Planet occurrence within 0.25AU 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 50days 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 _⊕. 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 /a. We consider first Kepler target stars within the "solar subset" having T _eff = 4100-6100K, 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 _⊕. 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 _⊕) and out to the longest orbital period (50days, 0.25AU) in our study. For P < 50 days, the distribution of planet radii is given by a power law, df/dlog R = k_RR ^α with k_R = 2.9^+0.5 _{- 0.4}, α = -1.92 ± 0.11, and R ≡ R _p/R _⊕. 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 2days are extremely rare; for R _p > 2 R _⊕ we measure an occurrence of less than 0.001 planets per star. For all planets with orbital periods less than 50days, 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 _⊕, 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 3600-7100K, spanning M0 to F2 dwarfs. Over this range, the occurrence of 2-4 R _⊕ planets in the Kepler field increases with decreasing T _eff, with these small planets being seven times more abundant around cool stars (3600-4100K) than the hottest stars in our sample (6600-7100K).