ADAM: a general method for using various data types in asteroid reconstruction

We introduce ADAM, the All-Data Asteroid Modelling algorithm. ADAM is simple and universal since it handles all disk-resolved data types (adaptive optics or other images, interferometry, and range-Doppler radar data) in a uniform manner via the 2D Fourier transform, enabling fast convergence in model optimization. The resolved data can be combined with disk-integrated data (photometry). In the reconstruction process, the difference between each data type is only a few code lines defining the particular generalized projection from 3D onto a 2D image plane. Occultation timings can be included as sparse silhouettes, and thermal infrared data are efficiently handled with an approximate algorithm that is sufficient in practice due to the dominance of the high-contrast (boundary) pixels over the low-contrast (interior) ones. This is of particular importance to the raw ALMA data that can be directly handled by ADAM without having to construct the standard image. We study the reliability of the inversion by using the independent shape supports of function series and control-point surfaces. When other data are lacking, one can carry out fast nonconvex lightcurve-only inversion, but any shape models resulting from it should only be taken as illustrative global-scale ones.Comment: 11 pages, submitted to A&

Shape reconstruction from generalized projections

In this thesis we develop methods for recovering the three-dimensional shape of an object from generalized projections. We particularly focus on the problems encountered when data are presented as discrete image fields. We demonstrate the usefulness of the Fourier transform in transferring the image data and shape model projections to a domain more suitable for gradient based optimization. To substantiate the general applicability of our methods to observational astronomy, we reconstruct shape models for several asteroids observed with adaptive optics, thermal infrared interferometry, or range-Doppler radar. The reconstructions are carried out with the ADAM software package that we have designed for general use

Volumes and bulk densities of forty asteroids from ADAM shape modeling

Disk-integrated photometric data of asteroids do not contain accurate information on shape details or size scale. Additional data such as disk-resolved images or stellar occultation measurements further constrain asteroid shapes and allow size estimates. We aim to use all available disk-resolved images of about forty asteroids obtained by the Near-InfraRed Camera (Nirc2) mounted on the W.M. Keck II telescope together with the disk-integrated photometry and stellar occultation measurements to determine their volumes. We can then use the volume, in combination with the known mass, to derive the bulk density. We download and process all asteroid disk-resolved images obtained by the Nirc2 that are available in the Keck Observatory Archive (KOA). We combine optical disk-integrated data and stellar occultation profiles with the disk-resolved images and use the All-Data Asteroid Modeling (ADAM) algorithm for the shape and size modeling. Our approach provides constraints on the expected uncertainty in the volume and size as well. We present shape models and volume for 41 asteroids. For 35 asteroids, the knowledge of their mass estimates from the literature allowed us to derive their bulk densities. We clearly see a trend of lower bulk densities for primitive objects (C-complex) than for S-complex asteroids. The range of densities in the X-complex is large, suggesting various compositions. Moreover, we identified a few objects with rather peculiar bulk densities, which is likely a hint of their poor mass estimates. Asteroid masses determined from the Gaia astrometric observations should further refine most of the density estimates.Comment: Accepted for publication in A&

(65) Cybele is the smallest asteroid at hydrostatic equilibrium, why?

Context - Cybele asteroids constitute an appealing reservoir of primitive material genetically linked to the outer Solar system. The physical properties (size, shape) of the largest members can be directly measured with high-angular resolution imagers mounted on large (8-m class) telescopes.Aim - We took advantage of the bright apparition of the most iconic member of the Cybele population, (65) Cybele, in July and August 2021 to acquire high angular resolution images and optical light curves of the asteroid that were used to analyze its shape, topography and bulk properties (volume, density).Methods - Eight series of images were acquired with SPHERE+ZIMPOL on the Very Large Telescope (ESO Program ID 107.22QN.001; PI: Marsset) and combined with optical light curves to reconstruct the shape of the asteroid using the ADAM (Viikinkoski et al. 2015), MPCD (Capanna et al. 2013) and SAGE (Bartczak & Dudziński 2018) algorithms.Results - We will present Cybele's bulk properties, including its volume-equivalent diameter and average density, in the context of other low-albedo P-type asteroids. We will show that Cybele's shape and rotation state are entirely compatible to those of a Maclaurin equilibrium figure, opening up the possibility that D≥260 km (M≥1.4x10^19 kg) small bodies from the outer Solar System formed at equilibrium. We will further present the results of N-body simulations used to explore whether the equilibrium shape of Cybele is the result of a large resetting impact (similarly to the case of Hygiea; Vernazza et al. 2020), or if it is primordial (i.e., the result of early internal heating due to the radioactive decay of short- and long-lived radionuclides)

