Can the orbital distribution of Neptune's 3:2 mean motion resonance result from stability sculpting?

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 be 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 (A{\phi}), 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.