Phase curves of small bodies from the SLOAN Moving Objects Catalog^★

¹ Instituto de Física Aplicada a las Ciencias y las Tecnologías, Universidad de Alicante, San Vicent del Raspeig, 03080 Alicante, Spain
e-mail: varobes@gmail.com
² Instituto de Astrofísica de Andalucía, CSIC, Apt 3004, 18080 Granada, Spain
³ Observatório Nacional / MCTIC, Rua General José Cristino 77, Rio de Janeiro 20921-400, Brazil
⁴ Departamento de Física Ingeniería de Sistemas y Teoría de la Señal, Universidad de Alicante, San Vicent del Raspeig, 03080 Alicante, Spain
⁵ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (IEEC-UB), Martí Franquès 1, 08028 Barcelona, Spain

Received: 9 April 2021
Accepted: 11 October 2021

Abstract

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 HG₁₂^* 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.