Phase curves of small bodies from the SLOAN Moving Objects Catalog

Context. Extensive photometric surveys continue to produce enormous stores of data on small bodies. These data are typically sparsely obtained at arbitrary (or unknown) rotational phases. Therefore, new methods for processing such data need to be developed to make the most of these vast catalogs. Aims. We aim to produce a method of recreating the phase curves of small bodies by considering the uncertainties introduced by the nominal errors in the magnitudes and the effect introduced by rotational variations. We use the SLOAN Moving Objects Catalog data as a benchmark to construct phase curves of all small bodies in u′, g′, r′, i′, and z′ filters. From the phase curves, we obtain the absolute magnitudes and we use them to set up the absolute colors, which are the colors of the asteroids that are not affected by changes in the phase angle. Methods. We selected objects with ≥3 observations taken in at least one filter and spanning over a minimum of 5 degrees in the phase angle. We developed a method that combines Monte Carlo simulations and Bayesian inference to estimate the absolute magnitudes using the HG$_{12}^*$ photometric system. Results. We obtained almost 15 000 phase curves, with about 12 000 of these including all five filters. The absolute magnitudes and absolute colors are compatible with previously published data that support our method. Conclusions. The method we developed is fully automatic and well suited for a run based on large amounts of data. Moreover, it includes the nominal uncertainties in the magnitudes and the whole distribution of possible rotational states of the objects producing what are possibly less precise values, that is, larger uncertainties, but more accurate, namely, closer to the actual value. To our knowledge, this work is the first to include the effect of rotational variations in such a manner