OSSOS: XIII. Fossilized Resonant Dropouts Imply Neptune's Migration was Grainy and Slow

The migration of Neptune's resonances through the early Kuiper belt has left signatures of the migration timescale and mode in the distribution of small bodies in the outer Solar System. Here we analyze five published Neptune migration models in detail, focusing on the high pericenter distance (q) trans-Neptunian Objects (TNOs) near Neptune's mean-motion resonances. We focus on the TNOs near the 5:2 and 3:1 resonances, because they have large detected populations, are outside the main classical belt, and are relatively isolated from other strong resonances. We compare the observationally biased output from these dynamical models with the detected TNOs from the Outer Solar System Origins Survey, via its Survey Simulator. All of the four new OSSOS detections of high-q non-resonant TNOs are on the Sunward side of the 5:2 and 3:1 resonances. We show that even after accounting for observation biases, this asymmetric distribution cannot be drawn from a uniform distribution of TNOs at 2-sigma confidence. We find that the dynamical model that uses grainy slow Neptune migration provides the best match to the real TNO orbital data. However, due to extreme observational biases, we have very few high pericenter distance TNO discoveries with which to statistically constrain the models. We show that a deeper survey (to a limiting r-magnitude of 26.0) with a similar survey area to OSSOS could statistically distinguish between these five Neptune migration models. We speculate that the cycle of resonance sticking and Kozai oscillation within a resonance, followed by resonant dropout into this fossilized high-q population, could potentially explain all but the two very highest-q TNOs discovered to date.