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(10) Hygiea is the fourth largest main belt asteroid and the only known asteroid whose surface composition appears similar to that of the dwarf planet (1) Ceres 1 , 2 , suggesting a similar origin for these two objects. Hygiea suffered a giant impact more than 2 Gyr ago 3 that is at the origin of one of the largest asteroid families. However, Hygeia has never been observed with sufficiently high resolution to resolve the details of its surface or to constrain its size and shape. Here, we report high-angular-resolution imaging observations of Hygiea with the VLT/SPHERE instrument (~20 mas at 600 nm) that reveal a basin-free nearly spherical shape with a volume-equivalent radius of 217 ± 7 km, implying a density of 1,944 ± 250 kg m − 3 to 1 σ . In addition, we have determined a new rotation period for Hygiea of ~13.8 h, which is half the currently accepted value. Numerical simulations of the family-forming event show that Hygiea’s spherical shape and family can be explained by a collision with a large projectile (diameter ~75–150 km). By comparing Hygiea’s sphericity with that of other Solar System objects, it appears that Hygiea is nearly as spherical as Ceres, opening up the possibility for this object to be reclassified as a dwarf planet. SPHERE at the VLT observed Hygiea, the fourth largest body in the main belt and the parent body of a big asteroid family, at unprecedented spatial resolution. Its unexpected spherical shape without any impact crater is explained by numerical simulations with a big impact that fluidized the body, reassembling it in a rotational equilibrium regime.

Dynamical models of Solar System evolution have suggested that P-/D-type volatile-rich asteroids formed in the outer Solar System and may be genetically related to the Jupiter Trojans, the comets and small KBOs. Indeed, their spectral properties resemble that of anhydrous cometary dust. High-angular-resolution images of P-type asteroid (87) Sylvia with VLT/SPHERE were used to reconstruct its 3D shape, and to study the dynamics of its two satellites. We also model Sylvia's thermal evolution. The shape of Sylvia appears flattened and elongated. We derive a volume-equivalent diameter of 271 +/- 5 km, and a low density of 1378 +/- 45 kg.m-3. The two satellites orbit Sylvia on circular, equatorial orbits. The oblateness of Sylvia should imply a detectable nodal precession which contrasts with the fully-Keplerian dynamics of the satellites. This reveals an inhomogeneous internal structure, suggesting that Sylvia is differentiated. Sylvia's low density and differentiated interior can be explained by partial melting and mass redistribution through water percolation. The outer shell would be composed of material similar to interplanetary dust particles (IDPs) and the core similar to aqueously altered IDPs or carbonaceous chondrite meteorites such as the Tagish Lake meteorite. Numerical simulations of the thermal evolution of Sylvia show that for a body of such size, partial melting was unavoidable due to the decay of long-lived radionuclides. In addition, we show that bodies as small as 130-150 km in diameter should have followed a similar thermal evolution, while smaller objects, such as comets and the KBO Arrokoth, must have remained pristine, in agreement with in situ observations of these bodies. NASA Lucy mission target (617) Patroclus (diameter~140 km) may, however, be differentiated.

Observations of a stellar occultation of Haumea, one of the four known trans-Neptunian dwarf planets, constrain its size, shape and density, and reveal a ring coplanar with Haumea’s largest moon. A ring around Haumea Haumea is a dwarf planet beyond the orbit of Neptune. It is rapidly rotating and very elongated, unlike the other three known trans-Neptunian dwarf planets. Jose Ortiz and collaborators obtained observations from multiple Earth-based telescopes as Haumea passed in front of a background star. This occultation enabled the team to constrain the density of Haumea to an upper limit of about 1,885 kilograms per cubic metre. They also constrained its ellipsoid shape and albedo (0.51). They did not detect an atmosphere around the planet, but found a ring circling it. They determined that the ring is 70 kilometres wide, has a radius of about 2,287 kilometres and lies in the same orbital plane as Haumea's equator and largest moon. It has an orbital period that is three times the spin period of Haumea. The ring absorbed roughly half of the star light coming through, giving it an opacity of 0.5. Haumea—one of the four known trans-Neptunian dwarf planets—is a very elongated and rapidly rotating body 1 , 2 , 3 . In contrast to other dwarf planets 4 , 5 , 6 , its size, shape, albedo and density are not well constrained. The Centaur Chariklo was the first body other than a giant planet known to have a ring system 7 , and the Centaur Chiron was later found to possess something similar to Chariklo’s rings 8 , 9 . Here we report observations from multiple Earth-based observatories of Haumea passing in front of a distant star (a multi-chord stellar occultation). Secondary events observed around the main body of Haumea are consistent with the presence of a ring with an opacity of 0.5, width of 70 kilometres and radius of about 2,287 kilometres. The ring is coplanar with both Haumea’s equator and the orbit of its satellite Hi’iaka. The radius of the ring places it close to the 3:1 mean-motion resonance with Haumea’s spin period—that is, Haumea rotates three times on its axis in the time that a ring particle completes one revolution. The occultation by the main body provides an instantaneous elliptical projected shape with axes of about 1,704 kilometres and 1,138 kilometres. Combined with rotational light curves, the occultation constrains the three-dimensional orientation of Haumea and its triaxial shape, which is inconsistent with a homogeneous body in hydrostatic equilibrium. Haumea’s largest axis is at least 2,322 kilometres, larger than previously thought, implying an upper limit for its density of 1,885 kilograms per cubic metre and a geometric albedo of 0.51, both smaller than previous estimates 1 , 10 , 11 . In addition, this estimate of the density of Haumea is closer to that of Pluto than are previous estimates, in line with expectations. No global nitrogen- or methane-dominated atmosphere was detected.

