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 that 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) (alpha(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 15% 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.