An Analytic Colar Model: Physical Principles and Mathematical Structure

Physical principles and mathematical structure involved in deriving an analytical representation of the internal structure of the Sun is discussed. For a two-parameter family of a non-linear matter density distribution, the run of mass, pressure, temperature, and luminosity throughout the Sun is presented in terms of Gauss' hypergeometric function. The system of differential equations governing hydrostatic equilibrium and energy conservation for the spherical Sun is proved to be a laboratory for the application of special functions.