The Radius Distribution of M dwarf-hosted Planets and its Evolution

M dwarf stars are the most promising hosts for detection and characterization of small and potentially habitable planets, and provide leverage relative to solar-type stars to test models of planet formation and evolution. Using \emph{Gaia} astrometry, adaptive optics imaging, and calibrated gyrochronologic relations to estimate stellar properties and filter binaries we refined the radii of 117 Kepler Objects of Interest (confirmed or candidate planets) transiting 74 single late K- and early M-type stars, and assigned stellar rotation-based ages to 113 of these. We constructed the radius distribution of 115 small ($<4R_{\oplus}$) planets and assessed its evolution. As for solar-type stars, the inferred distribution contains distinct populations of "super-Earths" (at $\approx$1.3$_{\oplus}$) and "sub-Neptunes" (at $\approx$2.2$R_{\oplus}$) separated by a gap or "valley" at $\approx$1.7$_{\oplus}$ that has a period dependence that is significantly weaker (power law index of -0.03$^{+0.01}_{-0.03}$) than for solar-type stars. Sub-Neptunes are largely absent at short periods ($<$2 days) and high irradiance, a feature analogous to the "Neptune desert" observed around solar-type stars. The relative number of sub-Neptunes to super-Earths declines between the younger and older halves of the sample (median age 3.86 Gyr), although the formal significance is low ($p = 0.08$) because of the small sample size. The decline in sub-Neptunes appears to be more pronounced on wider orbits and low stellar irradiance. This is not due to detection bias and suggests a role for H$_2$O as steam in inflating the radii of sub-Neptunes and/or regulating the escape of H/He from them.