Abstract
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 $R_p>6R_øplus$
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 ($>10R_øplus$) 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.
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