Syllabus
*1 Introduction 1.1 Origin of the theory 1.2 Model of our Sun
Lithium problem
Neutrino problem
*3 State equation 3.1 Mean molecular weight
Atomic mass
Amount of substance, gram-atom, gram-molecule
Molar weight, molecular weight
Mean molecular weight 3.2 Ideal gas 3.3 Radiation pressure 3.4 Electron degeneracy
Full degeneracy 3.5 Partial ionisation in subsurface layers
Iterative solution
More complicated state equations
Compact objects
*4 Basic equations of stellar structure 4.1 Equation of mass conservation 4.2 Equation of motion and equation of hydrostatic equilibrium 4.3 Equation of thermal equilibrium 4.3.1 Proton-proton chain 4.3.2 CNO cycle 4.3.3 Transformation of helium to carbon and other reactions 4.3.4 Thermal equilibrium and changes of entropy 4.4 Equation of energy transfer 4.4.1 Equation for radiation energy transfer
Equation of radiation transfer in spherical symmetry
Integral quantities 1st integral of the transfer equation 2nd integral of the transfer equation
Development of almost-isotropic intensity
Kirchhoff law
Rosseland mean opacity
An estimate of mean free path and flux
A note on diffusion formalism 4.4.2 Equation for convective energy transfer
A condition for convection
Derivation of adiabatic gradient of temperature
A common formalism of radiative and convective equilibrium
Subsurface layers
*5 Mathematical structure of equation of stellar interior 5.1 Stationary models 5.2 Evolutionary model 5.3 Dynamic model
*6 Initial and boundary conditions 6.1 Initial conditions 6.2 Boundary conditions in the centre 6.3 Boundary conditions at the surface 6.3.1 Photosphere 6.3.2 Subphotospheric layers
*7 Henyey method for integration of interior parts of a star 7.1 Method of complete linearisation
Discretization
Boundary conditions in the centre
Outer boundary conditions
Linearisation
Iterations
Time step 7.2 Limits of discretization
*8 Evolution of a solitary star 8.1 Illustrative example: evolution of a star with 4 M_Sun 8.2 Differences of stellar evolution dependent on stellar mass
The role of initial content of helium and more massive elements
*9 Comparison of theoretical predictions of stellar evolution and observations 9.1 How to acquire observational data?
Luminosities of stars
Effective temperature of stars
Masses and radii of stars
V versus (B-V) diagram for clusters 9.2 Explanation of major features of Hertzsprung-Russell diagram 9.3 Stellar evolution in star clusters 9.4 Stellar evolution in double stars 9.5 Changes of chemical composition observed in spectra 9.6 Test of internal structure with help of apsidal motion 9.6.1 Apsidal motion in classical mechanics 9.6.2 Relativistic apsidal motion 9.6.3 Total apsidal motion 9.7 Stellar evolution in course of human history
*10 Simple analytical models and estimates 10.1 Polytropic process
A concrete example of state equation of stellar matter
A mode general derivation from the 1st law of thermodynamics 10.2 Lane-Emden differential equation 10.3 Polytropic models of stars
Density
Pressure
Temperature
Mass contained in a sphere
Comparison of polytropic models with the standard solar model
Chandrasekhar limit
*11 Stellar wind and mass loss from stars 11.1 Observational facts
Observational confirmation of wind around cool stars
Confirmations for hot stars
Escape velocity 11.2 Parker theory for cold stars
Instability of isothermal atmosphere
Hydrodynamic equations 11.3 CAK theory of stellar wind driven by radiation
Acceleration caused by radiation
Influence of metallicity on wind
Temporal modulation of stellar wind 11.4 Influence of stellar wind on evolution of stars
Parametric description of wind
Influence of wind
*12 Influence of rotation 12.1 Roche model and simple estimates
Estimates of radii of stars
Minimum rotation period
Maximum rotation period 12.2 Models of stellar evolution with rotation
Vectorial form of stellar equations
