The Radius Distribution of Planets Around Cool Stars

We calculate an empirical, non-parametric estimate of the shape of the period-marginalized radius distribution of planets with periods less than 150 days using the small yet well-characterized sample of cool ($T_{\rm eff} <4000 $K) dwarf stars in the Kepler catalog. In particular, we present and validate a new procedure, based on weighted kernel density estimation, to reconstruct the shape of the planet radius function down to radii smaller than the completeness limit of the survey at the longest periods. Under the assumption that the period distribution of planets does not change dramatically with planet radius, we show that the occurrence of planets around these stars continues to increase to below 1 $R_\oplus$, and that there is no strong evidence for a turnover in the planet radius function. In fact, we demonstrate using many iterations of simulated data that a spurious turnover may be inferred from data even when the true distribution continues to rise toward smaller radii. Finally, the sharp rise in the radius distribution below $\sim$3 $R_\oplus$ implies that a large number of planets await discovery around cool dwarfs as the sensitivities of ground-based transit surveys increase.