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 to 16 R-circle plus, orbiting FGK stars with orbital periods from 0.5 to 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 efficiency of planets being recognized as threshold crossing events by Kepler's Transiting Planet Search pipeline and labeled as planet candidates 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 0.75-1.5 R-circle plus and orbital periods of 237-500 days, we find a rate of planets per FGK star of <0.27 (84.13th percentile). While the true rate of such planets could be lower by a factor of similar to 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 similar to 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) = 0.03-0.40 for 0.75-1.5 R-circle plus planets with orbital periods in 237-500 days, or a differential rate of Gamma(circle plus) (d(2)f)/[d(ln P) d (ln R-p)]= 0.06-0.76.