Tidal damping of the mutual inclination in hierachical systems

TL;DR

This paper demonstrates that tidal effects combined with gravitational interactions tend to damp high mutual inclinations in hierarchical two-planet systems, making very high inclinations unlikely over the system's lifetime.

Contribution

It introduces a mechanism showing how tidal effects and gravitational interactions reduce mutual inclinations in hierarchical systems, a process not solely due to tides on the orbits.

Findings

Mutual inclinations are damped to modest values by tidal and gravitational effects.

High mutual inclinations are unlikely if orbits are outside Lidov-Kozai regions.

The mechanism can be extended to binary stars and planet-satellite systems.

Abstract

Hierarchical two-planet systems, in which the inner body's semi-major axis is between 0.1 and 0.5 AU, usually present high eccentricity values, at least for one of the orbits. As a result of the formation process, one may expect that planetary systems with high eccentricities also have high mutual inclinations. However, here we show that tidal effects combined with gravitational interactions damp the initial mutual inclination to modest values in timescales that are shorter than the age of the system. This effect is not a direct consequence of tides on the orbits, but it results from a secular forcing of the inner planet's flattening. We then conclude that these hierarchical planetary systems are unlikely to present very high mutual inclinations, at least as long as the orbits remain outside the Lidov-Kozai libration areas. The present study can also be extended to systems of binary stars and to planet-satellite systems.