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Mapping Neptune’s resonances into the distant solar system

Presentation #305.01 in the session “The Hill Sphere, Trojans, Horseshoe Orbits, and Resonances”.

Published onJun 01, 2021
Mapping Neptune’s resonances into the distant solar system

The observed transneptunian population is well known to contain many objects in a wide range of Neptune’s exterior mean motion resonances. However, there is not a consensus in the literature about how far out in semimajor axis Neptune’s resonances maintain a significant influence. Currently the most distant securely resonant observed objects are found in Neptune’s 9:1 resonance at a=130 au; however the lack of observed objects in more distant resonances is due to observational biases against detecting high-a objects and insufficiently precise orbit fits for the few that are observed. For a constant perihelion distance range (we take q=~30-60 au), at some distant semimajor axis value, the stable libration zones of resonances tend to disappear; this is likely either because widths of adjacent resonances become large relative to their separation, causing resonance overlap and chaos, or because Neptune’s gravitational influence becomes too weak. Limits on the extent of Neptune’s resonances have been estimated based on analytical models and on numerical simulations of the scattering population, members of which often stick to Neptune’s resonances as they evolve in semimajor axis while maintaining relatively constant perihelion distances. However, both approaches have limitations. Scattering models can only probe temporary sticks to resonances for objects with perihelion distances relatively close to Neptune (q<~40 au), while analytical models typically consider resonances in isolation and do not adequately account for how neighboring resonances can cause stable libration zones to shrink. Here we address both limitations by directly examining surfaces of section for all of Neptune’s N:1, N:2, and N:3 resonances out to a=550 au at a wide range of perihelion distances (q=33-60 au) in the restricted three-body problem. We find that the widths of these resonances have complex behavior due to interactions with neighboring resonances. At large semimajor axes, the surviving libration zones of Neptune’s strongest resonances are generally wider for larger perihelion distances (lower eccentricities) due to less crowding from weaker neighboring resonances. We will present our results for the maximum extent of Neptune’s exterior resonances as a function of perihelion distance in the restricted three body problem as well as an assessment of how these outer boundaries shift when all four giant planets are considered.

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