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

Context. Cybele asteroids constitute an appealing reservoir of primitive material genetically linked to the outer Solar System, and the physical properties (size and shape) of the largest members can be readily accessed by large (8m class) telescopes. Aims. We took advantage of the bright apparition of the most iconic member of the Cybele population, (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. Methods. Eight series of images were acquired with VLT/SPHERE+ZIMPOL, seven of which 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. Results. Cybele has a volume-equivalent diameter of 263±3 km and a bulk density of 1.55 ± 0.19 g 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 of Cybele shows that it is dispersed by gravitational perturbations and chaotic diffusion over gigayears of evolution. Conclusions. The very close match between Cybele and an equilibrium figure opens up the possibility that D ≥ 260 km (M ≥ 1.5 × 1019 kg) small bodies from the outer Solar System all formed at equilibrium. However, we cannot currently rule out an old impact as the origin of the equilibrium shape of Cybele. Cybele itself is found to be dynamically unstable, implying that it was ‘recently’ (<1 Gyr ago) placed on its current orbit either through slow diffusion from a relatively stable orbit in the Cybele region or, less likely, from an unstable, Jupiter-family-comet orbit in the planet-crossing region.This work has been supported by the Czech Science Foundation through grants 20-08218S (J. Hanuš) and 21-11058S (M. Brož), as well as by the National Science Foundation under Grant No. 1743015 (F. Marchis). T. Santana-Ros acknowledges funding from the NEO-MAPP project (H2020-EU-2-1-6/870377). In addition, this work was partially funded by the Spanish MICIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” by the “European Union” through grant RTI2018-095076-B-C21, and the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia ‘María de Maeztu’) through grant CEX2019-000918-M. This research has made use of the Asteroid Families Portal maintained at the Department of Astronomy, University of Belgrade. TRAPPIST is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant PDR T.0120.21. TRAPPIST-North is a project funded by the University of Liège, in collaboration with the Cadi Ayyad University of Marrakech (Morocco). E. Jehin is F.R.S.-FNRS Senior Research Associate

Asteroid (16) Psyche’s primordial shape: A possible Jacobi ellipsoid

Context. Asteroid (16) Psyche is the largest M-type asteroid in the main belt and the target of the NASA Psyche mission. It is also the only asteroid of this size (D >  200 km) known to be metal rich. Although various hypotheses have been proposed to explain the rather unique physical properties of this asteroid, a perfect understanding of its formation and bulk composition is still missing. Aims. We aim to refine the shape and bulk density of (16) Psyche and to perform a thorough analysis of its shape to better constrain possible formation scenarios and the structure of its interior. Methods. We obtained disk-resolved VLT/SPHERE/ZIMPOL images acquired within our ESO large program (ID 199.C-0074), which complement similar data obtained in 2018. Both data sets offer a complete coverage of Psyche’s surface. These images were used to reconstruct the three-dimensional (3D) shape of Psyche with two independent shape modeling algorithms (MPCD and ADAM). A shape analysis was subsequently performed, including a comparison with equilibrium figures and the identification of mass deficit regions. Results. Our 3D shape along with existing mass estimates imply a density of 4.20  ±  0.60 g cm−3, which is so far the highest for a solar system object following the four telluric planets. Furthermore, the shape of Psyche presents small deviations from an ellipsoid, that is, prominently three large depressions along its equator. The flatness and density of Psyche are compatible with a formation at hydrostatic equilibrium as a Jacobi ellipsoid with a shorter rotation period of ∼3h. Later impacts may have slowed down Psyche’s rotation, which is currently ∼4.2 h, while also creating the imaged depressions. Conclusions. Our results open the possibility that Psyche acquired its primordial shape either after a giant impact while its interior was already frozen or while its interior was still molten owing to the decay of the short-lived radionuclide 26Al.Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere under ESO programme 199.C-0074 (principal investigator: P. Vernazza). P. Vernazza, A. Drouard, M. Ferrais and B. Carry were supported by CNRS/INSU/PNP. J.H. and J.D. were supported by grant 18-09470S of the Czech Science Foundation and by the Charles University Research Programme no. UNCE/SCI/023. E.J. is F.R.S.-FNRS Senior Research Associate. The work of TSR was carried out through grant APOSTD/2019/046 by Generalitat Valenciana (Spain). This work was supported by the MINECO (Spanish Ministry of Economy) through grant RTI2018-095076-B-C21 (MINECO/FEDER, UE)

