Chaos in Mean Motion Resonances of the Kuiper Belt

TL;DR

This study investigates chaos in Kuiper belt resonances, linking orbital eccentricity to stability and escape rates, and clarifies the boundary locations of the belt post-migration.

Contribution

It provides a detailed analysis of chaos levels in Kuiper belt resonances and relates them to observed eccentricities and stability boundaries, enhancing understanding of belt evolution.

Findings

Maximum observed eccentricities correspond to Lyapunov times of ~1000 orbital periods.

Most escapes at higher eccentricities have already occurred, but some continue to maintain the belt.

Inner and outer Kuiper belt boundaries are near 34 AU and 46 AU, respectively.

Abstract

In this paper on mean motion resonances in the Kuiper belt we consider effects on resonant bodies captured in an earlier migration by determining levels of chaos as a function of eccentricity, e, at the most stable orbital configuration. We find the the maximum observed e's at resonance very closely correspond to orbits with Lyapunov times ~ 1000 orbital periods of Neptune--much the same number as applies in the asteroid belt with Neptune's period replaced by Jupiter's. The fact that this number caps the e's of markedly chaotic but still existing bodies, implies that the great majority of escapes at equal and larger e's have already occurred. Yet escapes must continue at some level if the small population in the outermost belt is to be maintained because typical lifetimes of bodies there are only ~ 1/10 of the solar system's age. A study of stability at resonance also reinforces the claim that the post-migration boundary of the inner Kuiper belt lies near 34 AU and that the primordial, or pre-migration, outer one near 46 AU.