2011ApJ...728L..30G

When a planet falls onto the surface of its host star, the added high-metallicity material does not remain in the surface layers, as often assumed, but is diluted into the interior through fingering ("thermohaline") convection. Until now, however, the timescale over which this process happens remained very poorly constrained. Using recently measured turbulent mixing rates for fingering convection, I provide reliable numerical and semi-analytical estimates for the rate at which the added heavy elements drain into the interior. I find that the relative metallicity enhancement post-infall drops by a factor of 10 over a timescale that depends only on the structure of the host star and decreases very rapidly with increasing stellar mass (from about 1 Gyr for a 1.3 M_☉ star to 10 Myr for a 1.5 M_☉star). This result offers an elegant explanation to the lack of an observed trend between metallicity and convection zone mass in planet-bearing stars. More crucially, it strongly suggests that the statistically higher metallicity of planet-bearing stars must be of primordial origin. Finally, the fingering region is found to extend deeply into the star, a result which would provide a simple theoretical explanation of the measurements of higher lithium depletion rates in planet-bearing stars.