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

Aims. Asteroid (31) Euphrosyne is one of the biggest objects in the asteroid main belt and it is also the largest member of its namesake family. The Euphrosyne family occupies a highly inclined region in the outer main belt and contains a remarkably large number of members, which is interpreted as an outcome of a disruptive cratering event. Methods. The goals of this adaptive-optics imaging study are threefold: to characterize the shape of Euphrosyne, to constrain its density, and to search for the large craters that may be associated with the family formation event. Results. We obtained disk-resolved images of Euphrosyne using SPHERE/ZIMPOL at the ESO 8.2 m VLT as part of our large program (ID: 199.C-0074, PI: Vernazza). We reconstructed its 3D shape via the ADAM shape modeling algorithm based on the SPHERE images and the available light curves of this asteroid. We analyzed the dynamics of the satellite with the Genoid meta-heuristic algorithm. Finally, we studied the shape of Euphrosyne using hydrostatic equilibrium models. Conclusions. Our SPHERE observations show that Euphrosyne has a nearly spherical shape with the sphericity index of 0.9888 and its surface lacks large impact craters. Euphrosyne’s diameter is 268 ± 6 km, making it one of the top ten largest main belt asteroids. We detected a satellite of Euphrosyne – S/2019 (31) 1 – that is about 4 km across, on a circular orbit. The mass determined from the orbit of the satellite together with the volume computed from the shape model imply a density of 1665 ± 242 kg m−3, suggesting that Euphrosyne probably contains a large fraction of water ice in its interior. We find that the spherical shape of Euphrosyne is a result of the reaccumulation process following the impact, as in the case of (10) Hygiea. However, our shape analysis reveals that, contrary to Hygiea, the axis ratios of Euphrosyne significantly differ from those suggested by fluid hydrostatic equilibrium following reaccumulation.This work has been supported by the Czech Science Foundation through grant 18-09470S (J. Hanuš, O. Chrenko, P. Ševeček) and by the Charles University Research program No. UNCE/SCI/023. M.B. was supported by the Czech Science Foundation grant 18-04514J. Computational resources were supplied by the Ministry of Education, Youth and Sports of the Czech Republic under the projects CESNET (LM2015042) and IT4Innovations National Supercomputing Centre (LM2015070). P. Vernazza, A. Drouard, M. Ferrais and B. Carry were supported by CNRS/INSU/PNP. M.M. was supported by the National Aeronautics and Space Administration under grant No. 80NSSC18K0849 issued through the Planetary Astronomy Program. The work of TSR was carried out through grant APOSTD/2019/046 by Generalitat Valenciana (Spain). This work was supported by the MINECO (Spanish Ministry of Economy) through grant RTI2018-095076-B-C21 (MINECO/FEDER, UE). The research leading to these results has received funding from the ARC grant for Concerted Research Actions, financed by the Wallonia-Brussels Federation. TRAPPIST is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant FRFC 2.5.594.09.F. TRAPPIST-North is a project funded by the Université de Liège, and performed in collaboration with Cadi Ayyad University of Marrakesh. E. Jehin is a FNRS Senior Research Associate

