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Despite coronary artery calcium scoring being considered a largely solved problem within the realm of medical artificial intelligence, this paper argues that significant improvements can still be made. By shifting the focus from pathology detection to a deeper understanding of anatomy, the novel algorithm proposed in the paper both achieves high accuracy in coronary artery calcium scoring and offers enhanced interpretability of the results. This approach not only aids in the precise quantification of calcifications in coronary arteries, but also provides valuable insights into the underlying anatomical structures. Through this anatomically-informed methodology, the paper shows how a nuanced understanding of the heart's anatomy can lead to more accurate and interpretable results in the field of cardiovascular health. We demonstrate the superior accuracy of the proposed method by evaluating it on an open-source multi-vendor dataset, where we obtain results at the inter-observer level, surpassing the current state of the art. Finally, the qualitative analyses show the practical value of the algorithm in such tasks as labeling coronary artery calcifications, identifying aortic calcifications, and filtering out false positive detections due to noise.

The primary objective of this study was to utilize the newest Gaia FPR catalogue containing ultra-precise asteroid astrometry spanning over 66 months to detect the Yarkovsky effect, a non-gravitational acceleration that affects the orbits of small asteroids. Moreover, this study examines close approaches of near-Earth asteroids by comparing orbits calculated using the Gaia data. We used the conventional least-squares orbit computation method available in the OrbFit software. We used the latest Gaia Focused Product Release, complemented by data from the Minor Planet Center and radar astrometry from the Jet Propulsion Laboratory. We fitted orbital parameters for 446 Near-Earth Asteroids, including the additional non-gravitational transverse acceleration to model the Yarkovsky effect. Furthermore, we compared the results obtained using different datasets: Gaia Focused Product Release and the previous Gaia Data Release 3. We detected a robust Yarkovsky effect in 43 NEAs. As expected, we found an improvement in the orbital elements uncertainty and in the signal-to-noise ratio of the Yarkovsky effect detections when using the current Gaia FPR with double the observing arc compared to the DR3 catalog. We also found nine additional reliable detections of the Yarkovsky effect when using the new Gaia FPR catalog. Including the Yarkovsky effect in the force model can be important to reliably estimate close approach distances of near-Earth asteroids. Several of the detected Yarkovsky drifts already have a signal-to-noise ratio greater than 10, which is high enough for their Yarkovsky effect to be included in their reliable long-term orbital evolution, close approach, and Earth impact analysis. The final Gaia catalog may provide a much higher number of high signal-to-noise ratio detections of the Yarkovsky effect., Comment: 8 pages, 6 figures, accepted at Astronomy & Astrophysics. This study uses the latest Gaia FPR catalogue to assess the detection of the Yarkovsky effect on NEAs, comparing results with previous data releases and emphasizing improvements in orbital determination and close-approach predictions

Asteroids with companions constitute an excellent sample for studying the collisional and dynamical evolution of minor planets. The currently known binary population were discovered by different complementary techniques that produce, for the moment, a strongly biased distribution, especially in a range of intermediate asteroid sizes (approximately 20 to 100 km) where both mutual photometric events and high-resolution adaptive optic imaging are poorly efficient. A totally independent technique of binary asteroid discovery, based on astrometry, can help to reveal new binary systems and populate a range of sizes and separations that remain nearly unexplored. In this work, we describe a dedicated period detection method and its results for the Gaia DR3 data set. This method looks for the presence of a periodic signature in the orbit post-fit residuals. After conservative filtering and validation based on statistical and physical criteria, we are able to present a first sample of astrometric binary candidates, to be confirmed by other observation techniques such as photometric light curves and stellar occultations., Comment: 25 pages, 29 figures, Online table currently available at https://lagrange.oca.eu/fr/gaiamoons

