Orbital dynamics of circumbinary planets

Abstract

We investigate the dynamics of a nonzero mass, circular orbit planet around an eccentric orbit binary for various values of the binary eccentricity, binary mass fraction, planet mass, and planet semi-major axis by means of numerical simulations. Previous studies investigated the secular dynamics mainly by approximate analytic methods. In the stationary inclination state, the planet and binary precess together with no change in relative tilt. For both prograde and retrograde planetary orbits, we explore the conditions for planetary orbital libration versus circulation and the conditions for stationary inclination. As was predicted by analytic models, for sufficiently high initial inclination, a prograde planet's orbit librates about the stationary tilted state. For a fixed binary eccentricity, the stationary angle is a monotonically decreasing function of the ratio of the planet-to-binary angular momentum j. The larger j, the stronger the evolutionary changes in the binary eccentricity and inclination. We also calculate the critical tilt angle that separates the circulating from the librating orbits for both prograde and retrograde planet orbits. The properties of the librating orbits and stationary angles are quite different for prograde versus retrograde orbits. The results of the numerical simulations are in very good quantitative agreement with the analytic models. Our results have implications for circumbinary planet formation and evolution.

Orbital dynamics of two circumbinary planets around misaligned eccentric binaries

“…For a misaligned non-zero mass planet orbiting around an eccentric binary, the critical inclination for the planet to librate depends on the binary eccentricity and the angular momentum ratio of the planet to the binary. The angle of the stationary inclination, or polar alignment, occurs at less than 90 • if the planet is massive (Farago & Laskar 2010;Zanazzi & Lai 2018;Chen et al 2019;. Furthermore, in Chen et al (2019) we found that the angular momentum transfer between the binary and a massive planet can be significant and the binary eccentricity can oscillate during the nodal libration.…”

“…The angle of the stationary inclination, or polar alignment, occurs at less than 90 • if the planet is massive (Farago & Laskar 2010;Zanazzi & Lai 2018;Chen et al 2019;. Furthermore, in Chen et al (2019) we found that the angular momentum transfer between the binary and a massive planet can be significant and the binary eccentricity can oscillate during the nodal libration. The numerical simulation results are consistent with the analytic model in .…”

“…We describe the secular evolution of a two planet system around a binary by using analytic models in Section 2 for this case. We also extend the numerical three-body simulations in Chen et al (2019Chen et al ( , 2020) to four-body numerical simulations. In Section 3, we describe the initial set-up of our four-body simulations and we describe the results in Section 4.…”

“…The dynamics of a circumbinary planet around an eccentric orbit binary are also affected by the mass of the planet (Chen et al 2019). For a misaligned non-zero mass planet orbiting around an eccentric binary, the critical inclination for the planet to librate depends on the binary eccentricity and the angular momentum ratio of the planet to the binary.…”

Semianalytical model for planetary resonances

“…It is important to remark that outside the separatrix region, Ω circulates (prograde or retrograde direction). We recall that librating orbits and stationary angles change when brown dwarf companions are considered (Chen et al 2019), that is, for masses that are not compatible with CB detected planets. We explored the MMR location and widths around a wide variety of circumbinary inclined orbits for different binary mass ratios q = {0.2, 0.5, 1}.…”