Establish the equation of hydrostatic equilibrium in a spherical symmetric model in its differential and integral form and discuss its consequences. Present the equation of hydrostatic equilibrium in a rotating star and show that, for solid body rotation, the isobars, iso-density and isothermal surfaces coincide.
Starting from the equation of radiative transfer, establish the equation of radiation transport in stellar interiors. Justify the presence of the Rosseland mean opacity in the equation for the bolometric flux. At a given temperature, which transitions mainly affect the efficiency of this transport?
What is convection : origin, transport of energy ? Demonstrate the Schwarzschild criterion of convective instability and, on this base, discuss the conditions of apparition of a convective zone in stellar interiors.
Present in the great lines the degeneracy of the electron gas and its impact on the equation of state. What is the upper limit on the distribution of momentum imposed by the Pauli exclusion principle ? Starting from the pressure integral, establish the relation between pressure and density in a completely degenerated relativistic gas.
What is a polytropic sphere ? Establish the mass-radius relation in n=3/2 polytropic spheres of completely degenerated non-relativistic gas and the Chandrasekhar limiting mass of a n=3 polytropic sphere of completely degenerated relativistic gas. Based on homologous transformations, interpret both of them. Illustrate and discuss the mass-radius relation of white dwarfs.
What is the role of nuclear reactions in stellar cores? Present and discuss how the cross sections of nuclear fusion reactions depend on the energy. Starting from the relation between nuclear reaction rate and cross section, explain the need of computing the mean sigma v. Present and explain what is the Gamov peak.
