# 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
- (a) dynamic equilibrium,
- (b) local enegry conservation (existence of enegry sourse),
- (c) local radiative balance
- (d) stationary of enegry flux.

*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).