THE FALSE POSITIVE RATE OFKEPLERAND THE OCCURRENCE OF PLANETS

Abstract

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 (6-22 R ⊕ ) at 17.7%, reaching a low of 6.7% for small Neptunes (2-4 R ⊕ ), and increasing again for Earth-size planets (0.8-1.25 R ⊕ ) 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 1.25 R ⊕ 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.

Stellar statistics along the ecliptic and the impact on the K2 mission concept

“…though the latest effort by Rowe et al (2014) added 340 planetary systems with 851 planets to the validated count), probabilistic simulations have shown that a vast majority of these candidates are in fact planets (Morton & Johnson 2011;Fressin et al 2013). Orbital periods of exoplanets are consistent with a flat distribution in log space (Dong & Zhu 2013), at least in the ∼1-day to the ∼100-day regime that is of most interest for K2 targets.…”

Single transit candidates from K2: detection and period estimation

“…This is similar to the giant planet occurrence rates found by (Mayor et al 2011), with 14 ± 2 per cent of FGK stars with planets larger than >50M ⊕ . Accounting for transit probability (scaled with stellar radius and semimajor axis by R a ) and timing probability (scaled with observation campaign duration and orbital period by t obs P ) gives detectable multiand single-transiting planets around 0.15 and 0.03 per cent of stars from Fressin et al (2013) and 0.09 and 0.02 per cent from Mayor et al (2011) (Fig. 1).…”

“…Fressin et al 2013) suggest that a handful of longer period planets should be E-mail: h.p.osborn@warwick.ac.uk detected per K2 campaign. The reduced mission duration of 75 d (compared to 1400 in the primary mission) means that such planets are likely to only transit once.…”

The Emerging Paradigm of Pebble Accretion

“…One of the key surprises of the last decade has been the discovery of the superEarth planet population (Fressin et al 2013;Petigura et al 2013): close-in planets (r 0:1 AU) of mass between Earth and Neptune, which are rock-dominated but often have a gaseous envelope (Lopez et al 2012). Because super-Earths orbit their host stars at close distance, there is no longer a timescale problem for their assembly-even without gravitational focusing coagulation proceeds fast.…”