Asteroid phase curves reconstructed with light curve inversion – prospects for LSST

Asteroids’ phase curves – the dependence of their brightness on the solar phase angle – carry information about asteroid surface properties in terms of light scattering. Phase curves are related to surface roughness, albedo, and taxonomic classification. In its basic form, a phase curve plots an asteroid’s brightness reduced to unit distance from the Sun and the Earth as a function of the phase angle (Sun–asteroid–Earth). Observed phase curves fitted with a theoretical model serve to estimate the absolute magnitude H (Bowell et al. 1989; Muinonen et al. 2010). However, an asteroid’s brightness depends not only on the phase angle; it also varies with changing geometry and rotation, so these factors inevitably affect real phase curves. Several techniques have been used to account for these effects (Muinonen et al. 2020, 2022; Carry et al. 2024). 

In our approach, we use the light curve inversion method of Kaasalainen & Torppa (2001); Kaasalainen et al. (2001), where the phase curve is expressed as a combination of linear and exponential functions with three parameters that are optimized during the modeling. This way, the shape and geometry effects are
removed, and the phase curve is affected only by measurement errors. When observations in different filters are available, the color shift between the data sets is another information that we extract from the data. Moreover, phase curves are wavelength-dependent, so that each filter can have different parameters, and we can study the phase reddening effects.

In the case of LSST of the Vera Rubin Observatory, asteroid photometry will be available in six filters covering wavelengths 320–1050 nm. For a typical main-belt asteroid, 200–300 individual measurements will be taken over 10 years of the survey. Fitting of the phase function will be treated inside the processing pipeline, so the H and G12 parameters for each filter will be provided as part of the data releases. However, for those asteroids for which the light curve inversion will provide a unique model, it will be possible to derive more precise phase curves for all six filters.

As a preparatory work before the LSST data will be available, we processed asteroid photometry from these surveys: Catalina, Mt. Lemmon, Pan-STARRS, ZTF, ATLAS, TESS, ASAS-SN, USNO, and Gaia DR3. From about 330,000 processed asteroids, we were able to derive unique spin solutions and corresponding convex shape models for about 23,000. The most abundant data set was ATLAS photometry in cyan and orange filters with hundreds of data points per asteroid. For a subsample of about 15,000 asteroids with abundant ATLAS photometry, we used the model to remove outlying photometric points and derived precise phase curves from ATLAS observations in two filters. This allowed us to compare colors and phase curves of different collisional families, taxonomic types, etc. We also searched for phase coloring effects (Alvarez-Candal 2024; Wilawer et al. 2024; Colazo et al. 2025).

The left plot below shows photometric data of asteroid (1495) Helsinki from eight observatories collected over the past two decades. The brightness was reduced to unit distances from the Sun and the Earth and is shown in relative intensity units. The phase curves are affected by different filters, rotational variation, and geometry effects related to changing aspect. The right plot shows the mean phase curve obtained as a result of light curve inversion and residuals scattered around the mean curve.

References

Alvarez-Candal, A. 2024, A&A, 685, A29
Bowell, E., Hapke, B., Domingue, D., et al. 1989, in Asteroids II, ed. R. P. Binzel, T. Gehrels, & M. S. Matthews (Tucson: University of Arizona Press), 524–556
Carry, B., Peloton, J., Le Montagner, R., Mahlke, M., & Berthier, J. 2024, A&A, 687, A38
Colazo, M., Oszkiewicz, D., Alvarez-Candal, A., et al. 2025, Icarus, 436, 116577
Kaasalainen, M. & Torppa, J. 2001, Icarus, 153, 24
Kaasalainen, M., Torppa, J., & Muinonen, K. 2001, Icarus, 153, 37
Muinonen, K., Belskaya, I. N., Cellino, A., et al. 2010, Icarus, 209, 542
Muinonen, K., Torppa, J., Wang, X. B., Cellino, A., & Penttilä, A. 2020, A&A, 642, A138
Muinonen, K., Uvarova, E., Martikainen, J., et al. 2022, Frontiers in Astronomy and Space Sciences, 9, 821125
Wilawer, E., Muinonen, K., Oszkiewicz, D., Kryszczy´nska, A., & Colazo, M. 2024, MNRAS, 531, 2802