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, a, Neptune’s resonances maintain a significant influence. Currently the most distant observed objects securely classified as resonant are found in Neptune’s 9:1 resonance at a=130 au. The lack of observed objects in more distant resonances is due to observational biases against detecting more distant objects and large uncertainties of orbital parameters for the few that are known. Limits on the strengths and widths 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. Analytical models typically consider resonances in isolation and do not adequately account for how neighboring resonances can cause stable libration zones to shrink, while scattering models can only probe temporary sticks to resonances for objects with perihelion distances relatively close to Neptune (q≲40 au). Here we address both limitations by computing surfaces of section in the restricted three-body problem 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). 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 (i) the maximum extent of Neptune’s distant resonances as a function of perihelion distance in the restricted three body problem, (ii) an assessment of how these boundaries shift when all four giant planets’s perturbations are considered, and (iii) several case studies of the influence of Neptune’s resonances on the most distant known objects.