On the Abundance of Circumbinary Planets

We present here the first observationally based determination of the rate of occurrence of circumbinary planets. This is derived from the publicly available Kepler data, using an automated search algorithm and debiasing process to produce occurrence rates implied by the seven systems already known. These rates depend critically on the planetary inclination distribution: if circumbinary planets are preferentially coplanar with their host binaries, as has been suggested, then the rate of occurrence of planets with $R_p>6R_\oplus$ orbiting with $P_p<300$\ d is $10.0 ^{+18}_{-6.5}$\% (95\% confidence limits), higher than but consistent with single star rates. If on the other hand the underlying planetary inclination distribution is isotropic, then this occurrence rate rises dramatically, to give a lower limit of 47\%. This implies that formation and subsequent dynamical evolution in circumbinary disks must either lead to largely coplanar planets, or proceed with significantly greater ease than in circumstellar disks. As a result of this investigation we also show that giant planets (${>}10R_\oplus$) are significantly less common in circumbinary orbits than their smaller siblings, and confirm that the proposed shortfall of circumbinary planets orbiting the shorter period binaries in the Kepler sample is a real effect.