A Projected Normal Distribution for Improved Characterization of the Orbital Poles of the Plutinos

Music City Center 

The distribution of the orbital planes of the small bodies in the solar system has been of long-standing interest to astronomers. We propose the projected normal (PN) distribution to characterize the widely dispersed orbital poles of the Plutinos in the Kuiper belt. The PN distribution is able to describe the mean pole and the correlation between the directional components of the orbital pole unit vectors. These correlations have been ignored by the von Mises-Fisher model that has been used recently, but they provide a more comprehensive understanding of the astrophysical characteristics governing the orbital distribution of the small bodies in the solar system. The fitted PN mean pole of the Plutino samples describes the data distribution with more precision compared to the traditional methods including the von Mises-Fisher distribution and the debiased mean method. The correlations between the directional components of the orbital unit vectors of the plutinos, that are estimated for the first time by our fitted PN model, are found to be significant.

Directional variables

Astrostatistics

Numerical integration 

Astrostatistics Interest Group