The Occurrence of Potentially Habitable Planets Orbiting M Dwarfs Estimated from the Full Kepler Dataset and an Empirical Measurement of the Detection Sensitivity

We present an improved estimate of the occurrence rate of small planets orbiting small stars by searching the full four-year Kepler data set for transiting planets using our own planet detection pipeline and conducting transit injection and recovery simulations to empirically measure the search completeness of our pipeline. We identified 156 planet candidates, including one object that was not previously identified as a Kepler Object of Interest. We inspected all publicly available follow-up images, observing notes, and centroid analyses, and corrected for the likelihood of false positives. We evaluated the sensitivity of our detection pipeline on a star-by-star basis by injecting 2000 transit signals into the light curve of each target star. For periods shorter than 50 days, we find 0.56 (+0.06/-0.05) Earth-size planets (1-1.5 Earth radii) and 0.46 (+0.07/-0.05) super-Earths (1.5-2 Earth radii) per M dwarf. In total, we estimate a cumulative planet occurrence rate of $2.5\pm0.2$ planets per M dwarf with radii 1-4 Earth radii and periods shorter than 200 days. Within a conservatively defined habitable zone based on the moist greenhouse inner limit and maximum greenhouse outer limit, we estimate an occurrence rate of 0.16 (+0.17/-0.07) Earth-size planets and 0.12 (+0.10/-0.05) super-Earths per M dwarf habitable zone. Adopting the broader insolation boundaries of the recent Venus and early Mars limits yields a higher estimate of 0.24 (+0.18/-0.08) Earth-size planets and 0.21 (+0.11/-0.06) super-Earths per M dwarf habitable zone. This suggests that the nearest potentially habitable non-transiting and transiting Earth-size planets are $2.6\pm0.4$ pc and 10.6 (+1.6/-1.8) pc away, respectively. If we include super-Earths, these distances diminish to $2.1\pm0.2$ pc and 8.6 (+0.7/-0.8) pc.