Silicon and Nickel Enrichment in Planet-Host Stars: Observations and Implications for the Core-Accretion Theory of Planet Formation

We present evidence that stars with planets exhibit statistically significant silicon and nickel enrichment over the general metal-rich population. We also present simulations which predict silicon enhancement of planet hosts within the context of the core-accretion hypothesis for giant planet formation. Because silicon and oxygen are both alpha elements, [Si/Fe] traces [O/Fe], so the silicon enhancement in planet hosts predicts that these stars are oxygen-rich as well. We present new numerical simulations of planet formation by core accretion that establish the timescale on which a Jovian planet reaches rapid gas accretion, t_rga, as a function of solid surface density sigma_solid: (t_rga / 1 Myr) = (sigma_solid / 25.0 g cm^{-2})^{-1.44}. This relation enables us to construct Monte Carlo simulations that predict the fraction of star-disk systems that form planets as a function of [Fe/H], [Si/Fe], disk mass, outer disk radius and disk lifetime. Our simulations reproduce both the known planet-metallicity correlation and the planet-silicon correlation reported in this paper. The simulations predict that 16% of Solar-type stars form Jupiter-mass planets, in agreement with 12% predicted from extrapolation of the observed planet frequency-semimajor axis distribution. Although a simple interpretation of core accretion predicts that the planet-silicon correlation should be much stronger than the planet-nickel correlation, we observe the same degree of silicon and nickel enhancement in planet hosts. If this result persists once more planets have been discovered, it might indicate a complexity in the chemistry of planet formation beyond the simple accumulation of solids in the core accretion theory.