Combined spin orientation and phase function of asteroids

Abstract

Context. Large sky surveys provide numerous non-targeted observations of small bodies of the Solar System. The upcoming LSST of the Vera C. Rubin Observatory will be the largest source of small body 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*, and HG1G2), however, fail to reproduce the long-term photometry of many targets due to the change in the aspect angle between apparitions. Aims. We aim to derive a generic yet simple phase function model accounting for the variable geometry of the small bodies over multiple apparitions. Methods. As a spinoff of the HG1 G2 model, 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 applied this new model to 13 245 908 observations of 122 675 Solar System objects (SSOs). These observations were acquired in the g and r filters with the Zwicky Transient Facility between November 1, 2019 and December 1, 2023. We retrieved them and implemented the new sHG1G2 model in FINK, a broker of alerts designed for the LSST. Results. The sHG1G2 model leads to smaller residuals than other phase function models, providing a better description of the photometry of asteroids. We determined the absolute magnitude, H, and phase function coefficients (G1, G2) in each filter, the spin orientation (α0, δ0), and the polar-to-equatorial oblateness, R, for 95 593 SSOs, which constitutes about a tenfold increase in the number of characterized objects compared to the current census. Conclusions. The application of the sHG1 G2 model to ZTF alert data using the FINK broker shows that the model is appropriate for extracting physical properties of asteroids from multi-band and sparse photometry, such as the forthcoming LSST survey.