Cybele asteroids constitute an appealing reservoir of primitive material genetically linked to the outer Solar System, and the physical properties of the largest members can be readily accessed by large telescopes. We took advantage of the bright apparition of (65) Cybele in July and August 2021 to acquire high-angular-resolution images and optical light curves of the asteroid with which we aim to analyse its shape and bulk properties. 7 series of images acquired with VLT/SPHERE were combined with optical light curves to reconstruct the shape of the asteroid using the ADAM, MPCD, and SAGE algorithms. The origin of the shape was investigated by means of N-body simulations. Cybele has a volume-equivalent diameter of 263+/-3km and a bulk density of 1.55+/-0.19g.cm-3. Notably, its shape and rotation state are closely compatible with those of a Maclaurin equilibrium figure. The lack of a collisional family associated with Cybele and the higher bulk density of that body with respect to other large P-type asteroids suggest that it never experienced any large disruptive impact followed by rapid re-accumulation. This would imply that its present-day shape represents the original one. However, numerical integration of the long-term dynamical evolution of a hypothetical family shows that it is dispersed by gravitational perturbations and chaotic diffusion over Gyrs of evolution. The very close match between Cybele and an equilibrium figure opens up the possibility that D>260km small bodies from the outer Solar System all formed at equilibrium. However, we cannot rule out an old impact as the origin of the equilibrium shape. Cybele itself is found to be dynamically unstable, implying that it was recently (<1Ga) placed on its current orbit either through slow diffusion from a relatively stable orbit in the Cybele region or, less likely, from an unstable, JFC orbit in the planet-crossing region.

Violent and non violent crimes have been the subject of numerous studies designed for an examination of the probability of a crime occurring. The problem addressed by this quantitative study was to determine the association, if any, between time of day and frequency of crime, frequency of violent crime, age and gender through the use of chi square statistics. The data set for this study was the National Incident Based Reporting System and included 0.01% of the available population in the data. The results of this study supported the theory that crime has an association with time of day. The chi square results for the question examining the association between time of day and frequency of crime were statistically significant (χ2 (24, N = 31,131) = 4786.5, p < 0.001) and indicated an association of crime to time of day. The study results also indicated fewer than expected crimes occurred during the overnight hours between 1:00 a.m. and 5:00 a.m. The results for the examination of the association between time of day and violent crime were statistically significant (χ2 (24, N = 20,650) = 3256.671, p < 0.001). The question examining the association between time of day and non violent crime yielded statistically significant results (χ2 (24, N = 10,695) = 1320.748, p < 0.001). The association between time of day and females was significant (χ2 (2, N = 4162) = 794.944, p < 0.001) as was the association between time of day and males (χ2 (24, N = 12.454) = 1854.443, p < 0.001). The findings exploring time of day of offense and age breakdown were significant as well: ages 18 to 30 (χ2 (24, N = 6,134) = 1,018.596, p < 0.001), ages 31 to 40 (χ2 (24, N = 3,278) = 1,018.596, p < 0.001), ages 41 to 50 (χ2 (24, N = 2,151) = 367.026, p < 0.001), ages 51 to 60 (χ2 (24, N = 551) = 156.033, p < 0.001), ages 61 to 70 (χ2 (24, N = 169) = 54.817, p < 0.001), and ages 71 to 80 (χ2 (24, N = 39) = 5.897, p < 0.001). These age-related findings indicated an association between time of day and criminal activity. Future studies may include a specific breakdown of individual crimes by time of day in order to further predict types of crime that may be committed and allow pre-emptive enforcement through deployment of police and security forces.

