Non-perturbative investigation of low eccentricity exterior mean motion resonances

TL;DR

This study extends non-perturbative analysis of mean motion resonances to exterior resonances at low eccentricities, revealing complex resonance structures, bridges, and chaos influenced by perturber mass.

Contribution

It provides the first non-perturbative analysis of exterior mean motion resonances at low eccentricities, uncovering new resonance behaviors and secondary resonances.

Findings

First order exterior resonances have two low-eccentricity branches.

Higher order resonances dissolve into chaos with increasing perturber mass.

Secondary resonances significantly contribute to chaos near higher-mass resonances.

Abstract

Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel properties in the low eccentricity regime for interior mean motion resonances of Jupiter in the fundamental model of the circular planar restricted three body model. Here we extend the non-perturbative investigation to exterior mean motion resonances in the low eccentricity regime (up to about 0.1) and for perturber mass in the range 5e-5 to 1e-3 (in units of the central mass). Our results demonstrate that first order exterior resonances have two branches at low eccentricity as well as low-eccentricity bridges connecting neighboring first order resonances. With increasing perturber mass, higher order resonances dissolve into chaos whereas low order resonances persist with larger widths in their radial extent but smaller azimuthal widths. For low order resonances, we also detect secondary resonances arising from small integer commensurabilities between resonant librations and the synodic frequency. These secondary resonances contribute significantly to generating the chaotic sea that typically occurs near mean motion resonances of higher-mass perturbers.