A Derivation of the Luminosity Function of the Kuiper Belt from a Broken Power-Law Size Distribution

TL;DR

This paper develops a model linking the Kuiper belt's luminosity function to a broken power-law size distribution, enabling better understanding of the belt's structure and the size at which the distribution breaks.

Contribution

It introduces a model that directly relates the observed luminosity function to the underlying broken power-law size distribution of Kuiper belt objects.

Findings

Best-fit break diameter between 30 and 90 km.

Luminosity function consistent with a broken power-law.

Break at magnitude 26.0+0.7-1.8.

Abstract

We have derived a model of the Kuiper belt luminosity function exhibited by a broken power-law size distribution. This model allows direct comparison of the observed luminosity function to the underlying size distribution. We discuss the importance of the radial distribution model in determining the break diameter. We determine a best-fit break-diameter of the Kuiper belt size-distribution of 30<Db<90 km via a maximum-likelihood fit of our model to the observed luminosity function. We also confirm that the observed luminosity function for m(R) ~ 21-28 is consistent with a broken power-law size distribution, and exhibits a break at m(R)=26.0+0.7-1.8.