Understanding how galaxies quench their star formation is crucial for studies of galaxy evolution. Quenching is related to the cold gas decrease. In the first paper we showed that the dust removal timescale in early-type galaxies (ETGs) is about 2.5 Gyr. Here we present carbon monoxide (CO) and 21 cm hydrogen (H I) line observations of these galaxies and measure the timescale of removal of the cold interstellar medium (ISM). We find that all the cold ISM components (dust, molecular and atomic gas) decline at similar rates. This allows us to rule out a wide range of potential ISM removal mechanisms (including starburst-driven outflows, astration, a decline in the number of asymptotic giant branch stars), and artificial effects like stellar mass-age correlation, environmental influence, mergers, and selection bias, leaving ionization by evolved low-mass stars and ionization/outflows by supernovae Type Ia or active galactic nuclei as viable mechanisms. We also provide evidence for an internal origin of the detected ISM. Moreover, we find that the quenching of star formation in these galaxies cannot be explained by a reduction in gas amount alone, because the star formation rates (SFRs) decrease faster (on a timescale of about 1.8 Gyr) than the amount of cold gas. Furthermore, the star formation efficiency of the ETGs (SFE = SFR/MH2) is lower than that of star-forming galaxies, whereas their gas mass fractions (fH2 = MH2/M*) are normal. This may be explained by the stabilization of gas against fragmentation, for example due to morphological quenching, turbulence, or magnetic fields., Comment: Astrophysical Journal, published; 29 pages, 13 figures, 6 tables; V2: matched the published version and typos in the SFR and outflow equations fixed - no change in the conclusions

In the latest Gaia third data release one can find extremely small proper motion components for the star HD 7977. This, together with the radial velocity measurement lead to the conclusion that this star passed very close to the Sun in the recent past. Such a very close approach of a one solar mass star must result in noticeable changes in the motion of all Solar System bodies, especially those on less tight orbits, namely long-period comets (LPCs) and Kuiper belt objects. We estimate and present these effects. Our current knowledge on the stellar surroundings of the Sun found in the latest Gaia catalogues allowed us to perform numerical integrations and prepare a list of potential stellar perturbers of LPCs. We use this list, made available in the StePPeD database. To study the past motion of LPCs under the simultaneous action of the Galactic potential and passing stars, we use precise original cometary orbits taken from the current CODE catalogue. We examine the reliability of the extremely small proper motion of HD 7977 concluding that this star can be an unresolved binary but according to the astrometry covering more than a century, the current Gaia results cannot be ruled out. We present the parameters of a very close passage of this star near the Sun. We also show examples of the strong influence of this passage on the past motion of some LPCs. We also discuss the possible influence of this perturber on other Solar System bodies. It is possible that 2.47 Myr ago the one solar mass star HD 7977 passed as close as one thousand au from the Sun. Such an event constitutes a kind of dynamical horizon for all studies of the past Solar System bodies' dynamics., Comment: 15 pages, 13 figures, 5 tables, submitted to A&A

Infrared measurements of asteroids are crucial for the determination of physical and thermal properties of individual objects, and for the understanding of the small-body populations in the solar system as a whole. But standard radiometric methods can only be applied if the orbit of an object is known, hence its position at the time of the observation. We present MIRI observations of the outer-belt asteroid 10920 and an unknown object, detected in all 9 MIRI bands in close proximity to 10920. We developed a new method "STM-ORBIT" to interpret the multi-band measurements without knowing the object's true location. The method leads to a confirmation of radiometric size-albedo solution for 10920 and puts constraints on the asteroid's location and orbit in agreement with its true orbit. Groundbased lightcurve observations of 10920, combined with Gaia data, indicate a very elongated object (a/b >= 1.5), with a spin-pole at (l, b) = (178{\deg}, 81{\deg}), and a rotation period of 4.861191 h. A thermophysical study leads to a size of 14.5 - 16.5 km, a geometric albedo between 0.05 and 0.10, and a thermal inertia in the range 9 to 35 Jm-2s-0.5K-1. For the newly discovered MIRI object, the STM-ORBIT method revealed a size of 100-230 m. The new asteroid must be on a very low-inclination orbit and it was located in the inner main-belt region during JWST observations. A beaming parameter {\eta} larger than 1.0 would push the size even below 100 meter, a main-belt regime which escaped IR detections so far. These kind of MIRI observations can therefore contribute to formation and evolution studies via classical size-frequency studies which are currently limited to objects larger than about one kilometer in size. We estimate that MIRI frames with pointings close to the ecliptic and only short integration times of a few seconds will always include a few asteroids, most of them will be unknown objects., Comment: 17 pages, 10 figures, 4 tables, accepted for A&A publication on Nov 22, 2022

