Secular Structure of 1:2 and 1:3 Resonances with Neptune

TL;DR

This paper analyzes the detailed dynamical structures of the 1:2 and 1:3 Neptune resonances, revealing secular mechanisms and chaos that influence object distributions, aiding understanding of Solar System evolution.

Contribution

It provides a comprehensive analysis of the secular structures and mechanisms in the 1:2 and 1:3 Neptune resonances using frequency analysis and spectral maps, highlighting new dynamical insights.

Findings

Secular mechanisms like von-Zeipel-Lidov-Kozai influence resonance structures.

The $2g-s=s_8$ resonance affects population distribution between resonance islands.

Secondary resonances with Uranus and Neptune introduce chaos into the dynamics.

Abstract

The 1:N mean motion resonances with Neptune are of particular interest because they have two asymmetric resonance islands, where the distribution of trapped objects may bear important clues to the history of the Solar System. To explore the dynamics of these resonances and to investigate whether the imprints left by the early stage evolution can be preserved in the resonances, we conduct a comprehensive analyses on the 1:2 and 1:3 resonances. Adopt mainly the frequency analysis method, we calculate the proper frequencies of the motion of objects in the resonances, with which the secular mechanisms that influence the dynamics are determined. Use the spectral number as an indicator of orbital regularity, we construct dynamical maps on representative planes. By comparing the structures in the maps with the locations of the secular mechanisms, we find that the von-Zeipel-Lidov-Kozai mechanism and the $g=2s$ mechanism destabilize the influenced orbits and portray the overall structure of the 1:2 and 1:3 resonances. The secular resonance $2g-s=s_8$ opens a channel for objects to switch between the leading and trailing resonance islands, which can alter the population ratio between these two islands. The secondary resonances associated with the quasi 2:1 resonance between Uranus and Neptune are also detected, and they introduce more chaos to the motion. The fine dynamical structures of the 1:2 and 1:3 resonances revealed in this paper, combined with knowledge of resonant capture, provide a compelling explanation for the eccentricity distribution of observed Twotinos. And we anticipate a more complete understanding of the history of planetary migration in the Solar System can be achieved by comparing the results in this paper with the populations in the 1:N resonances in future when further observations bring us more objects.