Uranus's influence on Neptune's exterior mean motion resonances

Neptune's external mean motion resonances play an important role in sculpting the observed population of transneptunian objects (TNOs). The population of scattering TNOs are known to 'stick' to Neptune's resonances while evolving in semimajor axis ($a$), though simulations show that resonance sticking is less prevalent at $a\gtrsim200-250$ au. Here we present an extensive numerical exploration of the strengths of Neptune's resonances for scattering TNOs with perihelion distances $q=33$ au. We show that the drop-off in resonance sticking for the large $a$ scattering TNOs is not a generic feature of scattering dynamics, but can instead be attributed to the specific configuration of Neptune and Uranus in our solar system. In simulations with just Uranus removed from the giant planet system, Neptune's resonances are strong in the scattering population out to at least $\sim300$ au. Uranus and Neptune are near a 2:1 period ratio, and the variations in Neptune's orbit resulting from this near resonance are responsible for destabilizing Neptune's resonances for high-$e$ TNO orbits beyond the $\sim20$:1 resonance at $a\approx220$ au. Direct interactions between Uranus and the scattering population are responsible for slightly weakening Neptune's closer-in resonances. In simulations where Neptune and Uranus are placed in their mutual 2:1 resonance, we see almost no stable libration of scattering particles in Neptune's external resonances. Our results have important implications for how the strengths of Neptune's distant resonances varied during the epoch of planet migration when the Neptune-Uranus period ratio was evolving. These strength variations likely affected the distant scattering, resonant, and detached TNO populations.