Measuring the degree of clustering and diffusion of trans-Neptunian objects

Abstract

The outer solar system is populated by a broad aggregate of minor bodies, which occupy orbits whose dynamical character ranges from long-term stable to rapidly diffusive. We investigate the chaotic properties of known distant trans-Neptunian objects (TNOs) by numerically integrating TNO clones and statistically analyzing their orbital diffusion. Comparing the measured diffusion with an analytical criterion yields a dynamically motivated separation into classes of stable, metastable and unstable objects. We then measure the level of clustering of the longitudes of perihelia and of the orbital poles, as functions of orbital distance and of their stability properties. Distant (meta)stable objects appear increasingly clustered in perihelion around $\varpi \sim 50^{\circ }$ for increasing semi-major axis, while the orbits of unstable objects are well described by two, roughly equally-populated groups of “clustered” and “anti-clustered” objects, with means around $\sim 25^{\circ }$ and $\sim 205^{\circ }$ respectively. We further find that, compared to the solar system’s total angular momentum vector, the mean orbital poles of distant TNOs are significantly more misaligned for (meta)stable objects, while they remain roughly aligned for unstable objects. TNOs with intermediate orbital periods also appear to be misaligned with respect to the forced plane predicted by secular theory with the known planets. This gradation based on stability, if validated further by the upcoming VRO survey, necessitates a dynamical explanation.