2010PASP..122..905J

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 to intermediate-mass subgiants with masses as high as. 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. 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, indicating that giant planets continue to become rarer at sub-Solar metallicities. We also find that planet occurrence increases with stellar mass , characterized by a rise from 3% around M dwarfs to 14% around A stars , 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.