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&A

In the last decade, Python-powered physics simulations ecosystem has been growing steadily, allowing greater interoperability, and becoming an important tool in numerical exploration of physical phenomena, particularly in soft matter systems. Driven by the need for fast and precise numerical integration in colloidal dynamics, here we formulate the problem of Brownian Dynamics (BD) in a mathematically consistent formalism of the It\=o calculus, and develop a Python package to assist numerical computations. We show that, thanks to the automatic differentiation packages, the classical truncated Taylor-It\=o integrators can be implemented without the burden of computing the derivatives of the coefficient functions beforehand. Furthermore, we show how to circumvent the difficulties of BD simulations such as calculations of the divergence of the mobility tensor in the diffusion equation and discontinuous trajectories encountered when working with dynamics on $S^2$ and $SO(3)$. The resulting Python package, Pychastic, is capable of performing BD simulations including hydrodynamic interactions at speeds comparable to dedicated implementations in lower-level programming languages, but with a much simpler end-user interface., Comment: submitted to SciPost Physics Codebases

Context. In 2020, the initial version of the Stellar Potential Perturbers Database (StePPeD) was presented with the aim to deliver up-to-date information on the stars and stellar systems that may perturb a long-period comet motion. We used the minimal distance between a star and the Sun as a selecting tool when compiling a list of interesting objects with close encounters with the Solar System, and our selection for that study was based on Gaia DR2 data. Aims. When the Gaia EDR3 data release was published, it became necessary to update this database. Additionally, we performed Monte Carlo simulations to obtain uncertainties on the parameters of the closest approach to the Sun of each object. Methods. We recalculated the close approach parameters of all stars in the previous StePPeD release, which resulted in removing approximately one-third of the total. Then we searched for new candidates in the whole Gaia EDR3 catalogue. We also take into account the duplicity of the found stars and additionally searched for double stars passing near the Sun which had been overlooked in previous papers. We also found the necessary mass estimates for new objects and updated this information for previously selected stars. Results. After a careful checking of all the collected data, we composed a new list of 155 potential stellar perturbers of the long-period comet motion. We applied a new threshold of 2 pc for the minimum star-Sun distance. This list consists of 146 single stars and nine multiple systems. For each object, we also estimated the uncertainty of the parameters of their closest approach to the Sun. Among these stars, we found a new potential strong past perturber, HD 7977, and confirmed the plausibility of a similar action on the part of Gliese 710 in the future., Comment: 12 pages, 10 figures, accepted for publication in A&A

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., Comment: Accepted for publication in Astronomy and Astrophysics

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 $\chi^2$ 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., Comment: accepted in A&A

Kepler mission is a powerful tool in the study the different types of astrophysical objects or events in the distant Universe. However, the spacecraft gives also the opportunity to study Solar System objects passing in the telescope field of view. The aim of this paper is to determine for the first time the rotation periods of a number of asteroids observed by the Kepler satellite during the K2 Campaign 9. Using publicly available data from Kepler mission we have used the Modified Causal Pixel Model (MCPM) code to perform the aperture-like and PRF-like photometry of 1026 asteroids. The results allowed us to determine the rotation periods for 188 asteroids. For asteroids with rotation periods previously measured, we compared the results and found very good agreement. There are additional 20 asteroids for which we obtained lower limits on rotation periods and in all cases these limits are at least 100 h., Comment: 24 pages, 8 figures, submitted to ApJS

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., Comment: Accepted for publication in A&A

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., Comment: 12 pages, 6 figures, accepted to be published in A&A

Among the four known transneptunian dwarf planets, Haumea is an exotic, very elongated, and fast rotating body. In contrast to the other dwarf planets, its size, shape, albedo, and density are not well constrained. Here we report results of a multi-chord stellar occultation, observed on 2017 January 21. Secondary events observed around the main body are consistent with the presence of a ring of opacity 0.5, width 70 km, and radius 2,287$_{-45}^{+75}$ km. The Centaur Chariklo was the first body other than a giant planet to show a ring system and the Centaur Chiron was later found to possess something similar to Chariklo's rings. Haumea is the first body outside the Centaur population with a ring. The ring is coplanar with both Haumea's equator and the orbit of its satellite Hi'iaka. Its radius places close to the 3:1 mean motion resonance with Haumea's spin period. The occultation by the main body provides an instantaneous elliptical limb with axes 1,704 $\pm$ 4 km x 1,138 $\pm$ 26 km. Combined with rotational light-curves, it constrains Haumea's 3D orientation and its triaxial shape, which is inconsistent with a homogeneous body in hydrostatic equilibrium. Haumea's largest axis is at least 2,322 $\pm$ 60 km, larger than thought before. This implies an upper limit of 1,885 $\pm$ 80 kg m$^{-3}$ for Haumea's density, smaller and less puzzling than previous estimations, and a geometric albedo of 0.51 $\pm$ 0.02, also smaller than previous estimations. No global N$_2$ or CH$_4$ atmosphere with pressures larger than 15 and 50 nbar (3-$\sigma$ limits), respectively, is detected.

