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

TL;DR

This paper investigates how the formation and growth of planetary embryos depend on stellar mass and metallicity, explaining the observed differences in the occurrence of super-Earths and gas giants around FGKM stars through migration and core accretion processes.

Contribution

It introduces a model linking embryo merging and core formation to disk accretion rates, stellar properties, and metallicity, explaining the observed exoplanet occurrence trends.

Findings

Super-Earth occurrence is independent of stellar mass and metallicity.

Gas giant formation likelihood increases with stellar mass and metallicity.

Embryo merging into supercritical cores is more probable around massive, metal-rich 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_{\rm p} > 100 \ M_\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 $\eta_\oplus$-$\eta_{\rm J}$ dichotomy to conditions required for embryos to merge and to acquire supercritical core mass ($M_c \sim 10 \ M_\oplus$) 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 $Z_{\rm d}$. 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 $\eta_{\rm J}$-$M_\ast$. We also consider the $Z_{\rm d}$-$Z_\ast$ dispersed relationship and reproduce the observed $\eta_J$-$Z_\ast$ correlation.