Asteroid (31) Euphrosyne is one of the biggest objects in the asteroid main belt and the Euphrosyne family occupies a highly inclined region in the outer main belt and contains a remarkably large number of members, which is interpreted as an outcome of a disruptive cratering event. The goals of this adaptive-optics imaging study were threefold: to characterize the shape of Euphrosyne, to constrain its density, and to search for the large craters that may be associated with the family formation event. We obtained disk-resolved images of Euphrosyne using SPHERE/ZIMPOL at ESO's 8.2-m VLT as part of our large program (ID: 199.C-0074, PI: Vernazza). We reconstructed its 3D-shape using the adam shape modeling algorithm based on the SPHERE images and the available lightcurves of this asteroid. We analyzed the dynamics of the satellite with the genoid meta-heuristic algorithm. Finally, we studied the shape of Euphrosyne using hydrostatic equilibrium models. Our SPHERE observations show that Euphrosyne has a nearly spherical shape with the sphericity index of 0.9888 and its surface lacks large impact craters. Euphrosyne's diameter is 268+/-6 km, making it one of the top 10 largest main belt asteroids. We detected a satellite of Euphrosyne -- S/2019 (31) 1-- that is about 4 km across, on an circular orbit. The mass determined from the orbit of the satellite together with the volume computed from the shape model imply a density of 1665+/-242 kg/m^3, suggesting that Euphrosyne probably contain a large fraction of water ice in its interior. We find that the spherical shape of Euphrosyne is a result of the reaccumulation process following the impact, as in the case of (10) Hygiea. However, our shape analysis reveals that, contrary to Hygiea, the axis ratios of Euphrosyne significantly differ from the ones suggested by fluid hydrostatic equilibrium following reaccumulation.

The need for more accurate asteroid models is perhaps secondary to the need to measure their quality. The uncertainties of models' parameters propagate to quantities like volume or density -- the most important and informative properties of asteroids -- affecting conclusions about their physical nature. Our knowledge on shapes and spins of small solar system bodies comes mostly from visual, disk-integrated photometry. In this work we present a method for asteroid model uncertainty assessment based on visual photometry (lightcurves and sparse-in-time absolute measurements) allowing the determination of realistic volume uncertainty, as well as spin axis orientation, rotational period and local surface features. The sensitivity analysis is conducted by creating clones of the nominal model and accepting the ones that fit the observations within a confidence level. The uncertainties of model parameters are extracted from the extreme values found in the accepted clone population. Creation of such population of clones enables the conversion of a deterministic asteroid model into stochastic one, and can be utilized to create observation predictions with error bars. The method was used to assess the uncertainties of fictitious test models and real targets, i.e. (21) Lutetia, (89) Julia, (243) Ida, (433) Eros and (162173) Ryugu. We conclude that volumes, and subsequently, densities of asteroids derived from lightcurve-based models likely have vastly understated uncertainties, the biggest source of which is the inability to establish the extent of the model along its spin axis.

In this work we present SAGE (Shaping Asteroid models using Genetic Evolution) asteroid modelling algorithm based solely on photometric lightcurve data. It produces non-convex shapes, rotation axes orientati and rotational periods of asteroids. The main concept behind a genetic evolution algorithm is to produce random populations of shapes and spin orientations by mutating a seed shape and iterating the process until it converges to a stable global minimum. To test SAGE we have performed tes on five artificial shapes. We have also modelled (433) Eros and (9) Meti asteroids, as ground truth observations for them exist, allowing us to validate the models. We have compared derived Eros shape with NEAR Shoem model and Metis shape with adaptive optics and stellar occultation observations as with other available Metis models from various inversion methods.

Asteroid (7) Iris is an ideal target for disk-resolved imaging owing to its brightness (V\\(\\sim\\)7-8) and large angular size of 0.33 arcsec during its apparitions. Iris is believed to belong to the category of large unfragmented asteroids that avoided internal differentiation, implying that its current shape and topography may record the first few 100 Myr of the solar system's collisional evolution. We recovered information about the shape and surface topography of Iris from disk-resolved VLT/SPHERE/ZIMPOL images acquired in the frame of our ESO large program. We used the All-Data Asteroid Modeling (ADAM) shape reconstruction algorithm to model the 3D shape of Iris, using optical disk-integrated data and disk-resolved images from SPHERE as inputs. We analyzed the SPHERE images to infer the asteroid's global shape and the morphology of its main craters. We present the volume-equivalent diameter D\\(_{{\\rm eq}}\\)=214\\(\\pm\\)5 km, and bulk density \\(\\rho\\)=2.7\\(\\pm\\)0.3 g cm\\(^{-3}\\) of Iris. Its shape appears to be consistent with that of an oblate spheroid with a large equatorial excavation. We identified eight putative surface features 20--40 km in diameter detected at several epochs, which we interpret as impact craters. Craters on Iris have depth-to-diameter ratios that are similar to those of analogous 10 km craters on Vesta. The bulk density of Iris is consistent with that of its meteoritic analog, namely LL ordinary chondrites. Considering the absence of a collisional family related to Iris and the number of large craters on its surface, we suggest that its equatorial depression may be the remnant of an ancient (at least 3 Gyr) impact. Iris's shape further opens the possibility that large planetesimals formed as almost perfect oblate spheroids. Finally, we attribute the difference in crater morphology between Iris and Vesta to their different surface gravities.

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\\). Such a high density implies a high metal content and 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, we aim to constrain the mass and the shape of Kleopatra with high accuracy, hence its density. Methods. We combined our new VLT/SPHERE observations of Kleopatra recorded in 2017 and 2018 with archival data, as well as lightcurve, occultation, and delay-Doppler images, to derive its 3D shape model 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 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 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. 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. Kleopatra is a puzzling multiple system due to the unique characteristics of the primary. It deserves particular attention in the future, with the Extremely Large Telescopes and possibly a dedicated space mission.