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M. Ferrais

Publications and source records attributed to M. Ferrais.

At least 19 recordsLinked to original sources

The spin state of asteroid Apophis and a prediction of its change during the 2029 close encounter with Earth

On April 13, 2029, the asteroid Apophis will pass near Earth at a geocentric distance of about 38,000 km. Numerical models have suggested that the post-encounter spin state will critically depend on the orientation of Apophis during the flyby. We aim to determine the spin state of Apophis from its photometric observations collected during two apparitions in 2012-2013 and 2020-2021. This will enable us to accurately predict the pre-encounter rotation state and, by accounting for Earth's gravitational torque, predict a range of possible post-encounter states. We used the light curve inversion method for tumbling asteroids to reconstruct the spin state of Apophis and its convex shape model. The result is adopted as the initial condition of a numerical model describing Apophis's future rotation state. The data from the two apparitions are insufficient to determine Apophis's rotation and precession periods uniquely. The formally best-fit solution is 27.374 +/- 0.001 h for the precession period and 262.2 +/- 0.1 h for the rotation period, but at least two other combinations of the periods provide a similarly good fit to the available data. All the currently acceptable models result in approximately the same pre-encounter orientation of Apophis in early 2029. This is because the accurate photometric data were collected during two apparitions separated by 8 years, which is the same interval as from 2021 to 2029. Although the close encounter with Earth in April 2029 hugely increases the post-encounter uncertainty of Apophis's spin state, the short-axis spin mode will be preserved with a high likelihood. Additional observations taken in 2027 and 2028 will break the ambiguity in Apophis's pre-encounter spin solution and allow us to get a more accurate post-encounter spin state prediction

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A dynamical dichotomy in large binary asteroids

No less than 15% of large (diameter greater than 140 km) asteroids have satellites. The commonly accepted mechanism for their formation is post-impact reaccumulation. However, the detailed physical and dynamical properties of these systems are not well understood, and many of them have not been studied in detail. We aim to study the population of large binary asteroid systems. To do so, we compare the gravitational fields predicted from the shape of the primary body with the non-Keplerian gravitational components identified in orbital models of the satellites of each system. We also aim to contextualize these systems in the greater population of large binary systems, providing clues to asteroid satellite formation. We reduce all historical high-angular-resolution adaptive-optics (AO) images from ground-based telescopes to conduct astrometric and photometric measurements of each system's components. We then determine orbital solutions for each system using the genoid algorithm. We model the shapes of the system primaries using lightcurve-inversion techniques scaled with stellar occultations and AO images, and we develop internal structure models using SHTOOLS. Finally, we compare the distribution of the physical and orbital properties of the known binary asteroid systems. We find that differences between studies binary systems reflect an overall dichotomy within the population of large binary systems, with a strong correlation between primary elongation and satellite eccentricity observed in one group. We determine that there may be two distinct formation pathways influencing the end-state dichotomy in these binary systems, and that (762) Pulcova and (283) Emma belong to the two separate groups.

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Asteroid sizes determined with thermophysical model and stellar occultations

Context. The sizes of many asteroids, especially slowly rotating, low-amplitude targets, remain poorly constrained due to selection effects. These biases limit the availability of high-quality data, leaving size estimates reliant on spherical shape assumptions. Such approximations introduce significant uncertainties propagating, e.g. into density determinations or thermophysical and compositional studies, affecting our understanding of asteroid properties. Aims. This work targets poorly studied main-belt asteroids, most of which lacked shape models. Using only high-quality dense light curves, thermal IR observations (incl. WISE), and stellar occultations, we aimed to produce reliable shape models and scale them via two independent techniques, allowing size comparison. We conducted two campaigns to obtain dense photometric light curves and to acquire multi-chord stellar occultations. Methods. Shape and spin models were reconstructed using lightcurve inversion. Sizes were determined by (1) thermophysical modeling with the Convex Inversion Thermophysical Model (CITPM), optimizing spin and shape models to visible lightcurve and IR data, and (2) scaling shape models with stellar occultations. Results. We obtained precise sizes and shape models for 15 asteroids. CITPM- and occultation-derived sizes agree within 5% in most cases, demonstrating the modeling's reliability. Larger discrepancies usually stem from incomplete occultation chord coverage. The study also gives insights into surface properties incl. albedo, roughness and thermal inertia. Conclusions. Using high-quality data and an advanced TPM integrating thermal and visible data with shape adjustment enabled precise size estimates comparable to those from multi-chord stellar occultations. We resolved major inconsistencies in previous size estimates, providing solid input for future studies on asteroid densities and surfaces.

