The intrinsic Neptune Trojan orbit distribution: Implications for the primordial disk and planet migration

The present-day orbit distribution of the Neptune Trojans is a powerful probe of the dynamical environment of the outer Solar System during the late stages of planet migration. In this work, I conservatively debias the inclination, eccentricity, and libration amplitude distributions of the Neptune Trojans by reducing a priori unknown discovery and follow-up survey properties to nuisance parameters and using a likelihood-free Bayesian rejection sampler for parameter estimation. Using this survey-agnostic approach, I confirm that the Neptune Trojans are a dynamically excited population: at >95% confidence, the Neptune Trojans' inclination width must be σi>11°. For comparison and motivation purposes, I also model the Jupiter Trojan orbit distributions in the same basis and produce new estimates of their parameters (Jupiter Trojan σi=14.4°±0.5°, σL11=11.8°±0.5°, and σe=0.061±0.002). The debiased inclination, libration amplitude, and eccentricity distributions of the Neptune Trojans are nominally very similar to those of the Jupiter Trojans. I use these new constraints to inform a suite of simulations of Neptune Trojan capture by an eccentric, rapidly-migrating Neptune from an initially dynamically-hot disk. These simulations demonstrate that if migration and eccentricity-damping timescales were short (τa≲10 Myr, τe≲1 Myr), the disk that Neptune migrated into must have been pre-heated (prior to Neptune's appearance) to a width comparable to the Neptune Trojans' extant width to produce a captured population with an inclination distribution width consistent with that of the observed population.