On the Divergence of First Order Resonance Widths at Low Eccentricities

TL;DR

This paper investigates the divergence of first order resonance widths at low eccentricities, revealing the existence of resonance zones and bridges that could influence planetary migration.

Contribution

It provides a non-perturbative analysis showing resonance zone structures and introduces the concept of bridges connecting adjacent resonances at low eccentricities.

Findings

Resonance zones have two branches: pericentric and apocentric.

Widths of resonance zones shrink as eccentricity approaches zero.

Bridges connect neighboring first order resonances at low eccentricities.

Abstract

Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first order mean motion resonances diverge for nearly circular orbits. Here we examine the nature of this divergence with a non-perturbative analysis of a few first order resonances interior to a Jupiter-mass planet. We show that a first order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centers of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of "bridges" between adjacent first order resonances: at low eccentricities, the apocentric libration zone of a first order resonance smoothly connects with the pericentric libration zone of the neighboring first order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low eccentricity regime.