Asteroid Photometric and Polarimetric Phase Curve Modelling

The photometric and polarimetric phase curves of asteroids contain information about their surface properties. Physical modelling of these phase curves has been a major goal for decades. Focusing first on achieving good fits to polarimetric observations ([1] and references therein), we have taken different approaches to understanding light scattering from the surface of C-, S-, and E-class asteroids.

 

First, for the brighter S- and E-class asteroids, the parametrized [2,3] empirical scattering phase matrix for small (≤ 1 μm) ensemble-averaged olivine particles [4] is combined with a phase matrix describing the scattering of a size distribution of large (compared to the wavelength of light) olivine particles computed with the geometric optics approximation [5]. The combined single-scattering albedo is calculated and used in the multiple-scattering computation performed with the radiative-transfer coherent-backscattering (RT-CB) algorithm developed by Muinonen et al. [6]. The resulting phase curves are strong fits to polarimetric observations, and the resulting geometric albedos match levels representative of the asteroid classes. The high linear polarization maxima of C-class asteroids required us to choose the empirical scattering phase matrix of the iron and carbon containing Allende meteorite to represent the small particles likely present on low-albedo asteroids. Very large externally reflecting olivine particles were combined with the small particles to achieve a high linear polarization maximum. Secondly, we have calculated single-particle scattering matrices with a surface-integral-equation method (SIEM) [7] across different size distributions of randomly orientated Gaussian spheres. We will then repeat the analysis of the first approach by using the theoretical, numerically computed single-particle scattering and absorption properties. An even more realistic approach involves modelling light scattering by a layer of small particles on top of a semi-infinite homogeneous material (see Muinonen et al., Leppälä et al., present conference).

 

With the aim of finding the photometric phase functions that describe the intrinsic surface properties of individual asteroids, we retrieved opposition effect amplitudes and widths from photometric observations of asteroids (e.g., [8]) that have detailed shape models and spin parameters determined by Vernazza et al [9]. 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. [10] using photometric slopes obtained from lightcurve inversion by MacLennan et al [11].

 

References

[1] Gil-Hutton R. 2023, Catalogue of asteroid polarization curves.

[2] Muinonen K., Leppälä A., A&A 2025, 704, A106.

[3] Leppälä A., Muinonen K., Penttilä A., et al. JQSRT 2026, submitted.

[4] Muñoz O., Frattin E., Martikainen J., et al. JQSRT 2025, 331, 109252.

[5] Lindqvist H., Martikainen J., Räbinä J., et al. JQSRT 2018, 217, 329–337.

[6] Muinonen K., Leppälä A., Markkanen J., JQSRT 2025, 330, 109226.

[7] Markkanen J., JQSRT 2025, 341, 109467.

[8] Shevchenko V., Belskaya I., Muinonen K., et al. PSS 2016, 123, 101-116.

[9] Vernazza P., Ferrais M., Jorda L., et al. A&A 2021, 654, A56.

[10] Pentikäinen H., MacLennan E., Penttilä A., et al. A&A 2026, 707, A132.

[11] MacLennan E., Pentikäinen H., Uvarova E., et al. A&A 2026, 707, A131.