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Context. Asteroid (22) Kalliope is the second largest M-type asteroid in the main belt and is orbited by a satellite, Linus. Whereas the mass of Kalliope is already well constrained thanks to the presence of a moon, its volume is still poorly known, leading to uncertainties on its bulk density and internal structure. Aims. We aim to refine the shape of (22) Kalliope and thus its diameter and bulk density, as well as the orbit of its moon to better constrain its mass, hence density and internal structure. Methods. We acquired disk-resolved observations of (22) Kalliope using the VLT/SPHERE/ZIMPOL instrument to reconstruct its three-dimensional (3D) shape using three different modeling techniques. These images were also used together with new speckle observations at the C2PU/PISCO instrument as well as archival images from other large ground-based telescopes to refine the orbit of Linus. Results. The volume of (22) Kalliope given by the shape models, corresponding to D = 150 ± 5 km, and the mass constrained by its satellite’s orbit yield a density of ρ = 4.40 ± 0.46 g cm −3 . This high density potentially makes (22) Kalliope the densest known small body in the Solar System. A macroporosity in the 10–25% range (as expected for this mass and size), implies a grain density in the 4.8–5.9 g cm −3 range. Kalliope’s high bulk density, along with its silicate-rich surface implied by its low radar albedo, implies a differentiated interior with metal contributing to most of the mass of the body. Conclusions. Kalliope’s high metal content (40–60%) along with its metal-poor mantle makes it the smallest known Mercury-like body. A large impact at the origin of the formation of the moon Linus is likely the cause of its high metal content and density. 

Context. The recent estimates of the 3D shape of the M/Xe-type triple asteroid system (216) Kleopatra indicated a density of ~5 g cm −3 , which is by far the highest for a small Solar System body. Such a high density implies a high metal content as well as a low porosity which is not easy to reconcile with its peculiar “dumbbell” shape. Aims. Given the unprecedented angular resolution of the VLT/SPHERE/ZIMPOL camera, here, we aim to constrain the mass (via the characterization of the orbits of the moons) and the shape of (216) Kleopatra with high accuracy, hence its density. Methods. We combined our new VLT/SPHERE observations of (216) Kleopatra recorded during two apparitions in 2017 and 2018 with archival data from the W. M. Keck Observatory, as well as lightcurve, occultation, and delay-Doppler images, to derive a model of its 3D shape using two different algorithms (ADAM, MPCD). Furthermore, an N -body dynamical model allowed us to retrieve the orbital elements of the two moons as explained in the accompanying paper. Results. The shape of (216) Kleopatra is very close to an equilibrium dumbbell figure with two lobes and a thick neck. Its volume equivalent diameter (118.75 ± 1.40) km and mass (2.97 ± 0.32) × 10 18 kg (i.e., 56% lower than previously reported) imply a bulk density of (3.38 ± 0.50) g cm −3 . Such a low density for a supposedly metal-rich body indicates a substantial porosity within the primary. This porous structure along with its near equilibrium shape is compatible with a formation scenario including a giant impact followed by reaccumulation. (216) Kleopatra’s current rotation period and dumbbell shape imply that it is in a critically rotating state. The low effective gravity along the equator of the body, together with the equatorial orbits of the moons and possibly rubble-pile structure, opens the possibility that the moons formed via mass shedding. Conclusions. (216) Kleopatra is a puzzling multiple system due to the unique characteristics of the primary. This system certainly deserves particular attention in the future, with the Extremely Large Telescopes and possibly a dedicated space mission, to decipher its entire formation history. 

Aims. To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution of multiple moons orbiting an extremely irregular body and include their mutual interactions. Such orbits are generally non-Keplerian and orbital elements are not constants. Methods. Consequently, we used a modified N -body integrator, which was significantly extended to include the multipole expansion of the gravitational field up to the order ℓ = 10. Its convergence was verified against the ‘brute-force’ algorithm. We computed the coefficients C ℓm , S ℓm for Kleopatra’s shape, assuming a constant bulk density. For Solar System applications, it was also necessary to implement a variable distance and geometry of observations. Our χ 2 metric then accounts for the absolute astrometry, the relative astrometry (second moon with respect to the first), angular velocities, and silhouettes, constraining the pole orientation. This allowed us to derive the orbital elements of Kleopatra’s two moons. Results. Using both archival astrometric data and new VLT/SPHERE observations (ESO LP 199.C-0074), we were able to identify the true periods of the moons, P 1 = (1.822359 ± 0.004156) d, P 2 = (2.745820 ± 0.004820) d. They orbit very close to the 3:2 mean-motion resonance, but their osculating eccentricities are too small compared to other perturbations (multipole, mutual), meaning that regular librations of the critical argument are not present. The resulting mass of Kleopatra, m 1 = (1.49 ± 0.16) × 10 −12 M ⊙ or 2.97 × 10 18 kg, is significantly lower than previously thought. An implication explained in the accompanying paper is that (216) Kleopatra is a critically rotating body. 

