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 less than 14.0) having transiting planets over 0.5 Earth radius and periods less than 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 less than 3 days, compared to longer periods, almost certainly an astrophysical effect; the frequency of all planets in the population with periods less than 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 ∼ Pβ−1, with ≃ 0.71 ± 0.08; and an extrapolation to longer periods gives the frequency of terrestrial planets in the habitable zones of FGK stars as about (34 ± 14)%. Thus about one-third of FGK stars are predicted to have at least one terrestrial, habitable-zone planet.
The period and radius of Kepler planets in the sample, around bright stars,
are plotted. The lower right corner is relatively empty, probably owing to low SNR there, not because small planets are absent from long periods. The upper left corner is relatively sparse, in spite of an expected high SNR there, implying a deficit of large planets on short-period orbits. The left side of the diagram is relatively empty owing to an apparent paucity of planets of all sizes at periods less than 3 days. The right side of the diagram is not completely sampled in the current database, so should be ignored here.
In the current Kepler database (B2011), transits with periods less than 42 days for bright, “Sun-like” FGK target stars are analyzed in order to estimate the frequency of terrestrial, habitable-zone planets in the target population, giving ⊕ ≃ (34 ± 14)%. The quoted uncertainty is the formal error in projecting the numbers of short-period planets. The true uncertainty will remain unknown until Kepler observations of orbital periods in the 1000-day range become available.
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