Migration and Growth of Protoplanetary Embryos III: Mass and Metallicity Dependence for FGKM main-sequence starsAuthors:Liu et alAbstract: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 (ηJ) with masses Mp>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-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 η⊕-ηJ dichotomy to conditions required for embryos to merge and to acquire supercritical core mass (Mc∼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 Zd. 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 ηJ-M∗. We also consider the Zd-Z∗ dispersed relationship and reproduce the observed ηJ-Z∗ correlation.