The non-resonant, relativistic dynamics of circumbinary planets

TL;DR

This paper explores the complex, chaotic, and relativistically influenced long-term dynamics of circumbinary planetary systems, revealing significant differences from classical models especially at small semi-major axis ratios and high inclinations.

Contribution

It introduces a relativistic secular model for hierarchical circumbinary systems and demonstrates how relativistic effects alter stability and stationary solutions compared to Newtonian predictions.

Findings

Relativistic corrections significantly affect the system's stationary solutions.

High mutual inclinations can induce large eccentricities and chaos.

Relativistic effects are crucial even for relatively large secondary masses.

Abstract

We investigate the non-resonant, 3-D (spatial) model of the hierarchical system composed of point-mass stellar (or sub-stellar) binary and a low-mass companion (a circumbinary planet or a brown dwarf). We take into account the leading relativistic corrections to the Newtonian gravity. The secular model of the system relies on the expansion of the perturbing Hamiltonian in terms of the ratio of semi-major axes $\alpha$, averaged over the mean anomalies. We found that the low-mass object in a distant orbit may excite large eccentricity of the inner binary when the mutual inclination of the orbits is larger than about of 60 deg. This is related to strong instability caused by a phenomenon which acts similarly to the Lidov-Kozai resonance (LKR). The secular system may be strongly chaotic and its dynamics unpredictable over the long-term time scale. Our study shows that in the Jupiter-- or brown dwarf-- mass regime of the low-massive companion, the restricted model does not properly describe the long-term dynamics in the vicinity of the LKR. The relativistic correction is significant for the parametric structure of a few families of stationary solutions in this problem, in particular, for the direct orbits configurations (with the mutual inclination less than 90 degrees). We found that the dynamics of hierarchical systems with small $\alpha \sim 0.01$ may be qualitatively different in the realm of the Newtonian (classic) and relativistic models. This holds true even for relatively large masses of the secondaries.