On the Occurrence Rate of Hot Jupiters in Different Stellar Environments

Many Hot Jupiters (HJs) are detected by the Doppler and the transit techniques. From surveys using these two techniques, however, the measured HJ occurrence rates differ by a factor of two or more. Using the California Planet Survey sample and the Kepler sample, we investigate the causes for the difference of HJ occurrence rate. First, we find that $12.8\%\pm0.24\%$ of HJs are misidentified in the Kepler mission because of photometric dilution and subgiant contamination. Second, we explore the differences between the Doppler sample and the Kepler sample that can account for the different HJ occurrence rate. Third, we discuss how to measure the fundamental HJ occurrence rates by synthesizing the results from the Doppler and Kepler surveys. The fundamental HJ occurrence rates are a measure of HJ occurrence rate as a function of stellar multiplicity and evolutionary stage, e.g., the HJ occurrence rate for single and multiple stars or for main sequence and subgiant stars. While we find qualitative evidence that HJs occur less frequently in subgiants and multiple stellar systems, we conclude that our current knowledge of stellar properties and stellar multiplicity rate is too limited for us to reach any quantitative result for the fundamental HJ occurrence rates. This concern extends to $\eta_{\rm{Earth}}$, the occurrence rate of Earth-like planets.