Occurrence of the 2:1 commensurability in a gas giant-Super-Earth system

We investigate how the conditions occurring in a protoplanetary disc may determine the final structure of a planetary system emerging from such a disc. We concentrate our attention on the dynamical interactions between disc and planets leading to orbital migration, which in turn, in favourable circumstances, can drive planets into a mean-motion commensurability. We find that for a system containing a gas giant on the external orbit and a Super-Earth on the internal one, both embedded in a gaseous disc, the 2:1 resonance is a very likely configuration, so one can expect it as an outcome of the early phases of the planetary system formation. Our conclusion is based on an extensive computational survey in which we ask what are the disc properties (the surface density and the viscosity) for which the 2:1 commensurability may be attained. To answer this question we employ a full two-dimensional hydrodynamic treatment of the disc-planet interactions. In general terms, we can claim that the conditions which favour the 2:1 mean-motion resonance exist in the protoplanetary discs with mass accretion rates typical for slowly accreting T Tauri stars. For accretion rates higher than those needed for the 2:1 commensurability we observe a variety of behaviours, among them the passage to the 3:2 resonance, the scattering of the Super-Earth or the divergent migration caused by the outward migration of the gas giant. The results we have obtained from numerical simulations are compared with the predictions coming from the existing analytical expressions of the migration speed and the strength of the mean motion resonances. The conditions that we have found for the attainment of the 2:1 commensurability are discussed in the framework of the properties of protoplanetary discs that are known from the observations.Comment: 12 pages, 11 figures, accepted for publication in MNRA

Thermal properties of large main-belt asteroids observed by Herschel PACS

Non-resolved thermal infrared observations enable studies of thermal and physical properties of asteroid surfaces provided the shape and rotational properties of the target are well determined via thermo-physical models. We used calibration-programme Herschel PACS data (70, 100, 160 $\mu$m) and state-of-the-art shape models derived from adaptive-optics observations and/or optical light curves to constrain for the first time the thermal inertia of twelve large main-belt asteroids. We also modelled previously well-characterised targets such as (1) Ceres or (4) Vesta as they constitute important benchmarks. Using the scale as a free parameter, most targets required a re-scaling $\sim$5\% consistent with what would be expected given the absolute calibration error bars. This constitutes a good cross-validation of the scaled shape models, although some targets required larger re-scaling to reproduce the IR data. We obtained low thermal inertias typical of large main belt asteroids studied before, which continues to give support to the notion that these surfaces are covered by fine-grained insulating regolith. Although the wavelengths at which PACS observed are longwards of the emission peak for main-belt asteroids, they proved to be extremely valuable to constrain size and thermal inertia and not too sensitive to surface roughness. Finally, we also propose a graphical approach to help examine how different values of the exponent used for scaling the thermal inertia as a function of heliocentric distance (i.e. temperature) affect our interpretation of the results.Comment: Accepted for publication in Astronomy & Astrophysics (preprint version

(16) Psyche: A mesosiderite-like asteroid?

Asteroid (16) Psyche is the target of the NASA Psyche mission. It is considered one of the few main-belt bodies that could be an exposed proto-planetary metallic core and that would thus be related to iron meteorites. Such an association is however challenged by both its near- and mid-infrared spectral properties and the reported estimates of its density. Here, we aim to refine the density of (16) Psyche to set further constraints on its bulk composition and determine its potential meteoritic analog. We observed (16) Psyche with ESO VLT/SPHERE/ZIMPOL as part of our large program (ID 199.C-0074). We used the high angular resolution of these observations to refine Psyche's three-dimensional (3D) shape model and subsequently its density when combined with the most recent mass estimates. In addition, we searched for potential companions around the asteroid. We derived a bulk density of 3.99\,$\pm$\,0.26\,g$\cdot$cm$^{-3}$ for Psyche. While such density is incompatible at the 3-sigma level with any iron meteorites ($\sim$7.8\,g$\cdot$cm$^{-3}$), it appears fully consistent with that of stony-iron meteorites such as mesosiderites (density $\sim$4.25\,$\cdot$cm$^{-3}$). In addition, we found no satellite in our images and set an upper limit on the diameter of any non-detected satellite of 1460\,$\pm$\,200}\,m at 150\,km from Psyche (0.2\%\,$\times$\,R$_{Hill}$, the Hill radius) and 800\,$\pm$\,200\,m at 2,000\,km (3\%\,$\times$\,$R_{Hill}$). Considering that the visible and near-infrared spectral properties of mesosiderites are similar to those of Psyche, there is merit to a long-published initial hypothesis that Psyche could be a plausible candidate parent body for mesosiderites.Comment: 16 page

