Solar Structure in Terms of Gauss’ Hypergeometric Function

Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized solar fusion reactor. We assume a matter density distribution varying non-linearly through the central region of the Sun. The analytic solutions of the differential equations of mass conservation, hydrostatic equilibrium, and energy conservation, together with the equation of state of the perfect gas and a nuclear energy generation rate ǫ = ǫ0ρ T, are given in terms of Gauss’ hypergeometric function. This model for the structure of the Sun gives the run of density, mass, pressure, temperature, and nuclear energy generation through the central region of the Sun. Because of the assumption of a matter density distribution, the conditions of hydrostatic equilibrium and energy conservation are separated from the mode of energy transport in the Sun. 1 Hydrostatic Equilibrium In the following we are concerned with the hydrostatic equilibrium of the purely gaseous spherical central region of the Sun generating energy by nuclear reactions at a certain rate (Chandrasekhar, 1939/1957; Stein, 1966). For this gaseous sphere we assume that the matter density varies non-linearly from the center outward, depending on two parameters δ and γ,