A simple, empirical photometric function for low-albedo asteroids

Photometric functions of airless bodies serve two purposes. The first is to derive the physical properties of the surface such as the macroscopic roughness, compaction state of the upper regolith, the albedo, and the size and shape of surface particles. The second is to provide an empirical description of how a planetary surface reflects electromagnetic radiation. The derivation of a photometric function for the latter purpose is necessary to predict target brightness and intensity for efficient mission planning, instrument integration times, and quick-look data analysis. Radiative transfer models such as those of Hapke have served the first purpose well, provided that there is sufficient coverage in solar phase angles and a complement of disk-integrated and disk-resolved data. However, for practical purposes these models are often unduly complex, under-constrained, and dependent on the range of phase angles in the fit data set. Here we present simple, empirical photometric functions for low-albedo asteroids, which include D and C classifications, as well as some S-types, that are based on composite collections of asteroid phase curves covering a wide range of solar phase curves.