseous Spheres	174	(17)
Polytropic Relations	174	(1)
Polytropic Stellar Models	175	(2)
Properties of the Solutions	177	(1)
Application to Stars	178	(2)
Radiation Pressure and the Polytrope n = 3	180	(1)
Polytropic Stellar Models with Fixed K	180	(1)
Chandrasekhar's Limiting Mass	181	(2)
Isothermal Spheres of an Ideal Gas	183	(1)
Gravitational and Total Energy for Polytropes	184	(2)
Supermassive Stars	186	(1)
A Collapsing Polytrope	187	(4)
Homology Relations	191	(9)
Definitions and Basic Relations	191	(3)
Applications to Simple Material Functions	194	(4)
The Case δ = 0	194	(1)
The Case &alpha = δ = &phis; = 1, a = b = 0	194	(3)
The Role of the Equation of State	197	(1)
Homologous Contraction	198	(2)
Simple Models in the U-V Plane	200	(7)
The U-V Plane	200	(3)
Radiative Envelope Solutions	203	(2)
Fitting of a Convective Core	205	(1)
Fitting of an Isothermal Core	206	(1)
The Main Sequence	207	(9)
Surface Values	207	(3)
Interior Solutions	210	(2)
Convective Regions	212	(3)
Extreme Values of M	215	(1)
Other Main Sequences	216	(8)
The Helium Main Sequence	216	(2)
The Carbon Main Sequence	218	(1)
Main Sequences as Linear Series of Stellar Models	219	(2)
Generalized Main Sequences	221	(3)
The Hayashi Line	224	(10)
Luminosity of Fully Convective Models	224	(2)
A Simple Description of the Hayashi Line	226	(3)
The Neighbourhood of the Hayashi Line and the Forbidden Region	229	(2)
Numerical Results	231	(1)
Limitations for Fully Convective Models	232	(2)
Stability Considerations	234	(14)
General Remarks	234	(1)
Stability of the Piston Model	235	(3)
Dynamical Stability	236	(1)
Inclusion of Non-adiabatic Effects	236	(2)
Stellar Stability	238	(10)
Perturbation Equations	239	(1)
Dynamical Stability	240	(1)
Non-adiabatic Effects	241	(1)
The Gravothermal Specific Heat	242	(1)
Secular Stability Behaviour of Nuclear Burning	243	(5)
Part V Early Stellar Evolution
The Onset of Star Formation	248	(8)
The Jeans Criterion	248	(4)
An Infinite Homogeneous Medium	248	(2)
A Plane Parallel Layer in Hydrostatic Equilibrium	250	(2)
Instability in the Spherical Case	252	(1)
Fragmentation	253	(3)
The Formation of Protostars	256	(10)
Free-Fall Collapse of a Homogeneous Sphere	256	(2)
Collapse onto a Condensed Object	258	(1)
A Collapse Calculation	259	(1)
The Optically Thin Phase and the Formation of a Hydrostatic Core	260	(2)
Core Collapse	262	(2)
Evolution in the Hertzsprung-Russell Diagram	264	(2)
Pre-Main-Sequence Contraction	266	(5)
Homologous Contraction of a Gaseous Sphere	266	(3)
Approach to the Zero-Age Main Sequence	269	(2)
From the Initial to the Present Sun	271	(6)
Choosing the Initial Model	271	(4)
Solar Neutrinos	275	(2)
Chemical Evolution on the Main Sequence	277	(15)
Change in the Hydrogen Content	277	(1)
Evolution in the Hertzsprung-Russell Diagram	278	(2)
Time-scales for Central Hydrogen Burning	280	(1)
Complications Connected with Convection	280	(5)
Convective Overshooting	281	(3)
Semiconvection	284	(1)
The Schonberg-Chandrasekhar Limit	285	(7)
A Simple Approach - The Viral Theorem and Homology	286	(2)
Integrations for Core and Envelope	288	(1)