In this article we study weighted sums of $n$ i.i.d. Gamma($\alpha$) random variables with nonnegative weights. We show that for $n \geq 1/\alpha$ the sum with equal coefficients maximizes differential entropy when variance is fixed. As a consequence, we prove that among nonnegative quadratic forms in $n$ independent standard Gaussian random variables, a diagonal form with equal coefficients maximizes differential entropy, under a fixed variance. This provides a sharp lower bound for the relative entropy between a nonnegative quadratic form and a Gaussian random variable. Bounds on capacities of transmission channels subject to $n$ independent additive gamma noises are also derived.

Learning to rank is a key component of many e-commerce search engines. In learning to rank, one is interested in optimising the global ordering of a list of items according to their utility for users.Popular approaches learn a scoring function that scores items individually (i.e. without the context of other items in the list) by optimising a pointwise, pairwise or listwise loss. The list is then sorted in the descending order of the scores. Possible interactions between items present in the same list are taken into account in the training phase at the loss level. However, during inference, items are scored individually, and possible interactions between them are not considered. In this paper, we propose a context-aware neural network model that learns item scores by applying a self-attention mechanism. The relevance of a given item is thus determined in the context of all other items present in the list, both in training and in inference. We empirically demonstrate significant performance gains of self-attention based neural architecture over Multi-LayerPerceptron baselines, in particular on a dataset coming from search logs of a large scale e-commerce marketplace, Allegro.pl. This effect is consistent across popular pointwise, pairwise and listwise losses.Finally, we report new state-of-the-art results on MSLR-WEB30K, the learning to rank benchmark., Comment: 8 pages, published at SIGIR eCom'20

On 28th January 2018, the large Trans-Neptunian Object (TNO) 2002TC302 occulted a m$_v= $15.3 star with ID 130957813463146112 in the Gaia DR2 stellar catalog. 12 positive occultation chords were obtained from Italy, France, Slovenia and Switzerland. Also, 4 negative detections were obtained near the north and south limbs. This represents the best observed stellar occultation by a TNO other than Pluto, in terms of the number of chords published thus far. From the 12 chords, an accurate elliptical fit to the instantaneous projection of the body, compatible with the near misses, can be obtained. The resulting ellipse has major and minor axes of 543 $\pm$ 18 km and 460 $\pm$ 11 km, respectively, with a position angle of 3 $\pm$ 1 degrees for the minor axis. This information, combined with rotational light curves obtained with the 1.5m telescope at Sierra Nevada Observatory and the 1.23m telescope at Calar Alto observatory, allows us to derive possible 3D shapes and density estimations for the body, based on hydrostatic equilibrium assumptions. The effective area equivalent diameter is $\sim$ 84 km smaller than the radiometrically derived diameter using thermal data from Herschel and Spitzer Space Telescopes. This might indicate the existence of an unresolved satellite of up to $\sim$ 300 km in diameter, to account for all the thermal flux, although the occultation and thermal diameters are compatible within their error bars given the considerable uncertainty of the thermal results. The existence of a potential satellite also appears to be consistent with other ground-based data presented here. From the effective occultation diameter combined with H$_V$ measurements we derive a geometric albedo of 0.147 $\pm$ 0.005, which would be somewhat smaller if 2002TC302 has a satellite. The best occultation light curves do not show any signs of ring features or any signatures of a global atmosphere., Comment: Accepted for publication in Astronomy & Astrophysics. 14 pages, 9 figures

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)

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., Comment: Accepted for publication in A&A

