Planet Occurrence within 0.25 AU of Solar-Type Stars from Kepler

We report the distribution of planets as a function of planet radius, orbital period, and stellar effective temperature for orbital periods less than 50 days around solar-type (GK) stars. These results are based on the 1235 planets (formally "planet candidates") from the Kepler mission that include a nearly complete set of detected planets as small as 2 R-circle plus. For each of the 156,000 target stars, we assess the detectability of planets as a function of planet radius, R-p, and orbital period, P, using a measure of the detection efficiency for each star. We also correct for the geometric probability of transit, R-star/a. We consider first Kepler target stars within the "solar subset" having T-eff = 4100-6100 K, log g = 4.0-4.9, and Kepler magnitude Kp < 15 mag, i.e., bright, main-sequence GK stars. We include only those stars having photometric noise low enough to permit detection of planets down to 2 R-circle plus. We count planets in small domains of R-p and P and divide by the included target stars to calculate planet occurrence in each domain. The resulting occurrence of planets varies by more than three orders of magnitude in the radius-orbital period plane and increases substantially down to the smallest radius (2 R-circle plus) and out to the longest orbital period (50 days, similar to 0.25 AU) in our study. For P < 50 days, the distribution of planet radii is given by a power law, df/d log R = k(R)R(alpha) with k(R) = 2.9(-0.4)(+0.5), alpha = -1.92 +/- 0.11, and R equivalent to R-p/R-circle plus. This rapid increase in planet occurrence with decreasing planet size agrees with the prediction of core-accretion Formation but disagrees with population synthesis models that predict a desert at super-Earth and Neptune sizes for close-in orbits. Planets with orbital periods shorter than 2 days are extremely rare; for R-p > 2 R-circle plus we measure an occurrence of less than 0.001 planets per star. For all planets with orbital periods less than 50 days, we measure occurrence of 0.130 +/- 0.008, 0.023 +/- 0.003, and 0.013 +/- 0.002 planets per star for planets with radii 2-4, 4-8, and 8-32 R-circle plus, in agreement with Doppler surveys. We fit occurrence as a function of P to a power-law model with an exponential cutoff below a critical period P-0. For smaller planets, P-0 has larger values, suggesting that the "parking distance" for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over a broader stellar T-eff range of 3600-7100 K, spanning M0 to F2 dwarfs. Over this range, the occurrence of 2-4 R-circle plus planets in the Kepler field increases with decreasing T-eff, with these small planets being seven times more abundant around cool stars (3600-4100 K) than the hottest stars in our sample (6600-7100 K).