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Shape and spin-state model of tumbling asteroid (319) Leona

Stellar occultations by asteroids observed from several stations are routinely used to reconstruct the asteroid's sky-plane projections. Together with the asteroid's shape model reconstructed from photometry, such occultations enable us to precisely determine its size and reveal details of its shape. When reducing occultation timings, the usual assumption is that the star has a negligible angular diameter compared to the asteroid, so it is modeled as a point source. The occultation of Betelgeuse (alpha Orionis) by asteroid (319) Leona on 12 December 2023 was a rare exception - the apparent angular diameter of the star was $\sim 50$ mas, about the same as that of the asteroid. This work aimed to reconstruct the shape and spin model of asteroid Leona. Then, the projection of that model for the time of the occultation can be computed, which is necessary to interpret the occultation timings and infer valuable information about Betelgeuse itself. We collected available photometric data of Leona, carried out new observations, and reconstructed a unique convex shape model. Using three other occultations observed in 2023, we scaled this convex model. We also reconstructed an alternative nonconvex model with the same spin parameters and size but showing some surface details that explain better one of the occultations. We confirmed the tumbling rotation state of Leona and uniquely determined the rotation period $P_\psi = 1172.2 \pm 0.3$ h and the precession period $P_\phi = 314.27 \pm 0.02$ h. The volume-equivalent diameter determined by occultations is $59.1 \pm 0.9$ km. The reconstructed shape model of Leona enabled us to compute its sky-plane projection for the time of the Betelgeuse occultation. A reliable shape model can be used to interpret the observed occultation of Betelgeuse by Leona.

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Cross validation of albedo determination for 1627 Ivar from three different techniques

Near Earth Asteroids are of great interest to the scientific community due to their proximity to Earth, making them both potential hazards and possible targets for future missions, as they are relatively easy to reach by spacecraft. A number of techniques and models can be used to constrain their physical parameters and build a comprehensive assessment of these objects. In this work, we compare physical property results obtained from improved $H_V$ absolute magnitude values, thermophysical modeling, and polarimetry data for the well-known Amor-class NEO 1627 Ivar. We show that our fits for albedo are consistent with each other, thus demonstrating the validity of this cross-referencing approach, and propose a value for Ivar's albedo of $0.24^{+0.04}_{-0.02}$ . Future observations will extend this work to a larger sample size, increasing the reliability of polarimetry for rapid asteroid property characterization, as a technique independent of previously established methods and requiring significantly fewer observations.

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Scaling slowly rotating asteroids by stellar occultations

As evidenced by recent survey results, majority of asteroids are slow rotators (P>12 h), but lack spin and shape models due to selection bias. This bias is skewing our overall understanding of the spins, shapes, and sizes of asteroids, as well as of their other properties. Also, diameter determinations for large (>60km) and medium-sized asteroids (between 30 and 60 km) often vary by over 30% for multiple reasons. Our long-term project is focused on a few tens of slow rotators with periods of up to 60 hours. We aim to obtain their full light curves and reconstruct their spins and shapes. We also precisely scale the models, typically with an accuracy of a few percent. We used wide sets of dense light curves for spin and shape reconstructions via light-curve inversion. Precisely scaling them with thermal data was not possible here because of poor infrared data: large bodies are too bright for WISE mission. Therefore, we recently launched a campaign among stellar occultation observers, to scale these models and to verify the shape solutions, often allowing us to break the mirror pole ambiguity. The presented scheme resulted in shape models for 16 slow rotators, most of them for the first time. Fitting them to stellar occultations resolved previous inconsistencies in size determinations. For around half of the targets, this fitting also allowed us to identify a clearly preferred pole solution, thus removing the ambiguity inherent to light-curve inversion. We also address the influence of the uncertainty of the shape models on the derived diameters. Overall, our project has already provided reliable models for around 50 slow rotators. Such well-determined and scaled asteroid shapes will, e.g. constitute a solid basis for density determinations when coupled with mass information. Spin and shape models continue to fill the gaps caused by various biases.

