A Statistical Reconstruction of the Planet Population Around Kepler Solar-Type Stars

Abstract

Using the cumulative catalog of planets detected by the NASA Kepler mission, we reconstruct the intrinsic occurrence of Earth- to Neptune-size (1 - 4$R_{\oplus}$) planets and their distributions with radius and orbital period. We analyze 76,711 solar-type ($0.8<R_*/R_{\odot}<1.2 $) stars with 430 planets on 20-200~d orbits, excluding close-in planets that may have been affected by the proximity to the host star. Our analysis considers errors in planet radii and includes an "iterative simulation" technique that does not bin the data. We find a radius distribution that peaks at 2-2.8 Earth radii, with lower numbers of smaller and larger planets. These planets are uniformly distributed with logarithmic period, and the mean number of such planets per star is $0.46 \pm 0.03$. The occurrence is $\sim 0.66$ if planets interior to 20~d are included. We estimate the occurrence of Earth-size planets in the "habitable zone" (defined as 1-2$R_{\oplus}$, 0.99-1.7 AU for solar-like stars) as $6.4^{+3.4}_{-1.1} \%$. Our results largely agree with those of Petigura et al. (2013), although we find a higher occurrence of 2.8-4 Earth-radii planets. The reasons for this excess are the inclusion of errors in planet radius, updated Huber et al. (2014) stellar parameters, and also the exclusion of planets which may have been affected by proximity to the host star.