Fast Rise of "Neptune-size" Planets (4-8 R ⊕) from P ~ 10 to ~250 Days—Statistics of Kepler Planet Candidates up to ~0.75 AU

We infer the period (P) and size (R_p ) distribution of Kepler transiting planet candidates with R_p >= 1 R _⊕ and P < 250 days hosted by solar-type stars. The planet detection efficiency is computed by using measured noise and the observed time spans of the light curves for ~120,000 Kepler target stars. We focus on deriving the shape of planet periods and radius distribution functions. We find that for orbital periods P > 10 days, the planet frequency dN_p /dlog P for "Neptune-size" planets (R_p = 4-8 R _⊕) increases with period as vpropP ^{0.7 ± 0.1}. In contrast, dN_p /dlog P for "super-Earth-size" (2-4 R _⊕) as well as "Earth-size" (1-2 R _⊕) planets are consistent with a nearly flat distribution as a function of period (vpropP ^{0.11 ± 0.05} and vpropP ^{-0.10 ± 0.12}, respectively), and the normalizations are remarkably similar (within a factor of ~1.5 at 50 days). Planet size distribution evolves with period, and generally the relative fractions for big planets (~3-10 R _⊕) increase with period. The shape of the distribution function is not sensitive to changes in the selection criteria of the sample. The implied nearly flat or rising planet frequency at long periods appears to be in disagreement with the sharp decline at ~100 days in planet frequency for low-mass planets (planet mass m_p < 30 M _⊕) recently suggested by the HARPS survey. Within 250 days, the cumulative frequencies for Earth-size and super-Earth-size planets are remarkably similar (~28% and 25%), while Neptune-size and Jupiter-size planets are ~7% and ~3%, respectively. A major potential uncertainty arises from the unphysical impact parameter distribution of the candidates.