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We report the discovery with the Transiting Exoplanet Survey Satellite (TESS) of a third set of eclipses from V994 Herculis (V994 Her, TIC 424508303), previously only known as a doubly eclipsing system. The key implication of this discovery and our analyses is that V994 Her is the second fully characterized (2+2) + 2 sextuple system, in which all three binaries eclipse. In this work, we use a combination of ground-based observations and TESS data to analyse the eclipses of binaries A and B in order to update the parameters of the inner quadruple’s orbit (with a derived period of 1062 ± 2 d). The eclipses of binary C that were detected in the TESS data were also found in older ground-based observations, as well as in more recently obtained observations. The eclipse timing variations of all three pairs were studied in order to detect the mutual perturbations of their constituent stars, as well as those of the inner pairs in the (2 + 2) core. At the longest periods they arise from apsidal motion, which may help constraining parameters of the component stars’ internal structure. We also discuss the relative proximity of the periods of binaries A and B to a 3:2 mean motion resonance. This work represents a step forward in the development of techniques to better understand and characterize multiple star systems, especially those with multiple eclipsing components.

 

The hot nine-component system HD 93206, which contains a gravitationally bounded eclipsing Ac1+Ac2 binary ( P  = 5.9987 d) and a spectroscopic Aa1+Aa2 ( P  = 20.734 d) binary can provide important insights into the origin and evolution of massive stars. Using archival and new spectra, and a rich collection of ground-based and space photometric observations, we carried out a detailed study of this object. We provide a much improved description of both short orbits and a good estimate of the mutual period of both binaries of about 14 500 d (i.e. 40 years). For the first time, we detected weak lines of the fainter component of the 6.0 d eclipsing binary in the optical region of the spectrum, measured their radial velocities, and derived a mass ratio of M Ac2 / M Ac1  = 1.29, which is the opposite of what was estimated from the International Ultraviolet explorer (IUE) spectra. We confirm that the eclipsing subsystem Ac is semi-detached and is therefore in a phase of large-scale mass transfer between its components. The Roche-lobe filling and spectroscopically brighter component Ac1 is the less massive of the two and is eclipsed in the secondary minimum. We show that the bulk of the H α emission, so far believed to be associated with the eclipsing system, moves with the primary O9.7 I component Aa1 of the 20.73 d spectroscopic binary. However, the weak emission in the higher Balmer lines seems to be associated with the accretion disc around component Ac2. We demonstrate that accurate masses and other basic physical properties including the distance of this unique system can be obtained but require a more sophisticated modelling. A first step in this direction is presented in the accompanying Paper II (Brož et al.). 

Aims. The orbit of the outer satellite Alexhelios of (216) Kleopatra is already constrained by adaptive-optics astrometry obtained with the VLT/SPHERE instrument. However, there is also a preceding occultation event in 1980 attributed to this satellite. Here, we try to link all observations, spanning 1980–2018, because the nominal orbit exhibits an unexplained shift by + 60° in the true longitude. Methods. Using both a periodogram analysis and an ℓ = 10 multipole model suitable for the motion of mutually interacting moons about the irregular body, we confirmed that it is not possible to adjust the respective osculating period P 2 . Instead, we were forced to use a model with tidal dissipation (and increasing orbital periods) to explain the shift. We also analysed light curves spanning 1977–2021, and searched for the expected spin deceleration of Kleopatra. Results. According to our best-fit model, the observed period rate is Ṗ 2 = (1.8 ± 0.1) × 10 −8 d d −1 and the corresponding time-lag Δ t 2 = 42 s of tides, for the assumed value of the Love number k 2 = 0.3. This is the first detection of tidal evolution for moons orbiting 100 km asteroids. The corresponding dissipation factor Q is comparable with that of other terrestrial bodies, albeit at a higher loading frequency 2| ω − n |. We also predict a secular evolution of the inner moon, Ṗ 1 = 5.0 × 10 −8 , as well as a spin deceleration of Kleopatra, Ṗ 0 = 1.9 × 10 −12 . In alternative models, with moons captured in the 3:2 mean-motion resonance or more massive moons, the respective values of Δ t 2 are a factor of between two and three lower. Future astrometric observations using direct imaging or occultations should allow us to distinguish between these models, which is important for our understanding of the internal structure and mechanical properties of (216) Kleopatra. 

The complex binary system β Lyr A has an extensive observational dataset: light curves (from far UV to far IR), interferometric squared visibility, closure phase, triple product measurements, spectral-energy distribution, high-resolution spectroscopy, differential visibility amplitude, and also a differential phase. In particular, we used spectra from the Ondřejov 2m telescope from 2013 to 2015 to measure the emission in H α , He  I , Si  II , Ne  I , or C  II lines, and differential interferometry by CHARA/VEGA from the 2013 campaign to measure wavelength-dependent sizes across H α and He  I 6678. This allowed us to constrain not only optically thick objects (primary, secondary, accretion disc), but also optically thin objects (disc atmosphere, jets, shell). We extended our modelling tool, Pyshellspec (based on Shellspec; a 1D local thermodynamical equilibrium radiative transfer code), to include all new observables, to compute differential visibilities/phases, to perform a Doppler tomography, and to determine a joint χ 2 metric. After an optimisation of 38 free parameters, we derived a robust model of the β Lyr A system. According to the model, the emission is formed in an extended atmosphere of the disc, two perpendicular jets expanding at ∼700 km s −1 , and a symmetric shell with the radius ∼70  R ⊙ . The spectroscopy indicates a low abundance of carbon, 10 −2 of the solar value. We also quantified systematic differences between datasets, and we discuss here alternative models with higher resolutions, additional asymmetries, or He-rich abundances. 

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. 

ABSTRACT High angular resolution disc-resolved images of (7) Iris collected by VLT/SPHERE instrument are allowed for the detailed shape modelling of this large asteroid revealing its surface features. If (7) Iris did not suffer any events catastrophic enough to disrupt the body (which is very likely) by studying its topography, we might get insights into the early Solar system’s collisional history. When it comes to internal structure and composition, thoroughly assessing the volume and density uncertainties is necessary. In this work, we propose a method of uncertainty calculation of asteroid shape models based on light curve and adaptive optics (AO) images. We apply this method on four models of (7) Iris produced from independent Shaping Asteroids using Genetic Evolution and All-Data Asteroid Modelling inversion techniques and multiresolution photoclinometry by deformation. Obtained diameter uncertainties stem from both the observations from which the models were scaled and the models themselves. We show that despite the availability of high-resolution AO images, the volume and density of (7) Iris have substantial error bars that were underestimated in the previous studies. 

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. 

Aims. Asteroid (31) Euphrosyne is one of the biggest objects in the asteroid main belt and it is also the largest member of its namesake family. 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. Methods. The goals of this adaptive-optics imaging study are 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. Results. We obtained disk-resolved images of Euphrosyne using SPHERE/ZIMPOL at the ESO 8.2 m VLT as part of our large program (ID: 199.C-0074, PI: Vernazza). We reconstructed its 3D shape via the ADAM shape modeling algorithm based on the SPHERE images and the available light curves 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. Conclusions. 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 ten largest main belt asteroids. We detected a satellite of Euphrosyne – S/2019 (31) 1 – that is about 4 km across, on a 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 contains 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 those suggested by fluid hydrostatic equilibrium following reaccumulation.