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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.
Last update: Vokrouhlický David, prof. RNDr., DrSc. (10.01.2019)
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Oral examination. Last update: Vokrouhlický David, prof. RNDr., DrSc. (11.06.2019)
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in case of distant learning, via Zoom https://cesnet.zoom.us/j/6079238231
Carrol B.W., Ostlie D.A: An Introduction to Modern Astrophysics, Pearson, Addison Wesley, San Francisco, 2007. ISBN 0321442849.
Kippenhahn R., Weigert A.: Stellar structure and evolution, Springer, Heidelberg 1994.
Schatzman E.L., Praderie F.: The Stars, Springer, Heidelberg, 1993.
Oswalt T.D., Barstow M.A. (eds.): Planets, Stars and Stellar Systems, Volume 4: Stellar Structure and Evolution. Springer, Dordrecht, 2013. ISBN 9789400756144.
Maeder A.: Physics Formation and Evolution of Rotating Stars. Springer, Berlin, 2009. ISBN 9783540769484.
Hansen C.J., Kawaler S.D., Trimble V.: Stellar Interiors. Springer, New York, 2004. ISBN 0378200894.
Stix M.: The Sun. An Introduction, Astronomy and Astrophysics Library, Springer-Verlag, Berlin, 2002.
Shore S. N.: Astrophysical Hydrodynamics. Wiley-Vch, Weinheim, 2007. ISBN 9783527406692.
Mihalas D.: Stellar Atmospheres, W.H. Freeman and Co., San Francisco, 1980. Last update: Brož Miroslav, doc. Mgr., Ph.D. (01.03.2021)
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Přednáška Last update: T_AUUK (31.03.2008)
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Zkouška je ústní, sestávající ze 3 obsáhlejších otázek.
Požadavky odpovídají syllabu, resp. základní učebnici Harmanec a Brož (2011), v tom rozsahu, který byl prezentován na přednášce. Známka se stanovuje dle správnosti nebo chybnosti odpovědí, včetně doplňujících otázek.
Last update: Brož Miroslav, doc. Mgr., Ph.D. (06.10.2017)
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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 Last update: Vokrouhlický David, prof. RNDr., DrSc. (10.01.2019)
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