Bridges and gaps at low-eccentricity first-order resonances

TL;DR

This paper explores how the circular family of periodic orbits acts as a bridge between neighboring first-order mean-motion resonances during planetary migration, affecting resonance capture and transition in dissipative systems.

Contribution

It demonstrates that the circular family of periodic orbits can connect and separate resonances, influencing orbital evolution during migration under dissipative effects.

Findings

The circular family can bridge first and higher order resonances.

Gaps in the circular family act as boundaries for resonance transitions.

Migration speed determines resonance capture into different orbital configurations.

Abstract

Previous works on the divergence of first-order mean-motion resonances (MMRs) have studied in detail the extent of the pericentric and apocentric libration zones of adjacent first-order MMRs, highlighting possible bridges between them in the low-eccentricity circular restricted three-body problem. Here, we describe the previous results in the context of periodic orbits and show that the so-called circular family of periodic orbits is the path that can drive the passage between neighbouring resonances under dissipative effects. We illustrate that the circular family can bridge first and higher order resonances while its gaps at first-order MMRs can serve as boundaries that stop transitions between resonances. In particular, for the Sun-asteroid-Jupiter problem, we show that, during the migration of Jupiter in the protoplanetary disc, a system initially evolving below the apocentric branch of a first-order MMR follows the circular family and can either be captured into the pericentric branch of an adjacent first-order MMR if the orbital migration is rapid or in a higher order MMR in case of slow migration. Radial transport via the circular family can be extended to many small body and planetary system configurations undergoing dissipative effects (e.g., tidal dissipation, solar mass-loss and gas drag).