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Orbital plane distribution of Plutinos

Presentation #202.07 in the session TNO Theory and Physical Properties (Oral Presentation)

Published onOct 23, 2023
Orbital plane distribution of Plutinos

Within distinct dynamical groups of small Solar System bodies, individual objects often have widely dispersed orbital planes. When modeling the origin and evolution of these dynamical groups, it is useful to describe the distribution of the orbital planes with a well-founded probability distribution function. The usual practice is to model the two parameters (inclination i and longitude of ascending node Ω) of the orientation of the orbit plane separately, assuming small inclinations and treating the inclination distribution as a variation on the one-dimensional Gaussian normal distribution, while Ω is assumed to be uniform random. However, because the inclination is physically limited to the range 0–180° and the orbital plane orientation is a directional variable, it is better to model both parameters jointly by modeling the direction of the orbital pole with directional statistics. In this work, we describe how to apply the von Mises-Fisher (vMF) distribution to the orbital poles of small Solar System bodies. (The vMF distribution is the simplest analogue to the Gaussian normal distribution but defined on the surface of the unit sphere.) To demonstrate, we find a von Mises-Fisher distribution for the orbital poles of the Plutinos, which are the Kuiper Belt objects in Neptune’s 3:2 outer mean motion resonance. This distribution has a mean pole located at inclination i0 = 3.57° and a longitude of ascending node Ω0 = 124.38° (in the J2000 reference frame), with a 99.7 per cent confidence cone of half-angle 1.68°. Because the vMF mean pole is susceptible to bias in the sample, we use a different method to estimate a debiased mean pole located 4.6° away, at i0 = 2.26°, Ω0 = 292.69°, with a confidence cone of similar size. When measured relative to either mean pole, the Plutinos’ inclination distribution resembles a Rayleigh distribution with width parameter σ = 10.2°. To assess the significance of the measured mean pole of the Plutinos, further work is needed to produce a theory for the forced mean pole of a resonant population of small bodies. Reference: Matheson et al, MNRAS 522:3 (July 2023), pgs. 3298-3307, doi:10.1093/mnras/stad1208.

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