With an estimated diameter in the 320 to 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 $D$ $\lesssim$ 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. 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 ($D$ $\lesssim$ 200 km) bodies. 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 (ADAM) algorithm to reconstruct the 3D-shape model of Interamnia and to determine its spin state. Interamnia's volume-equivalent diameter of 332 $\pm$ 6 km implies a bulk density of $\rho$=1.98 $\pm$ 0.68 gcm$^{-3}$ , 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 2 $\sigma$ level. 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 ($D$ $\lesssim$ 300km) less massive ($m$ $\lesssim$ 3x10$^{19}$ kg) bodies., Comment: Accepted for publication in Astronomy and Astrophysics

An important aspect of quenching star formation is the removal of the cold interstellar medium (ISM; non-ionised gas and dust) from a galaxy. In addition, dust grains can be destroyed in a hot or turbulent medium. The adopted timescale of dust removal usually relies on uncertain theoretical estimates. It is tricky to track the dust removal, because usually dust is constantly replenished by consecutive generations of stars. Our objective is to measure observationally the timescale of dust removal. We here explore an approach to select galaxies which do have detectable amounts of dust and cold ISM but exhibit a low current dust production rate. Any decrease of the dust and gas content as a function of the age of such galaxies therefore must be attributed to processes governing the ISM removal. We used a sample of galaxies detected by Herschel in the far-infrared with visually assigned early-type morphology or spirals with red colours. We also obtained JCMT/SCUBA-2 observations for five of them. We discovered an exponential decline of the dust-to-stellar mass ratio with age, which we interpret as an evolutionary trend of dust removal from these galaxies. For the first time we directly measure the dust removal timescale in such galaxies to be tau=(2.5+-0.4) Gyr (the corresponding half-life time is (1.75+-0.25) Gyr). This quantity may be used in models in which it must be assumed a priori and cannot be derived. Any process which removes dust in these galaxies, such as dust grain destruction, cannot happen on shorter timescales. The timescale is comparable to the quenching timescales found in simulations for galaxies with similar stellar masses. The dust is likely of internal, not external origin. It was either formed in the past directly by supernovae, or from seeds produced by SNe and with grain growth in the ISM contributing substantially to the dust mass accumulation., Comment: Astronomy & Astrophysics, accepted; 13 pages, 9 figures, 1 table

We present a new non-convex model of the binary asteroid (809) Lundia. A SAGE (Shaping Asteroids with Genetic Evolution) method using disc-integrated photometry only was used for deriving physical parameters of this binary system. The model of (809) Lundia improves former system's pole solution and gives the ecliptic coordinates of the orbit pole - $\lambda=122^{\circ}$, $\beta=22^{\circ}$, $\sigma=\pm5^{\circ}$ - and the orbital period of $15.41574 \pm 0.00001$ h. For scaling our results we used effective diameter of $D_{eff} = 9.6 \pm 1.1$ km obtained from Spitzer observations. The non-convex shape description of the components permitted a refined calculation of the components' volumes, leading to a density estimation of $2.5\pm0.2$ g/cm$^3$ and macroporosity of 13-23\%. The intermediate-scale features of the model may also offer new clues on the components' origin and evolution.

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., Comment: Accepted for publication in Astronomy and Astrophysics

Context. Over the past decades, several interplanetary missions have studied small bodies in situ, leading to major advances in our understanding of their geological and geophysical properties. These missions, however, have had a limited number of targets. Among them, the NASA Dawn mission has characterised in detail the topography and albedo variegation across the surface of asteroid (4) Vesta down to a spatial resolution of approximately 20 m/pixel scale. Aims. Here our aim was to determine how much topographic and albedo information can be retrieved from the ground with VLT/SPHERE in the case of Vesta, having a former space mission (Dawn) providing us with the ground truth that can be used as a benchmark. Methods. We observed Vesta with VLT/SPHERE/ZIMPOL as part of our ESO large programme (ID 199.C-0074) at six different epochs, and deconvolved the collected images with a parametric point spread function (PSF). We then compared our images with synthetic views of Vesta generated from the 3D shape model of the Dawn mission, on which we projected Vesta's albedo information. Results. We show that the deconvolution of the VLT/SPHERE images with a parametric PSF allows the retrieval of the main topographic and albedo features present across the surface of Vesta down to a spatial resolution of approximately 20-30 km. Contour extraction shows an accuracy of approximately 1 pixel (3.6 mas). The present study provides the very first quantitative estimate of the accuracy of ground-based adaptive-optics imaging observations of asteroid surfaces. Conclusions. In the case of Vesta, the upcoming generation of 30-40m telescopes (ELT, TMT, GMT) should in principle be able to resolve all of the main features present across its surface, including the troughs and the north-south crater dichotomy, provided that they operate at the diffraction limit.

