The exoplanet census: A general method applied to Kepler

We develop a general method to fit the underlying planetary distribution function (PLDF) to exoplanet survey data. This maximum likelihood method accommodates more than one planet per star and any number of planet or target star properties. We apply the method to announced Kepler planet candidates that transit solar-type stars. The Kepler team's estimates of the detection efficiency are used and are shown to agree with theoretical predictions for an ideal transit survey. The PLDF is fit to a joint power law in planet radius, down to 0.5 R _⊕, and orbital period, up to 50days. The estimated number of planets per star in this sample is ∼0.7-1.4, where the range covers systematic uncertainties in the detection efficiency. To analyze trends in the PLDF we consider four planet samples, divided between shorter and longer periods at 7days and between large and small radii at 3 R _⊕. The size distribution changes appreciably between these four samples, revealing a relative deficit of ∼3 R_⊕ planets at the shortest periods. This deficit is suggestive of preferential evaporation and sublimation of Neptune- and Saturn-like planets. If the trend and explanation hold, it would be spectacular observational support of the core accretion and migration hypotheses, and would allow refinement of these theories.