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 1194 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 Msun to intermediate-mass subgiants
with masses as high as 1.9 Msun. 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 \propto 10^{1.2 [Fe/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 are
not likely due to convective envelope "pollution." Our data also rule out a
constant planet occurrence rate for [Fe/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 \propto Mstar), characterized by a
rise from 3.5% around M dwarfs (0.5 Msun) to 14% around A stars (2 Msun), 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.Comment: Fixed minor typos, modified the last paragraph of Section