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 (Vernazza et al., 2016, AJ 152, 154) and numerical modeling of their early thermal evolution (Bland & Travis, 2017, Sci. Adv. 3, e1602514). 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 (ID 199.C-0074, PI P. Vernazza) 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 3-D 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/cm3 (3 {\sigma}). This density is 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.

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 pages

The near-Earth asteroid 3200 Phaethon (1983 TB) is an attractive object not only from a scientific viewpoint but also because of JAXA's DESTINY+ target. The rotational lightcurve and spin properties were investigated based on the data obtained in the ground-based observation campaign of Phaethon. We aim to refine the lightcurves and shape model of Phaethon using all available lightcurve datasets obtained via optical observation, as well as our time-series observation data from the 2017 apparition. Using eight 1-2-m telescopes and an optical imager, we acquired the optical lightcurves and derived the spin parameters of Phaethon. We applied the lightcurve inversion method and SAGE algorithm to deduce the convex and non-convex shape model and pole orientations. We analysed the optical lightcurve of Phaethon and derived a synodic and a sidereal rotational period of 3.6039 h, with an axis ratio of a/b = 1.07. The ecliptic longitude (lambda) and latitude (beta) of the pole orientation were determined as (308, -52) and (322, -40) via two independent methods. A non-convex model from the SAGE method, which exhibits a concavity feature, is also presented., Comment: 14 pages, 4 figures, 1 figure in Appendix A. Accepted for publication in Astronomy & Astrophysics (A&A)

The available set of spin and shape modelled asteroids is strongly biased against slowly rotating targets and those with low lightcurve amplitudes. As a consequence of these selection effects, the current picture of asteroid spin axis distribution, rotation rates, or radiometric properties, might be affected too. To counteract these selection effects, we are running a photometric campaign of a large sample of main belt asteroids omitted in most previous studies. We determined synodic rotation periods and verified previous determinations. When a dataset for a given target was sufficiently large and varied, we performed spin and shape modelling with two different methods. We used the convex inversion method and the non-convex SAGE algorithm, applied on the same datasets of dense lightcurves. Unlike convex inversion, the SAGE method allows for the existence of valleys and indentations on the shapes based only on lightcurves. We obtained detailed spin and shape models for the first five targets of our sample: (159) Aemilia, (227) Philosophia, (329) Svea, (478) Tergeste, and (487) Venetia. When compared to stellar occultation chords, our models obtained an absolute size scale and major topographic features of the shape models were also confirmed. When applied to thermophysical modelling, they provided a very good fit to the infrared data and allowed their size, albedo, and thermal inertia to be determined. Convex and non-convex shape models provide comparable fits to lightcurves. However, some non-convex models fit notably better to stellar occultation chords and to infrared data in sophisticated thermophysical modelling (TPM). In some cases TPM showed strong preference for one of the spin and shape solutions. Also, we confirmed that slowly rotating asteroids tend to have higher-than-average values of thermal inertia., Comment: Accepted in astronomy astrophys. 39 pages, 49 figures

The combination of visible and thermal data from the ground and astrophysics space missions is key to improving the scientific understanding of near-Earth, main-belt, trojans, centaurs, and trans-Neptunian objects. To get full information on a small sample of selected bodies we combine different methods and techniques: lightcurve inversion, stellar occultations, thermophysical modeling, radiometric methods, radar ranging and adaptive optics imaging. The SBNAF project will derive size, spin and shape, thermal inertia, surface roughness, and in some cases bulk densities and even internal structure and composition, for objects out to the most distant regions in the Solar System. The applications to objects with ground-truth information allows us to advance the techniques beyond the current state-of-the-art and to assess the limitations of each method. We present results from our project's first phase: the analysis of combined Herschel-KeplerK2 data and Herschel-occultation data for TNOs; synergy studies on large MBAs from combined high-quality visual and thermal data; establishment of well-known asteroids as celestial calibrators for far-infrared, sub-millimetre, and millimetre projects; first results on near-Earth asteroids properties from combined lightcurve, radar and thermal measurements, as well as the Hayabusa-2 mission target characterisation. We also introduce public web-services and tools for studies of small bodies in general., Comment: Accepted for publication in Advances in Space Research, 43 pages, 5 figures

