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

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-circle dot) hosting inner super-Earths, we calculate P(GG divided by SE, [Fe/H] > 0) = 9.4 (+10.2 -3.1)% and P(GG divided by 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 divided by[Fe/H] > 0) = 10.3 (+6.9 -3.1)%, and P(GG divided by[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-circle dot) 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.