THE RADIUS DISTRIBUTION OF PLANETS AROUND COOL STARS

Abstract

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