Uncovering Circumbinary Planetary Architectural Properties from   Selection Biases
  The new discoveries of circumbinary planetary systems shed light on the 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 finite observation period and planetary orbital precession are included. Then, understanding of the architectural properties of the currently observed transiting systems is refined, based on Bayesian analysis and a series of hypothesis tests. We find 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 is consistent with a log uniform distribution of the planetary semi-major axis; 2) it is not a selection bias that the planetary and stellar orbits are nearly coplanar ($\lesssim 3^\circ$), and this together 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 planet 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. 
Gongjie Li, Matthew J. Holman and Molei Tao
astro-ph.EP