Phase curves of small bodies from the SLOAN Moving Objects Catalog

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.

The multiwavelength phase curves of small bodies

“…5), and care must be taken when using this database. -Candal et al (2022a) established that the method was reliable, and it provided comparable results with other methods used to compute H (e.g., Oszkiewicz et al 2011or Vereš et al 2015. Therefore, we proceed with the central issue of this article: Phase coloring.…”

“…We followed a similar approach as in AC22, with one modification. Alvarez-Candal et al (2022a) did not include any effect due to the possible rotational phase at which the objects could have been observed; this produced an artifact, a dip, in P A (∆m), as shown in Fig. 2 of AC22.…”

“…S21 also included the heliocentric and topocentric distances of the objects and the phase angle (along with other helpful information). As in Alvarez-Candal et al (2022a), AC22 hereafter, we did not make any cut in the database other than removing any m with an associated error of σ m ≥ 1. We used data of objects with at least three different α and with a minimum span of ∆α ≥ 5.0 deg (i.e., the distance between the maximum and minimum α).…”

“…Taking advantage of the serendipitous observations of small bodies in the SDSS data at different epochs and orbital configurations, Alvarez-Candal et al (2022a) developed a method for analyzing the apparent magnitudes, together with the ephemeris at the time of observations, in particular, topo-and heliocentric distances, ∆ and R, both in astronomical units (AU) and phase angle (α). The method produces multiwavelength PCs and absolute magnitudes in all the filter system (H λ ).…”

The Unusual Brightness Phase Curve of (65803) Didymos

“…Similarly to asteroid spectra, phase curves carry indirect information on the material reflectivity, grain size, surface irregularities, and granular packing. Such information is partially decoded through morphological parameters obtained from empirical or semiempirical models (Bowell et al 1989;Hapke 1993;Kaasalainen et al 2003;Muinonen et al 2010) and also their intercomparison with parameters, composition, and spectral types from other asteroids or meteoritic samples (Belskaya & Shevchenko 2000;Mahlke et al 2021;Ieva et al 2022a;Alvarez-Candal et al 2022). Furthermore, the phase curve characterization is of ultimate importance for the determination of absolute magnitude, a crucial parameter to estimate the diameter of atmosphereless small bodies from disk-unresolved observations (Harris & Lagerros 2002;.…”