Various models of rotating stars 12.3 Selected results for evolution of rotating stars
Evolution of rotational velocity
Influence on evolutionary paths in the HR diagram
Influence on surface chemical composition
Comparison with observations
Influence of metallicity on rotational instability
*13 Evolution of double stars 13.1 Roche model and simple estimates
Physical classification of double stars 13.2 Calculation of stellar evolution in the phase of mass exchange
Distance of components
Non-conservative mass transfer
Model of stellar interior 13.3 Selected results of double stars modelling
An example of a double star 4 M_Sun and 3.2 M_Sun 13.4 Models of double stars evolution versus observations
Evolutionary paradox
Be stars
Eccentric orbits
Magnetic polars
*14 Pulsations of stars * 14.1 Radial pulsations of spherical stars 14.1.1 Condition for onset of pulsations 14.1.2 Opacity mechanism of pulsations 14.1.3 A crude estimate of period of radial pulsations 14.1.4 Relations period - luminosity - colour 14.2 Kinematics of non-radial pulsations 14.2.1 Sectoral pulsations of rotating stars 14.3 Hydrodynamics for simple waves
Basic equations of hydrodynamics
Equilibrium state
Perturbations 14.3.1 Acoustic waves in homogeneous medium (p-modes) 14.3.2 Internal gravitation waves (g-modes) 14.3.3 Surface gravitation waves (f-modes)
Exact spherical solutions
*15 Gravitational collapse of protostars 15.1 Cooling processes 15.2 Evolution before main sequence 15.3 Position of the Hayashi line 15.3 Minimum Jeans mass 15.4 Eddington limit
*16 Explosive phase of stellar evolution 16.1 Core-collapse supernovae
Energetic balance
Observations of neutrinos from SN 1987 A 16.1.1 Mechanism of neutrino bomb 16.1.2 Gamma-ray bursts (GRB) 16.1.3 Nucleosynthesis by r-process 16.1.4 Afterglow and supernova remnants 16.2 Supernovae originating in an explosion of a white dwarf 16.2.1 Laminar velocity of deflagration 16.2.2 Chapman-Jouguet velocity of detonation 16.2.3 Rayleigh-Taylor instability
*17 Types of observed stars and their evolutionary stages * 17.1 Hot stars of spectral type O and Wolf-Rayet stars
O stars
Wolf-Rayet stars
O subdwarfs 17.2 Stars of spectral type B 17.2.1 Chemically peculiar Bp stars 17.2.2 Pulsating beta Cep stars 17.2.3 Slowly-pulsating B stars (SPB) 17.2.4 Be stars 17.2.5 Luminous blue variables (LBV) 17.3 Stars of spectral types A to F 17.3.1 Chemically peculiar Am stars 17.3.2 Magnetic Ap stars 17.3.3 Pulsating delta Scuti stars 17.3.4 SX Phe stars 17.3.5 gamma Dor stars 17.3.6 Lithium anf beryllium in F and G stars 17.4 Cold G, K and M stars 17.4.1 Chromospherically active stars: UV Cet, BY Dra, etc.
Stars of UV Cet type
Stars of BY Dra type
Spotted stars of RS CVn type
Close binaries of W UMa type
Stars of FK Com type 17.4.2 Pulsating stars: Cepheids, Miras, R CrB and AGB stars
Cepheids
Stars of W Vir type
Stars of RR Lyr type
Miras
Stars of R CrB type
Asymptotic Giant Branch stars (AGB)
Stars of RV Tau type 17.5 Stars in early evolutionary stages 17.5.1 T Tauri stars 17.5.2 FU Ori stars 17.6 Stars in late evolutionary stages 17.6.1 White dwarfs and ZZ Cet stars
White dwarfs
ZZ Cet stars 17.6.2 Novae, cataclysmic variables and polars
Recurrent novae
Dwarf novae
Polars of AM Her type
Intermediate polars DQ Her
Stars of AM CVn type 17.6.3 Supernovae
Annotation
Physics of stellar interiors and evolution. State equation, basic equations of stellar structure, mathematic structure of equations, initial and boundary conditions, Henyey numerical method.
Evolution of a solitary star, comparison of theoretical predictions and observations, simple analytical (polytropic) models.
Stellar wind, influence of rotation, evolution of double stars, pulsations of stars, gravitational collapse of protostars, explosive phase of stellar evolution.
Types of observed stars and their evolutionary stages.