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Close-to-fission dumbbell Jupiter-Trojan (17365) Thymbraeus

Every population of small bodies in the Solar system contains a sizable fraction of multiple systems. Among these, the Jupiter Trojans have the lowest number of known binary systems and the least characterized. We aim at characterizing the reported binary system (17365) Thymbraeus, one of the only seven multiple systems known among Jupiter Trojans. We conducted light curves observing campaigns in 2013, 2015, and 2021 with ground-based telescopes. We model these lightcurves using dumbbell equilibrium figures. We show that Thymbraeus is unlikely a binary system. Its light curves are fully consistent with a bilobated shape: a dumbbell equilibrium figure. We determine a low density of 830 +/- 50 kg.m-3 , consistent with the reported density of other Jupiter Trojan asteroids and small Kuiper-belt objects. The angular velocity of Thymbraeus is close to fission. If separated, its components would become a similarly-sized double asteroid such as the other Jupiter Trojan (617) Patroclus.

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An advanced multipole model of the (130) Elektra quadruple system

The Ch-type asteroid (130) Elektra is orbited by three moons, making it the first quadruple system in the main asteroid belt. We aim to characterise the irregular shape of Elektra and construct a complete orbital model of its unique moon system. We applied the All-Data Asteroid Modelling (ADAM) algorithm to 60 light curves of Elektra, including our new measurements, 46 adaptive-optics (AO) images obtained by the VLT/SPHERE and Keck/Nirc2 instruments, and two stellar occultation profiles. For the orbital model, we used an advanced $N$-body integrator, which includes a multipole expansion of the central body (with terms up to the order $\ell = 6$), mutual perturbations, internal tides, as well as the external tide of the Sun acting on the orbits. We fitted the astrometry measured with respect to the central body and also relatively, with respect to the moons themselves. We obtained a revised shape model of Elektra with the volume-equivalent diameter $(201\pm 2)\,{\rm km}$. Out of two pole solutions, $(\lambda, \beta) = (189; -88)\,{\rm deg}$ is preferred, because the other one leads to an incorrect orbital evolution of the moons. We also identified the true orbital period of the third moon S/2014 (130) 2 as $P_2 = (1.642112 \pm 0.000400)\,{\rm d}$, which is in between the other periods, $P_1 \simeq 1.212\,{\rm d}$, $P_3 \simeq 5.300\,{\rm d}$, of S/2014 (130) 1 and S/2003 (130) 1, respectively. The resulting mass of Elektra, $(6.606 \substack{+0.007 \\ -0.013}) \times 10^{18}\,{\rm kg}$, is precisely constrained by all three orbits. Its bulk density is then $(1.536 \pm 0.038)\,{\rm g\,cm}^{-3}$. The expansion with the assumption of homogeneous interior leads to the oblateness $J_2 = -C_{20} \simeq 0.16$. However, the best-fit precession rates indicate a slightly higher value, ${\simeq}\,0.18$.

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2021 occultations and transits of Linus orbiting (22) Kalliope: I. Polygonal and `cliptracing' algorithm

