Kepler Planet Occurrence Rates for Mid-Type M Dwarfs as a Function of Spectral Type

Previous studies of planet occurrence rates largely relied on photometric stellar characterizations. In this paper, we present planet occurrence rates for mid-type M dwarfs using spectroscopy, parallaxes, and photometry to determine stellar characteristics. Our spectroscopic observations have allowed us to constrain spectral type, temperatures, and in some cases metallicities for 337 out of 561 probable mid-type M dwarfs in the primary Kepler field. We use a random forest classifier to assign a spectral type to the remaining 224 stars. Combining our data with Gaia parallaxes, we compute precise ($\sim$3%) stellar radii and masses, which we use to update planet parameters and planet occurrence rates for Kepler mid-type M dwarfs. Within the Kepler field, there are seven M3 V to M5 V stars which host 13 confirmed planets between 0.5 and 2.5 Earth radii and at orbital periods between 0.5 and 10 days. For this population, we compute a planet occurrence rate of $1.19^{+0.70}_{-0.49}$ planets per star. For M3 V, M4 V, and M5 V, we compute planet occurrence rates of $0.86^{+1.32}_{-0.68}$, $1.36^{+2.30}_{-1.02}$, and $3.07^{+5.49}_{-2.49}$ planets per star, respectively.