Resonance Capture of a Test Particle by an Eccentric Planet in the Presence of Externally-Driven Apsidal Precession

TL;DR

This paper explores how external apsidal precession influences the capture of a test particle into mean-motion resonance with an eccentric planet, revealing critical precession rates that disrupt resonance even at low eccentricities.

Contribution

It introduces a detailed analysis of the impact of externally driven apsidal precession on resonance capture, extending the understanding beyond isolated two-body dynamics.

Findings

Capture sensitivity to differential precession even at low rates

Identification of two critical precession frequencies disrupting capture

Implications for resonant object capture in the Solar System

Abstract

Planets undergoing convergent migration can be captured into mean-motion resonance (MMR), in which the planets' periods are related by integer ratios. The dynamics of MMR are typically considered in isolation, including only the forces between the planets and with the central star. However, the planets are often subjected to external forces that induce apsidal precessions, which may split the MMR into two sub-resonances and give rise to chaotic motion due to resonance overlap. In this study, we investigate how such externally induced differential apsidal precession affects capture into first-order $j:j+1$ MMRs. We study the restricted three-body problem for a test particle outside of an eccentric planet, with the planet undergoing outward migration. We find that capture can be sensitive to the differential apsidal precession, even when the precession rate is much smaller than the resonance overlap criterion. We identify two critical precession frequencies -- related to resonance overlap and secular apsidal resonance -- around which capture is disrupted even for very small planet eccentricity. Our results may help clarify the capture process of resonant trans-Neptunian objects by outward-migrating Neptune in early Solar System.