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 \sigma _ { i } > 11 ^ { \circ } .
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 \sigma _ { i } = 14.4 ^ { \circ } \pm 0.5 ^ { \circ } , \sigma _ { L 11 } = 11.8 ^ { \circ } \pm 0.5 ^ { \circ } , and \sigma _ { e } = 0.061 \pm 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 ( \tau _ { a } \lesssim 10 Myr , \tau _ { e } \lesssim 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 .