2016ApJ...831...96L

Studying newly discovered circumbinary planetary systems improves our understanding of planetary system formation. Learning the architectural properties of these systems is essential for constraining the different formation mechanisms. We first revisit the stability limit of circumbinary planets. Next, we focus on eclipsing stellar binaries and obtain an analytical expression for the transit probability in a realistic setting, where a finite observation period and planetary orbital precession are included. Our understanding of the architectural properties of the currently observed transiting systems is then refined, based on Bayesian analysis and a series of tested hypotheses. We find that (1) it is not a selection bias that the innermost planets reside near the stability limit for eight of the nine observed systems, and this pile-up is consistent with a log uniform distribution of the planetary semimajor axis; (2) it is not a selection bias that the planetary and stellar orbits are nearly coplanar (<=3deg), and this-along with previous studies-may imply an occurrence rate of circumbinary planets similar to that of single star systems; (3) the dominance of observed circumbinary systems with only one transiting planet may be caused by selection effects; (4) formation mechanisms involving Lidov-Kozai oscillations, which may produce misalignment and large separation between planets and stellar binaries, are consistent with the lack of transiting circumbinary planets around short-period stellar binaries, in agreement with previous studies. As a consequence of (4), eclipse timing variations may better suit the detection of planets in such configurations.