The equilibrium shape of (65) Cybele: primordial or relic of a large impact?

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.Comment: 19 pages, 14 figures, 4 tables, accepted for publication in A&

(216) Kleopatra, a low density critically rotating M-type asteroid

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) × 1018 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

Evidence for differentiation of the most primitive small bodies

Context. Dynamical models of Solar System evolution have suggested that the so-called P- and D-type volatile-rich asteroids formed in the outer Solar System beyond Neptune's orbit and may be genetically related to the Jupiter Trojans, comets, and small Kuiper belt objects (KBOs). Indeed, the spectral properties of P- and D-type asteroids resemble that of anhydrous cometary dust. Aims. We aim to gain insights into the above classes of bodies by characterizing the internal structure of a large P- and D-type asteroid. Methods. We report high-angular-resolution imaging observations of the P-type asteroid (87) Sylvia with the Very Large Telescope Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument. These images were used to reconstruct the 3D shape of Sylvia. Our images together with those obtained in the past with large ground-based telescopes were used to study the dynamics of its two satellites. We also modeled Sylvia's thermal evolution. Results. The shape of Sylvia appears flattened and elongated (a/b 1.45; a/c 1.84). 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 its two satellites. This reveals an inhomogeneous internal structure, suggesting that Sylvia is differentiated. Conclusions. Sylvia's low density and differentiated interior can be explained by partial melting and mass redistribution through water percolation. The outer shell should be composed of material similar to interplanetary dust particles (IDPs) and the core should be 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 a 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, which is in agreement with in situ observations of these bodies. NASA Lucy mission target (617) Patroclus (diameter ≈140 km) may, however, be differentiated

(704) Interamnia: a transitional object between a dwarf planet and a typical irregular-shaped minor body

Context. With an estimated diameter in the 320–350 km range, (704) Interamnia is the fifth largest main belt asteroid and one of the few bodies that fills the gap in size between the four largest bodies with D > 400 km (Ceres, Vesta, Pallas and Hygiea) and the numerous smaller bodies with diameter ≤200 km. However, despite its large size, little is known about the shape and spin state of Interamnia and, therefore, about its bulk composition and past collisional evolution. Aims. We aimed to test at what size and mass the shape of a small body departs from a nearly ellipsoidal equilibrium shape (as observed in the case of the four largest asteroids) to an irregular shape as routinely observed in the case of smaller (D ≤ 200 km) bodies. Methods. We observed Interamnia as part of our ESO VLT/SPHERE large program (ID: 199.C-0074) at thirteen different epochs. In addition, several new optical lightcurves were recorded. These data, along with stellar occultation data from the literature, were fed to the All-Data Asteroid Modeling algorithm to reconstruct the 3D-shape model of Interamnia and to determine its spin state. Results. Interamnia’s volume-equivalent diameter of 332 ± 6 km implies a bulk density of ρ = 1.98 ± 0.68 g cm−3, which suggests that Interamnia – like Ceres and Hygiea – contains a high fraction of water ice, consistent with the paucity of apparent craters. Our observations reveal a shape that can be well approximated by an ellipsoid, and that is compatible with a fluid hydrostatic equilibrium at the 2σ level. Conclusions. The rather regular shape of Interamnia implies that the size and mass limit, under which the shapes of minor bodies with a high amount of water ice in the subsurface become irregular, has to be searched among smaller (D ≤ 300 km) less massive (m ≤ 3 × 1019 kg) bodies

VLT/SPHERE imaging survey of the largest main-belt asteroids: Final results and synthesis

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