Diffusion time scales and accretion in the Sun

Abstract

SURFACE abundances in the Sun could have been essentially caused by accretion, either of comets or of grains^1–3. It has been hypothesised that if surface convection zones could be smaller than is usually indicated by model calculations, then accretion could be especially important. Dust accretion by the Sun has also been suggested as the cause of ice ages on the earth⁴. Either the zone immediately below the surface convection zone is stable enough for diffusion to be important, however, or other transport processes (turbulence, meridional circulation) more efficient than diffusion, will tend to homogenise the star. Diffusion is the slowest of the transport processes and will become important when the other transport processes become inoperative. Using diffusion theory, we can determine the minimum mass of the convection zone, if transport processes at the bottom of the convection zone are not to influence the abundances in the convection zone. If diffusion time scales are shorter than the life of the star, diffusion will modify the abundances in the convection zone. The mass in the convection zone for which diffusion time scales are equal to the life of the star on the main sequence then determines the minimum mass in the convection zone to justify neglect of transport processes at the bottom of the convection zone. I determine here that, for the Sun, this mass is between 3 × 10⁻³ and 10⁻²M_⊙, and give a general expression for the diffusion time scale as a function of the mass of the convection zone.