The satellite Linus orbiting the main-belt asteroid (22) Kalliope exhibited occultation and transit events in late 2021. A photometric campaign was organized and observations were taken by the TRAPPIST-South, SPECULOOS-Artemis, OWL-Net, and BOAO telescopes, with the goal to constrain models of this system. Our dynamical model is complex, with multipoles (up to the order $\ell = 2$), internal tides, and external tides. The model was constrained by astrometry (spanning 2001--2021), occultations, adaptive-optics imaging, calibrated photometry, as well as relative photometry. Our photometric model was substantially improved. A new precise (${<}\,0.1\,{\rm mmag}$) 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, based again on polygon intersections, in which partial contributions to individual pixels are computed exactly. Both synthetic light curves and synthetic images are then very smooth. Based on our combined solution, we confirmed the size of Linus, $(28\pm 1)\,{\rm km}$. However, this solution exhibits some tension between the light curves and the PISCO speckle-interferometry dataset. In most solutions, Linus is darker than Kalliope, with the albedos $A_{\rm w} = 0.40$ vs. $0.44$. This is confirmed on deconvolved images. A~detailed revision of astrometric data allowed us to revise also the $J_2 \equiv -C_{20}$ value of Kalliope. Most importantly, a~homogeneous body is excluded. For a differentiated body, two solutions exist: low-oblateness ($C_{20} \simeq -0.12$), with a~spherical iron core, and alternatively, high-oblateness ($C_{20} \simeq -0.22$) with an elongated iron core. These correspond to the low- and high-energy collisions, respectively, studied by means of SPH simulations in our previous work.

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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.

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Discovery of an asteroid family linked to (22) Kalliope and its moon Linus

According to adaptive-optics observations by Ferrais et al., (22) Kalliope is a 150-km, dense and differentiated body. Here, we interpret (22) Kalliope in the context of bodies in its surroundings. While there is a known moon Linus, with a 5:1 size ratio, no family has been reported in the literature, which is in contradiction with the existence of the moon. Using the hierarchical clustering method (HCM) along with physical data, we identified the Kalliope family. Previously, it was associated to (7481) San Marcello. We then used various models (N-body, Monte-Carlo, SPH) of its orbital and collisional evolution, including the break-up of the parent body, to estimate the dynamical age of the family and address its link to Linus. The best-fit age is (900+-100) My according to our collisional model, in agreement with the position of (22) Kalliope, which was modified by chaotic diffusion due to 4-1-1 three-body resonance with Jupiter and Saturn. It seems possible to create Linus and the Kalliope family at the same time, although our SPH simulations show a variety of outcomes, for both satellite size and the family size-frequency distribution. The shape of (22) Kalliope itself was most likely affected by gravitational reaccumulation of `streams', which creates characteristic hills observed on the surface. If the body was differentiated, its internal structure is surely asymmetric.

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Properties of slowly rotating asteroids from the Convex Inversion Thermophysical Model

Results from the TESS mission showed that previous studies strngly underestimated the number of slow rotators, revealing the importance of studying those asteroids. For most slowly rotating asteroids (P > 12), no spin and shape model is available because of observation selection effects. This hampers determination of their thermal parameters and accurate sizes. We continue our campaign in minimising selection effects among main belt asteroids. Our targets are slow rotators with low light-curve amplitudes. The goal is to provide their scaled spin and shape models together with thermal inertia, albedo, and surface roughness to complete the statistics. Rich multi-apparition datasets of dense light curves are supplemented with data from Kepler and TESS. In addition to data in the visible range, we also use thermal data from infrared space observatories (IRAS, Akari and WISE) in a combined optimisation process using the Convex Inversion Thermophysical Model (CITPM). This novel method has so far been applied to only a few targets, and in this work we further validate the method. We present the models of 16 slow rotators. All provide good fits to both thermal and visible data. The obtained sizes are on average accurate at the 5% precision, with diameters in the range from 25 to 145 km. The rotation periods of our targets range from 11 to 59 hours, and the thermal inertia covers a wide range of values, from 2 to <400 SI units, not showing any correlation with the period. With this work we increase the sample of slow rotators with reliable spin and shape models and known thermal inertia by 40%. The thermal inertia values of our sample do not display a previously suggested increasing trend with rotation period, which might be due to their small skin depth.

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(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$^{-3}$. 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$\pm$1.40) km and mass (2.97$\pm$0.32) 10$^{18}$ kg imply a bulk density of (3.38$\pm$0.50) g cm$^{-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.

