K. O. Xenos, B. Carry, J. Peloton, M. Mahlke, J. Berthier, P. -A. Mattei

Large photometric surveys provide sparse multi-band photometry for millions of Solar System objects, offering an opportunity to jointly constrain their physical and compositional properties. However, current phase function models do not account for rotational variability, limiting their ability to retrieve accurate parameters. Similarly, methods that recover shape and rotational parameters remain both computationally and observationally expensive. We present a model capable of simultaneously retrieving the absolute magnitude, phase parameters, spin state, and shape proportions of SSOs from sparse photometric data, while remaining computationally efficient. We introduce the Shape, Orientation and Colors Combined approach for Asteroids (SOCCA), which extends the HG1G2 formalism by incorporating the projected surface of a rotating triaxial ellipsoid. The model jointly fits multi-band photometry, and includes a dedicated treatment of rotational period determination. We implement the model on a 10-year LSST simulation as well as on real data of asteroid (45) Eugenia for validation purposes. SOCCA significantly improves the fit to photometric data, reducing the mean residuals to half, compared to previous models. It retrieves the absolute magnitude with a scatter about three times smaller than existing approaches, and improves the determination of phase parameters by a similar factor. It also recovers the sidereal rotation period, spin axis orientation and the axes ratios of the best fitting ellipsoid. The inclusion of shape and rotation increases the number of physically meaningful solutions by 10-20% per filter, leading to an overall success rate of 53%. Its performance and scalability make it well suited for current and upcoming large surveys such as the Zwicky Transient Facility and the recently started Legacy Survey of Space and Time.