Element Diffusion in the Solar Interior

We study the diffusion of helium and other heavy elements in the solar interior, using the flow equations developed by Burgers (1969) for a multi-component fluid. The set of equations is solved exactly, including the residual heat flow terms. No approximation is made about the relative concentrations and no restriction is placed on the number of elements considered. For helium diffusion, we compare our results with those obtained by Bahcall and Loeb (1990) using a simplified treatment with heat flows neglected. We find that the inclusion of the residual heat flow terms leads to a significant increase in the helium diffusion velocity. However, we also find that the temperature and charge-dependence of the Coulomb logarithm has the opposite effect, leading to a decrease in the helium diffusion velocity. By coincidence, the two effects partially cancel each other out throughout most of the solar interior. Our complete treatment of element diffusion could be directly incorporated in a standard stellar evolution code, but, for convenience, we also give simple analytical fits of our numerical results. Burgers, J.M. 1969, Flow equations for composite gases(Academic Press, New York). Bahcall, J.N., and Loeb, A. 1990, Ap.J.,360, 267.