ELEMENT DIFFUSION IN THE SOLAR INTERIOR

We study the diffusion of helium and other heavy elements in the solar interior by solving exactly the set of flow equations developed by Burgers for a multicomponent fluid, including the residual heat-flow terms. No approximation is made concerning the relative concentrations, and no restriction is placed on the number of elements considered. We give improved diffusion velocities for hydrogen, helium, oxygen, and iron, in the analytic form derived previously by Bahcall & Loeb. These expressions for the diffusion velocities are simple to program in stellar evolution codes and are expected to be accurate to similar to 15%. We find that the inclusion of the residual heat flow terms leads to an increase in the hydrogen diffusion velocity. We compare our numerical results-with those obtained analytically by Bahcall & Loeb using a simplified treatment, as well as with those derived numerically by Michaud & Proffitt. We find that for conditions characteristic of the Sun, the results of Bahcall & Loeb for the hydrogen diffusion velocity are smaller than our more accurate numerical results by similar to 30%, except very near the center where the error becomes larger. The Michaud & Proffitt results differ from the numerical results derived here by less than or similar to 15%. Our complete treatment of element diffusion can be directly incorporated in a standard stellar evolution code by means of an exportable subroutine, but, for convenience, we also give simple analytical fits to our numerical results.