A basin-free spherical shape as an outcome of a giant impact on asteroid Hygiea

(10) Hygiea is the fourth largest main belt asteroid and the only known asteroid whose surface composition appears similar to that of the dwarf planet (1) Ceres1,2, suggesting a similar origin for these two objects. Hygiea suffered a giant impact more than 2 Gyr ago3 that is at the origin of one of the largest asteroid families. However, Hygeia has never been observed with sufficiently high resolution to resolve the details of its surface or to constrain its size and shape. Here, we report high-angular-resolution imaging observations of Hygiea with the VLT/SPHERE instrument (~20 mas at 600 nm) that reveal a basin-free nearly spherical shape with a volume-equivalent radius of 217 ± 7 km, implying a density of 1,944 ± 250 kg m−3 to 1σ. In addition, we have determined a new rotation period for Hygiea of ~13.8 h, which is half the currently accepted value. Numerical simulations of the family-forming event show that Hygiea’s spherical shape and family can be explained by a collision with a large projectile (diameter ~75–150 km). By comparing Hygiea’s sphericity with that of other Solar System objects, it appears that Hygiea is nearly as spherical as Ceres, opening up the possibility for this object to be reclassified as a dwarf planet.P.V., A.D. and B.C. were supported by CNRS/INSU/PNP. M.Brož was supported by grant 18-04514J of the Czech Science Foundation. J.H. and J.D. were supported by grant 18-09470S of the Czech Science Foundation and by the Charles University Research Programme no. UNCE/SCI/023. This project has received funding from the European Union’s Horizon 2020 research and innovation programmes under grant agreement nos 730890 and 687378. This material reflects only the authors’ views, and the European Commission is not liable for any use that may be made of the information contained herein. TRAPPIST-North is a project funded by the University of Liège, in collaboration with Cadi Ayyad University of Marrakech (Morocco). TRAPPIST-South is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant FRFC 2.5.594.09.F. E.J. and M.G. are F.R.S.-FNRS Senior Research Associates

Järjestysfunktiolliset kokonaisalueet ja valuaatiot

Koodausteorian tavoitteena on parantaa tietoliikenteen luotettavuutta kehittämällä menetelmiä häiriöiden aiheuttamien virheiden korjaamiseen. Algebrallisen geometrian ja koodausteorian yhteistyön merkittävimpiä teoreettisia tuloksia ovat 1980-luvulla kehitetyt geometriset Goppa-koodit, jotka paransivat silloin parasta tunnettua alarajaa, niin kutsuttua asymptoottista Gilbertin-Varshamovin rajaa. Nämä Goppa-koodit konstruoidaan evaluoimalla algebrallisen käyrän rationaalifunktioita käyrän pisteissä. Evaluaatiokoodit ovat Goppa-koodien yleistyksiä, jotka saadaan laskemalla variston rationaalifunktioiden arvoja pistejoukossa. Evaluaatiokoodin määritelmä on kuitenkin hyvin yleinen, joten dekoodausalgoritmin löytäminen ja jopa koodin parametrien määrittäminen on vaikeaa. Järjestysfunktiolliset kokonaisalueet ovat laaja joukko renkaita, joiden hyvät ominaisuudet mahdollistavat niistä saatavien evaluaatiokoodien ominaisuuksien tarkemman määrittämisen. Tämän lisensiaattityön aiheena ovat järjestysfunktiolliset kokonaisalueet ja valuaatiot. Tutkielmassa tarkastellaan järjestysfunktiollisten kokonaisalueiden perusominaisuuksia ja esimerkkejä järjestysfunktioiden konstruoimisesta muun muassa variston lipun avulla. Lisäksi todistetaan, että renkaan säännölliset suodatukset ja toisaalta komplementaariset valuaatiot ovat tiettyjen lievien ehtojen vallitessa ekvivalentteja järjestysfunktioiden määritelmän kanssa. Lopuksi osoitetaan astetta yksi olevien painofunktioiden ja affiinien käyrien välinen yhteys. Viimeisessä pykälässä tarkastellaan pinnan valuaatioiden luokittelua ja näiden valuaatioiden yhteyksiä järjestysfunktioihin