Secular and tidal evolution of circumbinary systems

TL;DR

This paper develops a vectorial formalism to study the long-term secular evolution of circumbinary systems under tidal effects, revealing mechanisms for orbital alignment, resonance, and chaos in eccentric and inclined configurations.

Contribution

It introduces a simplified vectorial approach to model the secular dynamics of three-body systems with tides, applicable to a wide range of hierarchical systems.

Findings

Circumbinary planets can become coplanar via secular resonance.

Libration of the inner orbit's pericenter leads to chaotic spin and eccentricity evolution.

The model applies to star-planet-satellite and triple stellar systems.

Abstract

We investigate the secular dynamics of three-body circumbinary systems under the effect of tides. We use the octupolar non-restricted approximation for the orbital interactions, general relativity corrections, the quadrupolar approximation for the spins, and the viscous linear model for tides. We derive the averaged equations of motion in a simplified vectorial formalism, which is suitable to model the long-term evolution of a wide variety of circumbinary systems in very eccentric and inclined orbits. In particular, this vectorial approach can be used to derive constraints for tidal migration, capture in Cassini states, and stellar spin-orbit misalignment. We show that circumbinary planets with initial arbitrary orbital inclination can become coplanar through a secular resonance between the precession of the orbit and the precession of the spin of one of the stars. We also show that circumbinary systems for which the pericenter of the inner orbit is initially in libration present chaotic motion for the spins and for the eccentricity of the outer orbit. Because our model is valid for the non-restricted problem, it can also be applied to any three-body hierarchical system such as star-planet-satellite systems and triple stellar systems.