The destabilization of Neptune’s distant mean motion resonances by Uranus

Many of Neptune’s external mean motion resonances (MMRs) are occupied by observed transneptunian objects (TNOs). Our prior work mapping Neptune’s external MMRs in the restricted three-body problem (Sun + Neptune + massless test particles) show that they are dynamically significant out to at least 250-500 au (depending on perihelion distance). However, the extent and strength of the MMRs change significantly for particles with perihelion distances consistent with the scattering TNO population (q < 37-38 au) when all four giant planets are included. We applied an expanded Poincare mapping approach (Volk & Malhotra 2022) to measure the widths and strengths of Neptune’s 10:1 through 30:1 MMRs at q=33 au for test particles perturbed by the Sun, Jupiter, Saturn, Uranus, and Neptune. This revealed a sudden drop in N:1 resonant strengths at the 20:1 (~220 au). To isolate the mechanism for this drop-off, we simulated test particles in the 20:1 at q=33 au with different combinations of giant planets. Only simulations with Uranus present showed a destabilized 20:1; a simulation with Jupiter, Saturn, Neptune, and a J2 parameter to induce Uranus’s secular effects resulted in a stable 20:1, ruling out secular effects as the mechanism. Additional simulations determined that the destabilization occurs only at low perihelia, and N:1 resonances appear dynamically strong for q=40-45 au.

We explored whether the near 2:1 period ratio of Neptune and Uranus could explain the destabilization of highly-eccentric distant resonances by adjusting Neptune’s semimajor axis in our simulations. The instabilities in Neptune’s MMRs are strongest when Neptune and Uranus’s period ratio is exactly 2:1; all MMRs beyond the 4:1 are completely destabilized for the scattering population. Distant MMRs generally strengthen when the Neptune-Uranus period ratio is farther away from the 2:1 in either direction from its present value. Neptune’s MMRs show a sharp drop-off very close to the 2:1 planetary period ratio, but where the MMRs re-appear as the planets are moved away from their mutual resonance doesn’t follow a simple pattern. The present-day semimajor axis beyond which resonance sticking becomes less important for the scattering TNOs (e.g. Lykawka & Mukai 2007) is tied to the current Neptune-Uranus period ratio. Our results raise important questions about how the likely varying Neptune-Uranus period ratio during the epoch of planet migration could affect the role of distant MMRs in sculpting the scattering and detached populations.

This work is supported by NASA grant 80NSSC19K0785.