Calculation of stellar structure. III - Solar models that satisfy the necessary conditions for a unique solution to the stellar structure equations

Calculations are presented for a series of provisional solar models that satisfy the necessary conditions for a unique solution to the stellar structure equation (Rouse, 1975). The models are shown to be qualitatively consistent with the solar neutrino experiment results through the magnitude of the central temperature or its variation near the center. A modification of one standard model assumption is employed in that each helium nucleus is not assumed to stay at the same radius where it is produced. It is found that the solar mass and radius could not be calculated using a standard model of the present sun, three different assumed photospheric helium abundances, and the spectroscopically determined high-Z element abundances unless, in outward integrations, the opacity was decreased in the inner zone before increasing to the large values in the outer convective zone. It is determined that, in order not to arbitrarily reduce the opacity in such a manner, the sun must have a small high-Z iron-like core with a mass of about 0.005 solar masses in a radius of about 0.05 solar radius.