Occurrence Rates of Planets orbiting FGK Stars: Combining Kepler DR25, Gaia DR2 and Bayesian Inference

We characterize the occurrence rate of planets, ranging in size from 0.5-16 R$_\oplus$, orbiting FGK stars with orbital periods from 0.5-500 days. Our analysis is based on results from the `DR25' catalog of planet candidates produced by NASA's Kepler mission and stellar radii from Gaia `DR2'. We incorporate additional Kepler data products to accurately characterize the the efficiency of planets being recognized as a `threshold crossing events' (TCE) by Kepler's Transiting Planet Search pipeline and labeled as a planet candidate by the robovetter. Using a hierarchical Bayesian model, we derive planet occurrence rates for a wide range of planet sizes and orbital periods. For planets with sizes 1-1.75 R$_\oplus$ and orbital periods of 237-500 days, we find a rate of planets per FGK star of $ 0.24^{+0.11}_{-0.10}$ ($68.3\%$ credible interval). While the true rate of such planets could be lower by a factor of $\sim~2$ (primarily due to potential contamination of planet candidates by false alarms), the upper limits on the occurrence rate of such planets are robust to $\sim~10\%$. We recommend that mission concepts aiming to characterize potentially rocky planets in or near the habitable zone of sun-like stars prepare compelling science programs that would be robust for a true rate in the range $f_{R,P} = 0.05-0.51$ for $1-1.75$ R$_\oplus$ planets with orbital periods in 237-500 days, or a differential rate of $\Gamma_\oplus \equiv (d^2 f)/[d(\ln P)~d(\ln R_{p})] = 0.11-1.2$.