Dynamical analysis of the Gliese-876 Laplace resonance

TL;DR

This study investigates the stabilizing role of the Laplace resonance in the GJ876 planetary system, revealing specific conditions under which the resonance promotes stability amidst chaotic dynamics.

Contribution

It provides a detailed dynamical analysis of the GJ876 system, identifying stable configurations and the resonance's role in system stability, which was not previously explored.

Findings

Laplace resonance acts as a stabilization mechanism.

Stable orbits are compatible with low eccentricities and inclinations.

Constraints on orbital parameters ensure system stability.

Abstract

The existence of multiple planetary systems involved in mean motion conmensurabilities has increased significantly since the Kepler mission. Although most correspond to 2-planet resonances, multiple resonances have also been found. The Laplace resonance is a particular case of a three-body resonance where the period ratio between consecutive pairs is n_1/n_2 near to n_2/n_3 near to 2/1. It is not clear how this triple resonance can act in order to stabilize (or not) the systems. The most reliable extrasolar system located in a Laplace resonance is GJ876 because it has two independent confirmations. However best-fit parameters were obtained without previous knowledge of resonance structure and no exploration of all the possible stable solutions for the system where done. In the present work we explored the different configurations allowed by the Laplace resonance in the GJ876 system by varying the planetary parameters of the third outer planet. We find that in this case the Laplace resonance is a stabilization mechanism in itself, defined by a tiny island of regular motion surrounded by (unstable) highly chaotic orbits. Low eccentric orbits and mutual inclinations from -20 to 20 degrees are compatible with the observations. A definite range of mass ratio must be assumed to maintain orbital stability. Finally we give constrains for argument of pericenters and mean anomalies in order to assure stability for this kind of systems.