Migration and Growth of Protoplanetary Embryos III. Mass and Metallicity Dependence for FGKM Main-sequence Stars

Radial velocity and transit surveys have found that the fraction of FGKM stars with close-in super-Earth(s) (η ⊕) is around 30%–50%, independent of the stellar mass M * and metallicity Z *. In contrast, the fraction of solar-type stars harboring one or more gas giants (η J) with masses M _p > 100 M _⊕ is nearly 10%–15%, and it appears to increase with both M * and Z *. Regardless of the properties of their host stars, the total mass of some multiple super-Earths 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 η ⊕–η J dichotomy to conditions required for embryos to merge and to acquire supercritical core mass (M_c ~ 10 M_⊕) 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 * and decreases with metallicity of disk gas Z _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 η J–M *. We also consider the dispersed relationship and reproduce the observed η J–Z * correlation.