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ABSTRACT We explore a simplified model of the outcome of an early outer Solar System gravitational upheaval during which objects were captured into Neptune’s 3:2 mean-motion resonance via scattering rather than smooth planetary migration. We use N-body simulations containing the sun, the four giant planets, and test particles in the 3:2 resonance to determine whether long-term stability sculpting over 4.5 Gyr can reproduce the observed 3:2 resonant population from an initially randomly scattered 3:2 population. After passing our simulated 3:2 resonant objects through a survey simulator, we find that the semimajor axis (a) and eccentricity (e) distributions are consistent with the observational data (assuming an absolute magnitude distribution constrained by prior studies), suggesting that these could be a result of stability sculpting. However, the inclination (i) distribution cannot be produced by stability sculpting and thus must result from a distinct process that excited the inclinations. Our simulations modestly under-predict the number of objects with high-libration amplitudes (Aϕ), possibly because we do not model transient sticking. Finally, our model under-populates the Kozai subresonance compared to both observations and to smooth migration models. Future work is needed to determine whether smooth migration occurring as Neptune’s eccentricity damped to its current value can resolve this discrepancy. 

Abstract There have been 77 TNOs discovered to be librating in the distant trans-Neptunian resonances (beyond the 2:1 resonance, at semimajor axes greater than 47.7 au) in four well-characterized surveys: the Outer Solar System Origins Survey (OSSOS) and three similar prior surveys. Here, we use the OSSOS Survey Simulator to measure their intrinsic orbital distributions using an empirical parameterized model. Because many of the resonances had only one or very few detections, j : k resonant objects were grouped by k in order to have a better basis for comparison between models and reality. We also use the Survey Simulator to constrain their absolute populations, finding that they are much larger than predicted by any published Neptune migration model to date; we also find population ratios that are inconsistent with published models, presenting a challenge for future Kuiper Belt emplacement models. The estimated population ratios between these resonances are largely consistent with scattering–sticking predictions, though further discoveries of resonant TNOs with high-precision orbits will be needed to determine whether scattering–sticking can explain the entire distant resonant population or not.