TERRESTRIAL, HABITABLE-ZONE EXOPLANET FREQUENCY FROMKEPLER

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 (HZ) 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 β−1 , with β 0.71 ± 0.08; and an extrapolation to longer periods gives the frequency of terrestrial planets in the HZs of FGK stars as η ⊕ (34 ± 14)%. Thus about one-third of FGK stars are predicted to have at least one terrestrial, HZ planet.

Characterization of exoplanets from their formation

“…False positives would also blur the upper radius limit of planets. A finding of Traub (2012) could also point in this direction: he finds that in the Kepler data there are significantly more candidates around faint stars than around brighter host stars for large planets with radii of about 8 to 40 R ⊕ . This is not to be expected for astrophysical reasons, so Traub (2012) puts forward the explanation that it is more difficult to distinguish background eclipsing binaries from planetary transits when the stars are faint.…”

“…We employ the function proposed by Traub (2011), which has four parameters b, M 0 , w, p and is given as…”

“…The power-law exponent β is given as d lnR/d ln M. The powerlaw exponent for Traub's (2011) fit is given as (ln is the natural logarithm)…”

“…Recently, the space missions Convection Rotation and planetary Transits (CoRoT) and Kepler yielded very precise measurements of the radius of a very large number of planet candidates (Léger et al 2009;Borucki et al 2011;Batalha et al 2012). The data from the Kepler satellite has stimulated a multitude of studies such as Howard et al (2012); Traub (2011); Demory & Seager (2011);Youdin (2011) ;Wolfgang & Laughlin (2012), and Gaidos et al (2012), to name just a few. The results of these studies will be used in this work to compare the radii of the actual and the synthetic population.…”

The PLATO 2.0 mission

“…For planets with periods longer than 90 days, no certain planet frequency of super-Earths is known to date, with frequency ranging from few up to 64% (Catanzarite & Shao 2011;Traub, 2012;Gaidos 2013;Petigura et al 2013). We therefore assume 40% of the stars have a super-Earth in the two distance bins considered (0.4-0.8 au and 0.8-1.2 au) as a typical, mean value.…”