Context. Until recently, the 3D shape, and therefore density (when combining the volume estimate with available mass estimates), and surface topography of the vast majority of the largest ( D   ≥ 100 km) main-belt asteroids have remained poorly constrained. The improved capabilities of the SPHERE/ZIMPOL instrument have opened new doors into ground-based asteroid exploration. Aims. To constrain the formation and evolution of a representative sample of large asteroids, we conducted a high-angular-resolution imaging survey of 42 large main-belt asteroids with VLT/SPHERE/ZIMPOL. Our asteroid sample comprises 39 bodies with D   ≥ 100 km and in particular most D   ≥ 200 km main-belt asteroids (20/23). Furthermore, it nicely reflects the compositional diversity present in the main belt as the sampled bodies belong to the following taxonomic classes: A, B, C, Ch/Cgh, E/M/X, K, P/T, S, and V. Methods. The SPHERE/ZIMPOL images were first used to reconstruct the 3D shape of all targets with both the ADAM and MPCD reconstruction methods. We subsequently performed a detailed shape analysis and constrained the density of each target using available mass estimates including our own mass estimates in the case of multiple systems. Results. The analysis of the reconstructed shapes allowed us to identify two families of objects as a function of their diameters, namely “spherical” and “elongated” bodies. A difference in rotation period appears to be the main origin of this bimodality. In addition, all but one object (216 Kleopatra) are located along the Maclaurin sequence with large volatile-rich bodies being the closest to the latter. Our results further reveal that the primaries of most multiple systems possess a rotation period of shorter than 6 h and an elongated shape ( c ∕ a ≤ 0.65). Densities in our sample range from ~1.3 g cm −3 (87 Sylvia) to ~4.3 g cm −3 (22 Kalliope). Furthermore, the density distribution appears to be strongly bimodal with volatile-poor ( ρ ≥ 2.7 g cm −3 ) and volatile-rich ( ρ ≤ 2.2 g cm −3 ) bodies. Finally, our survey along with previous observations provides evidence in support of the possibility that some C-complex bodies could be intrinsically related to IDP-like P- and D-type asteroids, representing different layers of a same body (C: core; P/D: outer shell). We therefore propose that P/ D-types and some C-types may have the same origin in the primordial trans-Neptunian disk. 

Context. CM-like asteroids (Ch and Cgh classes) are a major population within the broader C-complex, encompassing about 10% of the mass of the main asteroid belt. Their internal structure has been predicted to be homogeneous, based on their compositional similarity as inferred from spectroscopy and numerical modeling of their early thermal evolution. Aims. Here we aim to test this hypothesis by deriving the density of the CM-like asteroid (41) Daphne from detailed modeling of its shape and the orbit of its small satellite. Methods. We observed Daphne and its satellite within our imaging survey with the Very Large Telescope extreme adaptive-optics SPHERE/ZIMPOL camera and complemented this data set with earlier Keck/NIRC2 and VLT/NACO observations. We analyzed the dynamics of the satellite with our Genoid meta-heuristic algorithm. Combining our high-angular resolution images with optical lightcurves and stellar occultations, we determine the spin period, orientation, and 3D shape, using our ADAM shape modeling algorithm. Results. The satellite orbits Daphne on an equatorial, quasi-circular, prograde orbit, like the satellites of many other large main-belt asteroids. The shape model of Daphne reveals several large flat areas that could be large impact craters. The mass determined from this orbit combined with the volume computed from the shape model implies a density for Daphne of 1.77 ± 0.26 g cm −3 (3 σ ). This densityis consistent with a primordial CM-like homogeneous internal structure with some level of macroporosity (≈ 17%). Conclusions. Based on our analysis of the density of Daphne and 75 other Ch/Cgh-type asteroids gathered from the literature, we conclude that the primordial internal structure of the CM parent bodies was homogeneous.