Secular structure of 1:2 and 1:3 mean motion resonances with Neptune

Abstract

The 1:N mean motion resonances (MMRs) with Neptune are of particular interest in astrophysical research because they have two asymmetric resonance islands, where the distribution of trapped objects may bear important clues to resolving 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 conducted a comprehensive analysis of the 1:2 and 1:3 resonances. By mainly adopting the frequency analysis method, we calculated the proper frequencies of the motion of objects in the resonances and determined the secular mechanisms that influence the dynamics. Using the spectral number (SN) as an indicator of orbital regularity, we constructed dynamical maps on representative planes. After 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 thus sculpt the overall structure of the 1:2 and 1:3 resonances. The secular resonance of $2g-s=s_8$ 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 were also detected, likely introducing 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. Furthermore, 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, with forthcoming observations offering more objects for study in the future.