Terrestrial, Habitable-Zone Exoplanet Frequency from Kepler

Abstract: Data from Kepler's first 136 days of operation are analyzed to determine the distribution of exoplanets with respect to radius, period, and host-star spectral type. The analysis is extrapolated to estimate the percentage of terrestrial, habitable-zone exoplanets. The Kepler census is assumed to be complete for bright stars (magnitude <14.0) having transiting planets >0.5 Earth radius and periods <42 days. It is also assumed that the size distribution of planets is independent of orbital period, and that there are no hidden biases in the data. Six significant statistical results are found: there is a paucity of small planet detections around faint target stars, probably an instrumental effect; the frequency of mid-size planet detections is independent of whether the host star is bright or faint; there are significantly fewer planets detected with periods <3 days, compared to longer periods, almost certainly an astrophysical effect; the frequency of all planets in the population with periods <42 days is 29%, broken down as terrestrials 9%, ice giants 18%, and gas giants 3%; the population has a planet frequency with respect to period which follows a power-law relation dN/dP ~ P^{\beta - 1}, with \beta = 0.71 +/- 0.08; and an extrapolation to longer periods gives the frequency of terrestrial planets in the habitable zones of FGK stars as \eta_\oplus = (34 +/- 14)%. Thus about one-third of FGK stars are predicted to have at least one terrestrial, habitable-zone planet.