The Exoplanet Census: A General Method, Applied to Kepler

We develop a general method to fit the 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. Application to \Kepler data relies on estimates of the efficiency of discovering transits around Solar type stars by Howard et al. (2011). These estimates are shown to agree with theoretical predictions for an ideal transit survey. Using announced \Kepler planet candidates, we fit the PLDF as a joint powerlaw in planet radius, down to 0.5 R_Eart, and orbital period, up to 50 days. The estimated number of planets per star in this sample is ~ 0.7 --- 1.4, where the broad 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 7 days and between large and small radii at 3 R_Earth. At longer periods, the size distribution of the small planets, with index \alpha = -1.2 \pm 0.2 steepens to \alpha = -2.0 \pm 0.2 for the larger planet sample. For shorter periods, the opposite is seen: smaller planets follow a steep powerlaw, \alpha = -1.9 \pm 0.2 that is much shallower, \alpha = -0.7 \pm 0.2 at large radii. The observed deficit of intermediate-sized planets at the shortest periods may arise from the evaporation and sublimation of Neptune and Saturn-like planets. If the trend and explanation hold, it would be spectacular observational confirmation of the core accretion and migration hypotheses, and allow refinement of these theories.