The False Positive Rate of Kepler and the Occurrence of Planets

The Kepler Mission is uniquely suited to study the frequencies of extrasolar planets. This goal requires knowledge of the incidence of false positives such as eclipsing binaries in the background of the targets, or physically bound to them, which can mimic the photometric signal of a transiting planet. We perform numerical simulations of the Kepler targets and of physical companions or stars in the background to predict the occurrence of astrophysical false positives detectable by the Mission. Using real noise level estimates, we compute the number and characteristics of detectable eclipsing pairs involving main sequence stars and non-main sequence stars or planets, and we quantify the fraction of those that would pass the Kepler candidate vetting procedure. By comparing their distribution with that of the Kepler Objects of Interest (KOIs) detected during the first six quarters of operation of the spacecraft, we infer the false positive rate of Kepler and study its dependence on spectral type, candidate planet size, and orbital period. We find that the global false positive rate of Kepler is 9.4%, peaking for giant planets (6–22R⊕) at 17.7%, reaching a low of 6.7% for small Neptunes (2–4R⊕), and increasing again for Earth-size planets (0.8–1.25R⊕) to 12.3%. Most importantly, we also quantify and characterize the distribution and rate of occurrence of planets down to Earth size with no prior assumptions on their frequency, by subtracting from the population of actual Kepler candidates our simulated population of astrophysical false positives. We find that 16.5± 3.6% of main-sequence FGK stars have at least one planet between 0.8 and 1.25R⊕ with orbital periods up to 85 days. This result is a significant step towards the determination of eta-earth, the occurrence of Earth-like planets in the habitable zone of their parent stars. There is no significant dependence of the rates of planet occurrence between 0.8 and 4 Earth radii with spectral type. In the process, we derive also a prescription for the signal recovery rate of Kepler that enables a good match to both the KOI size and orbital period distribution, as well as their signal-to-noise distribution.