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

Abstract The observed correlation between inner super-Earths (SE) and outer gas giants (GG) places strong constraints on formation theories. Building on previous work, M. L. Bryan & E. J. Lee 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 ⊙ ) hosting inner super-Earths, we calculate P(GG∣SE, [Fe/H] > 0) = 9.4 (+10.2 −3.1)% and P(GG∣SE, [Fe/H] ≤ 0) < 3.1%. Compared to the field gas giant frequency calculated from the L. J. Rosenthal et al. sample, we find P(GG∣[Fe/H] > 0) = 10.3 (+6.9 −3.1)%, and P(GG∣[Fe/H] ≤ 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 M. L. Bryan & E. J. Lee, we resolve the SE/GG correlation in stellar mass (0.3–1.5 M ⊙ ) 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.