A derivation of the luminosity function of the Kuiper belt from a broken power-law size distribution

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 < D b < 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 −1.8 +0.7 .