Migration and Growth of Protoplanetary Embryos III: Mass and Metallicity Dependence for FGKM main-sequence stars

Abstract

Radial velocity and transit surveys have found that the fraction of FGKM stars with close-in super-Earth(s) (${\eta }_{\oplus }$) is around $30\%-50\%$, independent of the stellar mass $M_{\ast }$ and metallicity $Z_{\ast }$. In contrast, the fraction of solar-type stars harboring one or more gas giants (${\eta }_J$) with masses $M_{\mathrm{p}}>100M_{\oplus }$ is nearly $10\%-15\%$, and it appears to increase with both $M_{\ast }$ and $Z_{\ast }$. Regardless of the properties of their host stars, the total mass of some multiple super-Earth systems exceeds the core mass of Jupiter and Saturn. We suggest that both super-Earths and supercritical cores of gas giants were assembled from a population of embryos that underwent convergent type I migration from their birthplaces to a transition location between viscously heated and irradiation heated disk regions. We attribute the cause for the ${\eta }_{\oplus }$-${\eta }_{\mathrm{J}}$ dichotomy to conditions required for embryos to merge and to acquire supercritical core mass ($M_c\sim 10M_{\oplus }$) for the onset of efficient gaseous envelope accretion. We translate this condition into a critical disk accretion rate, and our analysis and simulation results show that it weakly depends on $M_{\ast }$ and decreases with metallicity of disk gas $Z_{\mathrm{d}}$. We find that embryos are more likely to merge into supercritical cores around relatively massive and metal-rich stars. This dependence accounts for the observed ${\eta }_{\mathrm{J}}$-$M_{\ast }$. We also consider the $Z_{\mathrm{d}}$-$Z_{\ast }$ dispersed relationship and reproduce the observed ${\eta }_J$-$Z_{\ast }$ correlation.

20 pages, 10 figure, accepted in ApJ