Dynamical Evolution of Multi-Resonant Systems: the Case of GJ876

TL;DR

This paper analyzes the chaotic dynamics and formation of the multi-resonant GJ876 planetary system, providing a perturbative model and insights into its turbulent formation environment.

Contribution

It introduces a simple perturbative model for the system's stochasticity and explores the formation conditions involving turbulence and dissipation.

Findings

Chaotic motion is inherent to the GJ876 system.

Modest turbulence and dissipation can reproduce the observed resonance structure.

Analytic estimates of Lyapunov time and chaotic diffusion are derived.

Abstract

The GJ876 system was among the earliest multi-planetary detections outside of the Solar System, and has long been known to harbor a resonant pair of giant planets. Subsequent characterization of the system revealed the presence of an additional Neptune mass object on an external orbit, locked in a three body Laplace mean motion resonance with the previously known planets. While this system is currently the only known extrasolar example of a Laplace resonance, it differs from the Galilean satellites in that the orbital motion of the planets is known to be chaotic. In this work, we present a simple perturbative model that illuminates the origins of stochasticity inherent to this system and derive analytic estimates of the Lyapunov time as well as the chaotic diffusion coefficient. We then address the formation of the multi-resonant structure within a protoplanetary disk and show that modest turbulent forcing in addition to dissipative effects is required to reproduce the observed chaotic configuration. Accordingly, this work places important constraints on the typical formation environments of planetary systems and informs the attributes of representative orbital architectures that arise from extended disk-driven evolution.