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We infer the period ($P$) and size ($R_p$) distribution of Kepler transitingplanet candidates with $R_p\ge 1 R_{\rm Earth}$ and $P < 250$ days hosted bysolar-type stars. The planet detection efficiency is computed by using measurednoise and the observed timespans of the light curves for $\sim 120,000$ Keplertarget stars. We focus on deriving the shape of planet period and radiusdistribution functions. We find that for orbital period $P>10$ days, the planetfrequency d$N_p$/d$\log$P for "Neptune-size" planets ($R_p = 4-8 R_{\rmEarth}$) increases with period as $\propto P^{0.7\pm0.1}$. In contrast,d$N_p$/d$\log$P for "super-Earth-size" ($2-4 R_{\rm Earth}$) as well as"Earth-size" ($1-2 R_{\rm Earth}$) planets are consistent with a nearly flatdistribution as a function of period ($\propto P^{0.11\pm0.05}$ and $\proptoP^{-0.10\pm0.12}$, respectively), and the normalizations are remarkably similar(within a factor of $\sim 1.5$ at $50 $ days). Planet size distribution evolveswith period, and generally the relative fractions for big planets ($\sim 3-10R_{\rm Earth}$) increase with period. The shape of the distribution function isnot sensitive to changes in selection criteria of the sample. The impliednearly flat or rising planet frequency at long period appears to be in tensionwith the sharp decline at $\sim 100$ days in planet frequency for low massplanets (planet mass $m_p < 30 M_{\rm Earth}$) recently suggested by HARPSsurvey. Within $250$ days, the cumulative frequencies for Earth-size andsuper-Earth-size planets are remarkably similar ($\sim 28 %$ and $25%$), whileNeptune-size and Jupiter-size planets are $\sim 7%$, and $\sim 3%$,respectively. A major potential uncertainty arises from the unphysical impactparameter distribution of the candidates.

astrophysical journal/the astrophysical journal

Fast Rise of "Neptune-Size" Planets ($4-8 R_{\rm Earth}$) from $P\sim10$  to $\sim250$ days -- Statistics of Kepler Planet Candidates Up to $\sim 0.75  {\rm AU}$