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An advanced multipole model for (216) Kleopatra triple system

To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution of multiple moons, orbiting an extremely irregular body and including their mutual interactions. Such orbits are generally non-Keplerian and orbital elements are not constants. Consequently, we use a modified $N$-body integrator, which was significantly extended to include the multipole expansion of the gravitational field up to the order $\ell = 10$. Its convergence was verified against the `brute-force' algorithm. We computed the coefficients $C_{\ell m},S_{\!\ell m}$ 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 (2nd moon with respect to 1st), angular velocities, and also silhouettes, constraining the pole orientation. This allowed us to derive the orbital elements of Kleopatra's two moons. 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, $P_1 = (1.822359\pm0.004156)\,{\rm d}$, $P_2 = (2.745820\pm0.004820)\,{\rm d}$. They orbit very close to the 3:2 mean-motion resonance, but their osculating eccentricities are too small compared to other perturbations (multipole, mutual), so that regular librations of the critical argument are not present. The resulting mass of Kleopatra, $m_1 = (1.49\pm0.16)\cdot10^{-12}\,M_\odot$ or $2.97\cdot10^{18}\,{\rm kg}$, is significantly lower than previously thought. An implication explained in the accompanying paper (Marchis et al.) is that (216) Kleopatra is a critically rotating body.

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(208) Lacrimosa: A case that missed the Slivan state?

The largest asteroids in the Koronis family (sizes $\geq 25$ km) have very peculiar rotation state properties, with the retrograde- and prograde-rotating objects being distinctly different. A recent e-analysis of observations suggests that one of the asteroids formerly thought to be retrograde-rotating, 208~Lacrimosa, in reality exhibits prograde rotation, yet other properties of this object are discrepant with other members this group. We seek to understand whether the new spin solution of Lacrimosa invalidates the previously proposed model of the Koronis large members or simply reveals more possibilities for the long-term evolutionary paths, including some that have not yet been explored. We confirm and substantiate the previously suggested prograde rotation of Lacrimosa. Its spin vector has an ecliptic longitude and latitude of $(λ,β)=(15^\circ \pm 2^\circ, 67^\circ\pm 2^\circ)$ and a sidereal rotation period $P=14.085734\pm 0.000007$ hr. The thermal and occultation data allow us to calibrate a volume equivalent size of $D=44\pm 2$ km of Lacrimosa. The observations also constrain the shape model relatively well. Assuming uniform density, the dynamical ellipticity is $Δ=0.35\pm 0.05$. Unlike other large prograde-rotating Koronis members, Lacrimosa spin is not captured in the Slivan state. We propose that Lacrimosa differed from this group in that it had initially slightly larger obliquity and longer rotation period. With those parameters, it jumped over the Slivan state instead of being captured and slowly evolved into the present spin configuration. In the future, it is likely to be captured in the Slivan state corresponding to the proper (instead of forced) mode of the orbital plane precession in the inertial space.

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Evidence for differentiation of the most primitive small bodies

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.

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Binary asteroid (31) Euphrosyne: Ice-rich and nearly spherical

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.

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Physical parameters of selected Gaia mass asteroids

Thanks to the Gaia mission, it will be possible to determine the masses of approximately hundreds of large main belt asteroids with very good precision. We currently have diameter estimates for all of them that can be used to compute their volume and hence their density. However, some of those diameters are still based on simple thermal models, which can occasionally lead to volume uncertainties as high as 20-30%. The aim of this paper is to determine the 3D shape models and compute the volumes for 13 main belt asteroids that were selected from those targets for which Gaia will provide the mass with an accuracy of better than 10%. We used the genetic Shaping Asteroids with Genetic Evolution (SAGE) algorithm to fit disk-integrated, dense photometric lightcurves and obtain detailed asteroid shape models. These models were scaled by fitting them to available stellar occultation and/or thermal infrared observations. We determine the spin and shape models for 13 main belt asteroids using the SAGE algorithm. Occultation fitting enables us to confirm main shape features and the spin state, while thermophysical modeling leads to more precise diameters as well as estimates of thermal inertia values. We calculated the volume of our sample of main-belt asteroids for which the Gaia satellite will provide precise mass determinations. From our volumes, it will then be possible to more accurately compute the bulk density, which is a fundamental physical property needed to understand the formation and evolution processes of small solar system bodies.

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