Uncovering Circumbinary Planetary Architectural Properties From Selection Biases

Abstract

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 ( 3 • ), 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.

Searching for Exoplanets around X-Ray Binaries with Accreting White Dwarfs, Neutron Stars, and Black Holes

“…If they exist, planets in XRB systems may certainly populate orbits beyond the stability limit. Yet in the currently known CB systems discovered with Kepler-if they can provide us with any direction-the planets are mostly close to the stability limit (Welsh et al 2015;Li et al 2016). The general trend is for both transit and ingress/egress durations to increase with binary Transit and ingress/egress duration of planets in the smallest possible circumbinary orbits (i.e., at the stability limit) around a binary consisting of a white dwarf with mass 0.8 M  .…”

“…Li et al (2016) show that P tran depends on the ratio of the relative displacement of the planet and star with respect to the observer, dl, and the projected width of the stellar orbit. The relative displacements are …”

“…Thus our second step is to determine the planet transit probability, given that it intersects the binary orbit. We provide the following summary of the probability calculations and refer the reader to Li et al (2016) for the full details.…”

“…Precession is described by time variation in the codependent quantities i d and Ω, the longitude of ascending node of the planet. Li et al (2016) derive the probability for a planet to cross the binary orbit, P cr , as…”

“…To estimate transit probabilities for circumbinary planets orbiting XRB systems, we follow Li et al (2016), who provide analytical expressions for calculating transit probabilities involving eclipsing stellar binaries. The transit criterion can be separated into two parts.…”