The minor planets on orbits that are dynamically stable in Neptunes 1:1 resonance on Gyr timescales were likely emplaced by Neptunes outward migration. We explore the intrinsic libration amplitude, eccentricity, and inclination distribution of Neptunes stable Trojans, using the detections and survey efficiency of the Outer Solar System Origins Survey (OSSOS) and Pan-STARRS1. We find that the libration amplitude of the stable Neptunian Trojan population can be well modeled as a Rayleigh distribution with a libration amplitude width $sigma_{A_phi}$ of 15$^circ$. When taken as a whole, the Neptune Trojan population can be acceptably modeled with a Rayleigh eccentricity distribution of width $sigma_e$ of 0.045 and a typical sin(i) x Gaussian inclination distribution with a width $sigma_i$ of 14 +/- 2 degrees. However, these distributions are only marginally acceptable. This is likely because, even after accounting for survey detection biases, the known large Hr < 8 and small Hr >= 8 Neptune Trojans appear to have markedly different eccentricities and inclinations. We propose that like the classical Kuiper belt, the stable intrinsic Neptunian Trojan population have dynamically `hot and dynamically `cold components to its eccentricity/inclination distribution, with $sigma_{e-cold}$ ~ 0.02 / $sigma_{i-cold}$ ~ 6$^circ$ and $sigma_{e-hot}$~ 0.05 / $sigma_{i-hot}$ ~ 18$^circ$. In this scenario, the `cold L4 Neptunian Trojan population lacks the Hr >= 8 members and has 13 +11/-6 `cold Trojans with Hr < 8. On the other hand, the `hot L4 Neptunian Trojan population has 136 +57/-48 Trojans with Hr < 10 -- a population 2.4 times greater than that of the L4 Jovian Trojans in the same luminosity range.
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