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Description
Asteroids exhibit special features in the way they scatter unpolarised incident sunlight: the nonlinear increase in brightness at small phase angles (the angle between the Sun and the observer seen from the object, α) and the negative degree of linear polarisation at α < 30°. Furthermore, there is a linear dependence of brightness on the phase angle in the magnitude scale at α > 10° due to shadowing and multiple scattering in the regolith. The linear behaviour is characterised by the photometric slope determined at α = 20°. The shape of the photometric and polarimetric phase curves provide information about the surface properties of asteroids (Muinonen et al., Light Scattering Reviews 5, 477, 2010).
With the aim of finding the phase functions that describe the intrinsic surface properties of individual asteroids, we retrieved opposition amplitudes and widths from photometric observations of asteroids that have detailed shape models and spin parameters determined by Vernazza et al (A&A 654, A56, 2021). Subsequently, the photometric slopes were optimised by including the shape models, spin parameters, fitted opposition effect values, and Gaia DR3 observations, which contain high-precision photometry at around 10° < α < 30°. The resulting slope values categorised by asteroid class agree with classification results by Pentikäinen et al. (A&A, in press) using photometric slopes obtained from lightcurve inversion by MacLennan et al (A&A, in press).
Next, light scattering from the asteroid surfaces is modelled with the radiative-transfer coherent-backscattering (RT-CB) algorithm developed by Muinonen et al. (JQSRT 330, 109226, 2025) using empirical scattering matrices from the Granada-Amsterdam Light Scattering Database (Muñoz et al., JQSRT 331, 109252, 2025) for which the matrix elements have been parametrized (Muinonen and Leppälä, A&A 704, A106, 2025). The photometric and polarimetric phase curves are fitted by tuning the parameters of the RT-CB modelling.