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Abstract The orientations of orbital planes of minor planets are directional random variables. Their free inclination is the deviation of the orbit plane from the plane forced by the major planets. We construct a model of the distribution of free inclinations of classical Kuiper Belt objects (CKBOs) based on the von Mises–Fisher (vMF) distribution function, the analog of the normal distribution for directional statistics. The CKBOs are known to have a “cold” component of orbit planes concentrated near the forced plane and a more widely dispersed “hot” component. Adopting a model with a linear combination of two vMF functions, we find that the cold and hot components account for 57% and 43%, characterized by widths of 1.°7 and 12.°9, respectively. This model improves upon previous models based on smaller observational samples and empirical choices of functional forms for inclination distributions.
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A von Mises–Fisher distribution for the orbital poles of the plutinos
ABSTRACT Small Solar system bodies have widely dispersed orbital poles, posing challenges to dynamical models of Solar system origin and evolution. To characterize the orbit pole distribution of dynamical groups of small bodies it helps to have a functional form for a model of the distribution function. Previous studies have used the small-inclination approximation and adopted variations of the normal distribution to model orbital inclination dispersions. Because the orbital pole is a directional variable, its distribution can be more appropriately modelled with directional statistics. We describe the von Mises–Fisher (vMF) distribution on the surface of the unit sphere for application to small bodies’ orbital poles. We apply it to the orbit pole distribution of the observed Plutinos. We find a mean pole located at inclination i0 = 3.57° and 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°. We also estimate a debiased mean pole located 4.6° away, at i0 = 2.26°, Ω0 = 292.69°, of similar-size confidence cone. The vMF concentration parameter of Plutino inclinations (relative to either mean pole estimate) is κ = 31.6. This resembles a Rayleigh distribution function, with width parameter σ = 10.2°. Unlike previous models, the vMF model naturally accommodates all physical inclinations (and no others), whereas Rayleigh or Gaussian models must be truncated to the physical inclination range 0–180°. Further work is needed to produce a theory for the mean pole of the Plutinos against which to compare the observational results.
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- Award ID(s):
- 1824869
- PAR ID:
- 10410785
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 522
- Issue:
- 3
- ISSN:
- 0035-8711
- Format(s):
- Medium: X Size: p. 3298-3307
- Size(s):
- p. 3298-3307
- Sponsoring Org:
- National Science Foundation
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