Distinguishing Polar and Co-planar Circumbinary Exoplanets by Eclipsing Timing Variations

Circumbinary Planets (CBPs) can be misaligned with their host binary stars. Orbital dynamics, simulations, and recent observations of proto-planetary disks all suggest that the planet can stably orbit in a plane perpendicular to that of an eccentric host binary star (i.e., a polar orbit). No solid claim of detection of such a configuration has been made; the nine systems detected by the transit technique are nearly coplanar, but their discovery is also biased towards that configuration. Here, we develop Eclipse Timing Variations (ETVs) as a method to detect misaligned CBPs. We find that since apsidal motion (periastron precession) of the host binary is prograde for a coplanar planet and retrograde for a polar planet, the mean eclipse period of primary and secondary eclipses differ in a way that distinguishes those configurations. Secondly, the Eclipse Duration Variations (EDVs) vary in a way that can confirm that inference, over and against a polar model. Thirdly, the relative phasing of primary and secondary ETVs on the planet's orbital timescale also distinguishes the two configurations, which we explain analytically and quantify through a grid of numerical models. We apply these methods to Kepler-34, a transiting planet known to be nearly coplanar by detailed photodynamic modeling. In this system, we find that the binary eclipse times alone suffice to distinguish these orbital configurations, using the effects introduced here. Our work provides a tool for discovering potential polar CBPs, or misaligned CBPs of milder inclinations, from the existing ETV dataset of the Kepler, as well as future observations by TESS or PLATO.