Resolving the Super-Earth/Gas Giant Connection in Stellar Mass and Metallicity

Abstract

The observed correlation between inner super-Earths and outer gas giants places strong constraints on formation theories. Building on previous work, Bryan $\&$ Lee 2024 showed that there is a statistically significant positive correlation between super-Earths and outer gas giants around metal-rich FGK stars, and that this correlation disappears for metal-poor hosts. Here we consider how this connection evolves across stellar mass. Starting with our sample of 85 M-dwarfs ($<$0.6 M$_{\odot}$) hosting inner super-Earths, we calculate P(GG|SE, [Fe/H]$>$0) = 9.4 (+10.2 -3.1)$\%$ and P(GG|SE, [Fe/H]$\leq$0)$<$3.1$\%$. Compared to the field gas giant frequency calculated from the Rosenthal et al 2021 sample, we find P(GG|[Fe/H]$>$0) = 10.3 (+6.9 -3.1)$\%$, and P(GG|[Fe/H]$\leq$0)$<$2.6$\%$ for M-dwarfs. While we see a higher gas giant frequency around metal-rich M-dwarfs for both samples, we find no significant correlations between super-Earths and gas giants. Combining our 85 M-dwarf sample with our FGK sample from Bryan $\&$ Lee 2024, we resolve the SE/GG correlation in stellar mass (0.3--1.5 M$_{\odot}$) and metallicity. We show the positive correlation emerges in metal-rich K-dwarfs and strengthens with increasing stellar mass. Gas giant properties also impact the correlation -- for metal rich stars, the positive correlation is strengthened by: 1) dynamically hot gas giants for all stellar masses; 2) distant gas giants only for higher mass stars; and 3) single gas giants for K-dwarfs and multiple gas giants around more massive stars. We discuss how the stellar mass dependence of the inner-outer planet correlation can be understood from the increasing disk mass budget for higher mass stars.