Tidal evolution of hierarchical and inclined systems

TL;DR

This paper develops a vectorial model for the long-term tidal evolution of hierarchical, inclined three-body systems, applying it to exoplanetary systems to understand their orbital and spin dynamics.

Contribution

It introduces a new averaged vectorial formalism for modeling tidal evolution in hierarchical systems, applicable to various mass configurations and orbital inclinations.

Findings

Probability density peaks at 53 and 109 degrees for HD80606 misalignment.

Initial prograde orbits can become retrograde in HD98800 due to tides.

Tidal dissipation can reduce mutual inclination and circularize orbits in HD11964.

Abstract

We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20 degrees). Using the quadrupolar non-restricted approximation for the gravitational interactions and the viscous linear model for tides, we derive the averaged equations of motion in a vectorial formalism which is suitable to model the long-term evolution of a large variety of exoplanetary systems in very eccentric and inclined orbits. In particular, it can be used to derive constraints for stellar spin-orbit misalignment, capture in Cassini states, tidal-Kozai migration, or damping of the mutual inclination. Because our model is valid for the non-restricted problem, it can be used to study systems of identical mass or for the outer restricted problem, such as the evolution of a planet around a binary of stars. Here, we apply our model to three distinct situations: 1) the HD80606 planetary system, for which we obtain the probability density function distribution for the misalignment angle, with two pronounced peaks of higher probability around 53 and 109 degrees; 2) the HD98800 binary system, for which we show that initial prograde orbits inside the observed disc may become retrograde and vice-versa, only because of tidal migration within the binary stars; 3) the HD11964 planetary system, for which we show that tidal dissipation combined with gravitational perturbations may lead to a decrease in the mutual inclination, and a fast circularization of the inner orbit.