The occurrence and the distribution of masses and radii of exoplanets

We analyze the statistics of Doppler-detected planets and Keplere-detected planet candidates of high integrity. We determine the number of planets per star as a function of planet mass, radius, and orbital period, and the occurrence of planets as a function of stellar mass. We consider only orbital periods less than 50 days around Solar-type (GK) stars, for which both Doppler and Kepler offer good completeness. We account for observational detection effects to determine the actual number of planets per star. From Doppler-detected planets discovered in a survey of 166 nearby G and K main sequence stars we find a planet occurrence of 15⁺⁵_-4% for planets with M sin i = 3-30 M_E and P < 50 d, as described in Howard et al. (2010). From Keplere, the planet occurrence is 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_E, consistent with Doppler-detected planets. From Keplere, the number of planets per star as a function of planet radius is given by a power law, df/dlog R = k_R R^α with k_R = 2.9^+0.5_-0.4, α = -1.92 +/- 0.11, and R = R_P/R_E. Neither the Doppler-detected planets nor the Keplere-detected planets exhibit a ``desert'' at super-Earth and Neptune sizes for close-in orbits, as suggested by some planet population synthesis models. The distribution of planets with orbital period, P, shows a gentle increase in occurrence with orbital period in the range 2-50 d. The occurrence of small, 2-4 R_E planets increases with decreasing stellar mass, with seven times more planets around low mass dwarfs (3600-4100 K) than around massive stars (6600-7100 K).