Combined spin orientation and phase function of asteroids^★

¹ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Nice, France
e-mail: benoit.carry@oca.eu
² Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France
³ Institut d’Astrophysique Spatiale, Université Paris-Saclay, CNRS, 91405 Orsay, France
⁴ IMCCE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ Paris 06, Univ. Lille, Paris, France

Received: 29 February 2024
Accepted: 4 April 2024

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.