Chaotic Diffusion in the Gliese-876 Planetary System

TL;DR

This study investigates the chaotic diffusion in the Gliese-876 planetary system, revealing that resonant multi-planet systems can remain stable despite high chaos, with distinct regions of diffusion within the Laplace resonance.

Contribution

It demonstrates that highly chaotic resonant planetary systems can exhibit minimal diffusion and remain stable over long timescales, challenging previous assumptions about chaos and stability.

Findings

Inner resonance region shows low chaos and slow diffusion

Outer resonance region exhibits larger dynamical indicators

The Laplace resonance's stochastic borders prevent system destruction

Abstract

Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disk, and a natural consequence of irregular motion. In this paper we show that resonant multi-planetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over timescales comparable to their age.Using the GJ-876 system as an example, we analyze the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding regions of the Laplace resonance. We numerically integrate ensembles of close initial conditions, compute Poincar\'e maps and estimate the chaotic diffusion present in this system. Our results show that, the Laplace resonance contains two different regions: an inner domain characterized by low chaoticity and slow diffusion, and an outer one displaying larger values of dynamical indicators. In the outer resonant domain, the stochastic borders of the Laplace resonance seem to prevent the complete destruction of the system. We characterize the diffusion for small ensembles along the parameters of the outermost planet. Finally, we perform a stability analysis of the inherent chaotic, albeit stable Laplace resonance, by linking the behavior of the resonant variables of the configurations to the different sub-structures inside the three-body resonance.