Giant Planet Occurrence in the Stellar Mass-Metallicity Plane

Correlations between stellar properties and the occurrence rate of exoplanets can be used to inform the target selection of future planet-search efforts and provide valuable clues about the planet-formation process. We analyze a sample of 1266 stars drawn from the California Planet Survey targets to determine the empirical functional form describing the likelihood of a star harboring a giant planet as a function of its mass and metallicity. Our stellar sample ranges from M dwarfs with masses as low as 0:2 M⊙ to intermediate-mass subgiants with masses as high as 1:9 M⊙. In agreement with previous studies, our sample exhibits a planet-metallicity correlation at all stellar masses; the fraction of stars that harbor giant planets scales as f ∝ 101:21⁄2Fe=H . We can rule out a flat metallicity relationship among our evolved stars (at 98% confidence), which argues that the high metallicities of stars with planets is not likely due to convective envelope “pollution.” Our data also rule out a constant planet occurrence rate for 1⁄2Fe=H < 0, indicating that giant planets continue to become rarer at sub-Solar metallicities. We also find that planet occurrence increases with stellar mass (f ∝ M⋆), characterized by a rise from 3% around M dwarfs (0:5 M⊙) to 14% around A stars (2 M⊙), at Solar metallicity. We argue that the correlation between stellar properties and giant planet occurrence is strong supporting evidence of the core-accretion model of planet formation.