2021 occultations and transits of Linus orbiting (22) Kalliope. I. Polygonal and cliptracing algorithms

Aims: The satellite Linus orbiting the main-belt asteroid (22) Kalliope exhibited mutual occultation and transit events in late 2021. A photometric campaign was organised and observations were undertaken by the TRAPPIST-South, SPECULOOS-Artemis, OWL-Net, and BOAO telescopes, with the goal to further constrain dynamical and photometric models of this sizeable asteroid-satellite system. Methods: Our dynamical model is sufficiently complex, featuring multipoles (up to the order of ℓ = 2), internal tides, and external tides. The model was constrained by astrometry (spanning 2001-2021), occultations, adaptive-optics imaging, and calibrated photometry, as well as relative photometry. Our photometric model was substantially improved. A new precise (<0.1 mmag) light curve algorithm was implemented, based on polygon intersections, which are computed exactly by including partial eclipses and partial visibility of polygons. Moreover, we implemented a `cliptracing' algorithm, again based on polygon intersections, in which partial contributions to individual pixels are computed exactly. Both synthetic light curves and synthetic images then become very smooth. Results: Based on our combined solution, we confirmed the size of Linus, namely, (28 ± 1)km. However, this solution exhibits some tension among the light curves and the PISCO speckle-interferometry dataset, acquired simultaneously with the 2021 events. This indicates that improvements of the shape are still possible. In most solutions, Linus is darker than Kalliope, with the single-scattering albedos A<SUB>w</SUB> = 0.40 vs. 0.44. This is confirmed on deconvolved images. A detailed revision of astrometric data has allowed us to revise also the J<SUB>2</SUB> ≡ −C<SUB>20</SUB> value of Kalliope. Most importantly, a homogeneous body is excluded. For a differentiated body, two solutions exist: low-oblateness (C<SUB>20</SUB> ≃ −0.12), with a spherical iron core, and, alternatively, high-oblateness (C<SUB>20</SUB> ≃ −0.22) with an elongated iron core. These values correspond, respectively, to the low- and high-energy collisions we studied via SPH simulations in our previous work.