Combined spin orientation and phase function of asteroids

Large surveys provide numerous non-targeted observations of small bodies (SSOs). The upcoming LSST of the Rubin observatory will be the largest source of SSO photometry in the next decade. With non-coordinated epochs of observation, colors, and therefore taxonomy and composition, can only be computed by comparing absolute magnitudes obtained in each filter by solving the phase function (evolution of brightness of the small body against the solar phase angle). Current models in use in the community (HG, HG12*, HG1G2) however fail to reproduce the long-term photometry of many targets due to the change in aspect angle between apparitions. We aim at deriving a generic yet simple phase function model accounting for the variable geometry of the SSOs over multiple apparitions. We propose the sHG1G2 phase function model in which we introduce a term describing the brightness changes due to spin orientation and polar oblateness. We apply this new model to 13, 245, 908 observations of 122, 675 SSOs. These observations were acquired in the g and r filters with the Zwicky Transient Facility. We retrieve them and implement the new sHG1G2 model in Fink, a broker of alerts designed for the LSST. The sHG1G2 model leads to smaller residuals than other phase function models, providing a better description of the photometry of asteroids. We determine the absolute magnitude H and phase function coefficients (G1, G2) in each filter, the spin orientation (RA₀, DEC₀), and the polar-to-equatorial oblateness R for 95, 593 Solar System Objects (SSOs), which constitutes about a tenfold increase in the number of characterised objects compared to current census. The application of the sHG1G2 model on ZTF alert data using the FINK broker shows that the model is appropriate to extract physical properties of asteroids from multi-band and sparse photometry, such as the forthcoming LSST survey.