Occurrence Rates of Planets Orbiting M Stars: Applying ABC to Kepler DR25, Gaia DR2, and 2MASS Data.

We present robust planet occurrence rates for Kepler planet candidates around M stars for planet radii $R_p = 0.5-4~\textrm{R}_\oplus$ and orbital periods $P = 0.5-256$ days using the approximate Bayesian computation (ABC) technique. This work incorporates the final Kepler DR25 planet candidate catalog and data products and augment them with updated stellar properties using Gaia DR2 and 2MASS PSC. We analyze a clean sample of $1,530$ Kepler targets that host $89$ associated planet candidates. These early M-dwarfs and late K-dwarfs were selected from cross-referenced targets using several photometric quality flags from Gaia DR2 and color-magnitude cuts using 2MASS magnitudes. We identify a habitable zone occurrence rate of $f_{\textrm{HZ}} = 0.38^{+0.04}_{-0.05}$ for planets with $0.75-1.5$ R$_\oplus$ size. We caution that occurrence rate estimates for Kepler's M stars are sensitive to the choice of prior due to the small sample of target stars and planet candidates. For example, we find an occurrence rate of $8.9^{+1.2}_{-0.9}$ or $4.8^{+0.7}_{-0.6}$ planets per M-dwarf (integrating over $R_p = 0.5-4~\textrm{R}_\oplus$ and $P = 0.5-256$ days) for our two choices of prior. These occurrence rates are greater than those for FGK-dwarf target when compared at the same range of orbital periods, but similar to occurrence rates when computed as a function of equivalent stellar insolation. This suggests that stellar irradiance has a significant and possibly dominant role in planet formation processes regardless of spectral type. Combining our result with recent studies of exoplanet architectures indicates that most, and potentially all, early-M dwarfs harbor planetary systems.