Internal Structure and Physics of the Sun

Historical scatch of the problem progress
What is a sourse of energy in the stars? How to look inside? Modern challengies - neutrino deficite, oscillations.
Introduction in the problem of internal structure of the Sun
Postulates and hypothesises during Standard Solar Model construction. Main course - an evolution of hydrogen abundance. Main work - a sequence of stationary models. What is a stationary model - postulates of Input physics: Equation of State (EOS), opacity, nuclear cross-sections, convective flux, atmospheric boundary conditions.
Observational parameters: radius, mass, luminosity, age.
Equilibrium of gravity and gas pressure
Differential equation for hydrostatic equilibrium. Virial theorem. Variational principal. Dynamictime estimations: collaps time, circle satelite time, sound travel time.
Profile of gravity acceleration. Gradient of sound speed. Model with known dencity, or pressure profile (as function of radius). Equation for pressure disturbace as result of sound speed changes (liniarization of hydrostatic equation)
Theory of politropic models
Basic hypothesys - pressure is function of dencity only. Dimensionless variables - transformation for arbitrary function, special cases power function and isothermal relation. Vector form of the basic equation. Boundary conditions. Star configuration with a) given mass and radius b) known politropic temperature. Expression for mass, radius, K, central pressure, Potential energy. Other forms of Emden-equation, analytical solutions for n=0, 1, 5. Proper solution for n>3.
Transformation of symmetry for politropic equation. Homological family of solutions. Variables substitutions which is invariant to symmetry transformation and lead to lower of the system order. Topology of the solution in (z,y) and (u,v) variables. Clasification of the solution: regular in center E-solution, singular in center M-solution, and two-zero solutions (F-type). Asymthotic behaviour of M-solution near center - change of type in point n=3 (appearing second special point).