Chaotic Excitation and Tidal Damping in the GJ 876 System

TL;DR

This paper investigates how chaotic gravitational interactions and tidal forces influence the orbital eccentricity of the innermost planet in the GJ 876 system, revealing a balance that maintains its eccentricity over cosmic timescales.

Contribution

It introduces a combined approach of stochastic secular perturbation theory and N-body simulations to explain the eccentricity maintenance in a multi-planet system.

Findings

The inner planet's eccentricity results from a balance between chaos and tidal damping.

Estimated tidal Q factor for GJ 876d is between 10,000 and 100,000.

The system's architecture constrains the planet's tidal dissipation properties.

Abstract

The M-dwarf GJ 876 is the closest known star to harbor a multi-planetary system. With three outer planets locked in a chaotic Laplace-type resonance and an appreciably eccentric short-period Super-Earth, this system represents a unique exposition of extrasolar planetary dynamics. A key question that concerns the long-term evolution of this system, and the fate of close-in planets in general, is how the significant eccentricity of the inner-most planet is maintained against tidal circularization on timescales comparable to the age of the universe. Here, we employ stochastic secular perturbation theory and N-body simulations to show that the orbit of the inner-most planet is shaped by a delicate balance between extrinsic chaotic forcing and tidal dissipation. As such, the planet's orbital eccentricity represents an indirect measure of its tidal quality factor. Based on the system's present-day architecture, we estimate that the extrasolar Super-Earth GJ 876d has a tidal Q~10,000-100,000 - a value characteristic of solar system gas giants.