GRAVITATIONAL SETTLING IN SOLAR MODELS

We present calculations of the effects of gravitational settling and atomic diffusion in solar models, with the goal of constraining the actual amount of gravitational settling that has occurred in the Sun. Most of the discrepancies between the results of previous workers are explained. We use the observed solar Li abundance to constrain the amount of turbulent mixing below the solar convection zone and thereby set a lower limit to the amount of gravitational settling in the Sun. Comparison of the different formulations for calculating diffusion velocities used by previous authors shows that, for solar models, the differences in these formulations are too small to explain the variation in results found by these authors. Of the total increase in the central He mass fraction during evolution to the solar age, only about 0.013 out of the total increase of almost-equal-to 0.37 is due to gravitational settling. Because the change in central He abundance due to diffusion is small compared with the change due to nuclear reactions, direct comparison of the total change in the central He abundance between diffusing and nondiffusing models is a poor measure of the effects of gravitational settling on the central regions of the model. Minor variations in the amount of nuclear burning caused by small changes in the parameters of the model can give differences comparable to the total change due to diffusion. The difference in the required initial He abundance in solar models, or the change in the final luminosity in models with the same initial parameters, are better measures of the effects of central gravitational settling. The gravitational settling of metals can, by changing the opacity, have structural effects that are almost as large as the changes resulting from the gravitational settling of He alone. If diffusion is added to evolutionary models without changing any of the physical parameters (such as alpha and the initial He abundance), the total change in the central He abundance, as compared with a model without diffusion, is much larger than when both models are constrained to reproduce the solar luminosity and radius at a given age. Gravitational settling reduces the surface He abundance by roughly 10% below its initial value. The predicted reduction in the heavy-element abundance is somewhat smaller but is also subject to greater uncertainties. If the turbulent mixing needed to account for the current solar Li abundance is included, the change in the surface abundances are moderated, and the abundance profiles below the convection zone are modified. However, turbulent mixing below the surface convection zone cannot reduce the amount of surface settling by more than a factor of 2. Larger amounts of turbulence would cause the destruction of too much Li and/or Be.