Among asteroids there exist ambiguities in their rotation period determinations. They are due to incomplete coverage of the rotation, noise and/or aliases resulting from gaps between separate lightcurves. To help to remove such uncertainties, basic characteristic of the lightcurves resulting from constraints imposed by the asteroid shapes and geometries of observations should be identified. We simulated light variations of asteroids which shapes were modelled as Gaussian random spheres, with random orientations of spin vectors and phase angles changed every $5^\circ$ from $0^\circ$ to $65^\circ$. This produced 1.4 mln lightcurves. For each simulated lightcurve Fourier analysis has been made and the harmonic of the highest amplitude was recorded. From the statistical point of view, all lightcurves observed at phase angles $\alpha < 30^\circ$, with peak-to-peak amplitudes $A>0.2$ mag are bimodal. Second most frequently dominating harmonic is the first one, with the 3rd harmonic following right after. For 1% of lightcurves with amplitudes $A < 0.1$ mag and phase angles $\alpha < 40^\circ$ 4th harmonic dominates., Comment: 9 pages, 3 figures, 6 tables, accepted for publication in Monthly Notices of the Royal Astronomical Society

Despite the large amount of high quality data generated in recent space encounters with asteroids, the majority of our knowledge about these objects comes from ground based observations. Asteroids travelling in orbits that are potentially hazardous for the Earth form an especially interesting group to be studied. In order to predict their orbital evolution, it is necessary to investigate their physical properties. This paper briefly describes the data requirements and different techniques used to solve the lightcurve inversion problem. Although photometry is the most abundant type of observational data, models of asteroids can be obtained using various data types and techniques. We describe the potential of radar imaging and stellar occultation timings to be combined with disk-integrated photometry in order to reveal information about physical properties of asteroids., Comment: From Assessment and Mitigation of Asteroid Impact Hazards book

We consider the quasi-static evolution of the thermo-plasticity model in which the evolution equation law for the inelastic strain is given by the Prandtl-Reuss flow rule. The thermal part of the Cauchy stress tensor is not linearised in the neighbourhood of a references temperature. This nonlinear thermal part imposed to add a damping term to the balance of the momentum, which can be interpreted as external forces acting on the material. In general the dissipation term occurring in the heat equation is integrable function only and the standard methods can not be applied. Combining truncation techniques and Boccardo-Gallou\"et approach with monotone methods we prove an existence of renormalised solutions.

We report the detection of the radio afterglow of a long gamma-ray burst (GRB) 111005A at 5-345 GHz, including the very long baseline interferometry observations with the positional error of 0.2 mas. The afterglow position is coincident with the disk of a galaxy ESO 580-49 at z= 0.01326 (~1" from its center), which makes GRB 111005A the second closest GRB known to date, after GRB 980425. The radio afterglow of GRB 111005A was an order of magnitude less luminous than those of local low-luminosity GRBs, and obviously than those of cosmological GRBs. The radio flux was approximately constant and then experienced an unusually rapid decay a month after the GRB explosion. Similarly to only two other GRBs, we did not find the associated supernovae (SN), despite deep near- and mid-infrared observations 1-9 days after the GRB explosion, reaching ~20 times fainter than other SNe associated with GRBs. Moreover, we measured twice solar metallicity for the GRB location. The low gamma-ray and radio luminosities, rapid decay, lack of a SN, and super-solar metallicity suggest that GRB 111005A represents a different rare class of GRBs than typical core-collapse events. We modelled the spectral energy distribution of the GRB 111005A host finding that it is a dwarf, moderately star-forming galaxy, similar to the host of GRB 980425. The existence of two local GRBs in such galaxies is still consistent with the hypothesis that the GRB rate is proportional to the cosmic star formation rate (SFR) density, but suggests that the GRB rate is biased towards low SFRs. Using the far-infrared detection of ESO 580-49, we conclude that the hosts of both GRBs 111005A and 980425 exhibit lower dust content than what would be expected from their stellar masses and optical colours., Comment: Accepted by A&A. 17 pages, 16 figures, 5 tables

