Scaling K2 VIII: Short-Period Sub-Neptune Occurrence Rates Peak Around Early-Type M Dwarfs

We uniformly combined data from the NASA Kepler and K2 missions to compute planet occurrence rates across the entire FGK and M dwarf stellar range. The K2 mission, driven by targets selected by guest observers, monitored nine times more M dwarfs than the Kepler mission. Combined, Kepler and K2 observed 130 short-period ($P=1-40$ days) Earth to Neptune-sized candidate planets orbiting M dwarfs. K2 observed 3.5 times more of these planets than Kepler for host stars below 3700 K. Our planet occurrence rates show that short-period sub-Neptunes peak at $3750^{+153}_{-97}$ K and drop for cooler M dwarfs. A peak near this location was predicted by pebble accretion planet formation models and confirmed here by observations for the first time. Super-Earths continue to increase in occurrence toward cooler stars and show no clear evidence of a peak in the host star range considered here (3200 K$-$6900 K). Our observations provide critical input to further refine planet formation models. We strongly recommend further study of mid-to-late M dwarfs with TESS and soon the Nancy Grace Roman Space Telescope and PLATO to identify additional small planet trends.