PLANET OCCURRENCE WITHIN 0.25 AU OF SOLAR-TYPE STARS FROM KEPLER

Abstract

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 ⊕ . 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 = 4100–6100 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 ⊕ . 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 (50 days, ∼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 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 2 days 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 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 ⊕ , 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 ⊕ 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).