We present the Gaia-Groundbased Observational Service for Asteroids (GOSA). Gaia-GOSA is an interactive tool which supports observers in planning photometric observations of asteroids. Each user is able to personalise the observation plan taking into account the equipment used and the observation site. The list of targets has been previously selected among the most relevant and scientifically remarkable objects, while the prediction of the transits in the Gaia's field of view have been calculated at the Observatoire de la C\^ote d'Azur. The data collected by the GOSA community will be exploited to enhance the reliability of the Gaia's Solar system science. The service is publicly available at www.gaiagosa.eu., Comment: Vol. 10, EPSC2015-131, 2015 European Planetary Science Congress 2015

We investigated the reliability of the genetic algorithm which will be used to invert the photometric measurements of asteroids collected by the European Space Agency Gaia mission. To do that, we performed several sets of simulations for 10 000 asteroids having different spin axis orientations, rotational periods and shapes. The observational epochs used for each simulation were extracted from the Gaia mission simulator developed at the Observatoire de la C\^{o}te d'Azur, while the brightness was generated using a Z-buffer standard graphic method. We also explored the influence on the inversion results of contaminating the data set with Gaussian noise with different $\sigma$ values. The research enabled us to determine a correlation between the reliability of the inversion method and the asteroid's pole latitude. In particular, the results are biased for asteroids having quasi-spherical shapes and low pole latitudes. This effect is caused by the low lightcurve amplitude observed under such circumstances, as the periodic signal can be lost in the photometric random noise when both values are comparable, causing the inversion to fail. Such bias might be taken into account when analysing the inversion results, not to mislead it with physical effects such as non-gravitational forces. Finally, we studied what impact on the inversion results has combining a full lightcurve and Gaia photometry collected simultaneously. Using this procedure we have shown that it is possible to reduce the number of wrong solutions for asteroids having less than 50 data points. The latter will be of special importance for planning ground-based observations of asteroids aiming to enhance the scientific impact of Gaia on Solar system science., Comment: Accepted in MNRAS

We study a thermodynamically consistent model describing phenomena in a visco-plastic metal subjected to temperature changes. We complete the model with the mixed boundary condition on displacement and stress and Neumann-type condition for temperature. The main result is an existence of solution.

We present a new non-convex model of the 90 Antiope binary asteroid, derived with a modified version of the SAGE (Shaping Asteroids with Genetic Evolution) method using disk-integrated photometry only. A new variant of the SAGE algorithm capable of deriving models of binary systems is described. The model of 90 Antiope confirms the system's pole solution ($\lambda=199^{\circ}$, $\beta=38^{\circ}$, $\sigma=\pm5^{\circ}$) and the orbital period ($16.505046 \pm 0.000005$ h). A comparison between the stellar occultation chords obtained during the 2011 occultation and the projected shape solution has been used to scale the model. The resulting scaled model allowed us to obtain the equivalent radii ($R_{1}=40.4\pm0.9$ km and $R_{2}=40.2\pm0.9$ km) and the distance between the two system components ($176\pm4$ km), leading to a total system mass of ($9.14\pm0.62$)$\cdot10^{17}$ kg. The non-convex shape description of the components permitted a refined calculation of the components' volumes, leading to a density estimation of $1.67\pm0.23$ g cm$^{-3}$. The intermediate-scale features of the model may also offer new clues on the components' origin and evolution.

A numerical model of the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect for objects defined in terms of a triangular mesh is described. The algorithm requires that each surface triangle can be handled independently, which implies the use of a 1D thermal model. Insolation of each triangle is determined by an optimized ray-triangle intersection search. Surface temperature is modeled with a spectral approach; imposing a quasi-periodic solution we replace heat conduction equation by the Helmholtz equation. Nonlinear boundary conditions are handled by an iterative, FFT based solver. The results resolve the question of the YORP effect in rotation rate independence on conductivity within the nonlinear 1D thermal model regardless of the accuracy issues and homogeneity assumptions. A seasonal YORP effect in attitude is revealed for objects moving on elliptic orbits when a nonlinear thermal model is used., Comment: 15 pages, 10 figures, accepted to MNRAS, before language editing