Complete Solutions for Stars with Isothermal Cores	289	(3)
Part VI Post-Main-Sequence Evolution
Evolution Through Helium Burning - Massive Stars	292	(16)
Crossing the Hertzsprung Gap	292	(4)
Central Helium Burning	296	(4)
The Cepheid Phase	300	(1)
To Loop or Not to Loop	301	(5)
After Central Helium Burning	306	(2)
Evolution Through Helium Burning - Low-Mass Stars	308	(20)
Post-Main-Sequence Evolution	308	(1)
Shell-Source Homology	309	(4)
Evolution to the Helium Flash	313	(3)
The Helium Flash	316	(1)
Numerical Results for the Helium Flash	317	(3)
Evolution after the Helium Flash	320	(1)
Evolution from the Zero-Age Horizontal Branch	321	(3)
Equilibrium Models with Helium Cores - Continued	324	(4)
Later Phases	328	(16)
Nuclear Cycles	328	(2)
Shell Sources and Their Stability	330	(3)
Thermal Pulses of a Shell Source	333	(3)
Evolution of the Central Region	336	(6)
The Core-Mass-Luminosity Relation for Large Core Masses	342	(2)
Final Explosions and Collapse	344	(22)
The Evolution of the C-O Core	344	(4)
Carbon Burning in Degenerate Cores	348	(8)
The Carbon Flash	348	(1)
Nuclear Statistical Equilibrium	349	(2)
Hydrostatic and Convective Adjustment	351	(1)
Combustion Fronts	352	(2)
Numerical Solutions	354	(2)
Carbon Burning in Accreting White Dwarfs	356	(1)
Collapse of Cores of Massive Stars	356	(10)
Simple Collapse Solutions	357	(2)
The Reflection of the Infall	359	(1)
Effects of Neutrinos	360	(2)
Numerical Results	362	(1)
Pair-Creation Instability	362	(4)
Part VII Compact Objects
White Dwarfs	366	(14)
Chandrasekhar's Theory	366	(4)
The Corrected Mechanical Structure	370	(4)
Thermal Properties and Evolution of White Dwarfs	374	(6)
Neutron Stars	380	(10)
Cold Matter Beyond Neutron Drip	380	(3)
Models of Neutron Stars	383	(7)
Black Holes	390	(8)
Part VIII Pulsating Stars
Adiabatic Spherical Pulsations	398	(9)
The Eigenvalue Problem	398	(4)
The Homogeneous Sphere	402	(1)
Pulsating Polytropes	403	(4)
Non-adiabatic Spherical Pulsations	407	(11)
Vibrational Instability of the Piston Model	407	(1)
The Quasi-adiabatic Approximation	408	(1)
The Energy Integral	409	(3)
The κ Mechanism	411	(1)
The &epsi Mechanism	412	(1)
Stars Driven by the κ Mechanism - The Instability Strip	412	(5)
Stars Driven by the ε Mechanism	417	(1)
Non-radial Stellar Oscillations	418	(10)
Perturbations of the Equilibrium Model	418	(2)
Normal Modes and Dimensionless Variables	420	(2)
The Eigenspectra	422	(3)
Stars Showing Non-radial Oscillations	425	(3)
Part IX Stellar Rotation
The Mechanics of Rotating Stellar Models	428	(7)
Uniformly Rotating Liquid Bodies	428	(3)
The Roche Model	431	(2)
Slowly Rotating Polytropes	433	(2)
The Thermodynamics of Rotating Stellar Models	435	(9)
Conservative Rotation	435	(1)
Von Zeipel's Theorem	436	(1)
Meridional Circulation	437	(1)
The Non-conservative Case	438	(1)
The Eddington-Sweet Time-scale	439	(3)
Meridional Circulation in Inhomogeneous Stars	442	(2)
The Angular-Velocity Distribution in Stars	444	(11)
Viscosity	444	(2)
Dynamical Stability	446	(5)
Secular Stability	451	(4)
References	455	(6)
Subject Index	461