Orbital dynamics of two circumbinary planets around misaligned eccentric binaries

Abstract

We investigate the orbital dynamics of circumbinary planetary systems with two planets around a circular or eccentric orbit binary. The orbits of the two planet are initially circular and coplanar to each other, but misaligned with respect to the binary orbital plane. The binary-planet and planet-planet interactions result in complex planet tilt oscillations. We use analytic models and numerical simulations to explore the effects of various values of the planet semi-major axes, binary eccentricity, and initial inclination. Around a circular orbit binary, secular tilt oscillations are driven by planet-planet interactions and are periodic. In that case, planets undergo mutual libration if close together and circulation if far apart with an abrupt transition at a critical separation. Around an eccentric orbit binary, secular tilt oscillations are driven by both planet-planet interactions and binary-planet interactions. These oscillations generally display more than one frequency and are generally not periodic. The transition from mutual planet libration to circulation is not sharp and there is a range of separations for which the planets are on orbits that are sometimes mutually librating and sometimes circulating. In addition, at certain separations, there are resonances for which tilt oscillations are complicated but periodic. For planets that are highly misaligned with respect to an eccentric orbit binary, there are stationary (non-oscillating) tilt configurations that are generalisations of polar configurations for the single planet case. Tilt oscillations of highly inclined planets occur for initial tilts that depart from the stationary configuration.

Misalignment of terrestrial circumbinary planets as an indicator of their formation mechanism

“…Once a gap is opened in a circumbinary disk, planet-disk interactions may lead to lower levels of misalignment (Pierens & Nelson 2018). Planet-planet interactions could help maintain the misalignment after gas dissipation (Chen et al 2022) although for very close binaries, stellar tides may realign a highly inclined planet on Gyr timescales (Correia et al 2016). Our simulations including giant planets show that misaligned exterior giant planets do not have a significant effect on the orbits of the inner aligned terrestrial planets.…”

“…The giant planets undergo inclination oscillations in all systems, as a result of planet-planet interactions around the circular orbit binary and both planet-planet and planet-binary interactions around the eccentric binary (Chen et al 2022). Jupiter is able to remain highly inclined in all systems, except in one run in C60 JS .…”

Grid-Based Simulations of Polar Circumbinary Disks: Polar Alignment and Vortex Formation

“…Planets on circumbinary orbits exhibit large transit timing variations, on the order of hours or days (Armstrong et al 2013). Inclined orbits are more likely to produce single or irregular transits due to the orbital precession induced by the binary torque (Martin & Triaud 2014;Chen et al 2019Chen et al , 2022, rendering most detection methods used for single planets unusable and requiring the use of special transit folding methods (e.g. Martin & Fabrycky 2021).…”

Coplanar Circumbinary Planets Can Be Unstable to Large Tilt Oscillations in the Presence of an Inner Polar Planet

“…Giant planets that form in a warped or broken disk may form with a mutual misalignment. The misalignment could also arise from later planet-planet or planet-binary interactions (Chen et al 2022).…”