arXiv subjects

A. Longobardo

Publications and source records attributed to A. Longobardo.

At least 19 recordsLinked to original sources

arXiv2026

SHARP -- A spectrograph proposal to fully exploit ELT capabilities and look beyond JWST

The Extremely Large Telescopes (ELTs), with their large apertures and cutting-edge Multi-Conjugate Adaptive Optics (MCAO) systems, promise to deliver data that is both sharper and deeper than even the James Webb Space Telescope (JWST) across large fields. SHARP is a concept study for a near-IR (0.95-2.45 $\mu$m) spectrograph specifically designed to fully exploit the collecting area and angular resolution capabilities of the upcoming ESO's ELT. The instrument concept is driven by the goal of tackling the most important questions in astrophysics and cosmology, from exploring primordial galaxies to studying the formation of young stellar object and planetary systems in the nearby dust-enshrouded regions, bridging the gap between the local and the distant Universe. This requires versatility to accommodate diverse observational needs. SHARP is composed of two main units: NEXUS, a Multi-Object Spectrograph (MOS) optimized for detecting the faintest sources, and VESPER, a multi-object Integral Field Unit (multi-IFU) designed for brighter ones. This article provides an overview of the scientific design drivers, the solutions developed to meet them, and the resulting optical design that achieves the required performance.

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arXiv2025

SHARP: Beyond JWST -- Revealing the galaxy birth and growth with the resolution of the ELT

A deep understanding of the life-cycle of galaxies, particularly those of high mass, requires clarifying the mechanisms that regulate star formation (SF) and its abrupt shutdown (quenching), often capable of stopping SF rates of hundreds of solar masses per year. What initially triggers quenching, and what sustains the quiescent state thereafter, especially given the frequent presence of large gas reservoirs or even massive gas inflows, are unsolved key issues. Ultimately, the crucial connection between the galaxy life-cycle and the surrounding Intergalactic (IGM) and Circumgalactic (CGM) Medium remains largely unclear. Addressing these issues requires studying star formation, chemical enrichment, and quenching homogeneously up to high redshift. The upcoming AO-assisted Extremely Large Telescope (ELT), will deliver sharper and deeper data than the JWST. SHARP is a concept study for a near-IR (0.95-2.45 mu) spectrograph designed to fully exploit the capabilities of ELT. Designed for multi-object slit spectroscopy and multi-Integral Field spectroscopy, SHARP points to achieve angular resolutions (~30 mas) far superior to NIRSpec at JWST(100 mas) to decipher and reconstruct the life-cycle oa galaxies.

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arXiv2024

SHARP -- A near-IR multi-mode spectrograph conceived for MORFEO@ELT

The Extremely Large Telescopes (ELTs), thanks to their large apertures and cutting-edge Multi-Conjugate Adaptive Optics (MCAO) systems, promise to deliver sharper and deeper data even than the JWST. SHARP is a concept study for a near-IR (0.95-2.45 $\mu$m) spectrograph conceived to fully exploit the collecting area and the angular resolution of the upcoming generation of ELTs. In particular, SHARP is designed for the 2nd port of MORFEO@ELT. Composed of a Multi-Object Spectrograph, NEXUS, and a multi-Integral Field Unit, VESPER, MORFEO-SHARP will deliver high angular ($\sim$30 mas) and spectral (R$\simeq$300, 2000, 6000, 17000) resolution, outperforming NIRSpec@JWST (100 mas). SHARP will enable studies of the nearby Universe and the early Universe in unprecedented detail. NEXUS is fed by a configurable slit system deploying up to 30 slits with $\sim$2.4 arcsec length and adjustable width, over a field of about 1.2"$\times$1.2" (35 mas/pix). Each slit is fed by an inversion prism able to rotate by an arbitrary angle the field that can be seen by the slit. VESPER is composed of 12 probes of 1.7"$\times$1.5" each (spaxel 31 mas) probing a field 24"$\times$70". SHARP is conceived to exploit the ELTs apertures reaching the faintest flux and the sharpest angular resolution by joining the sensitivity of NEXUS and the high spatial sampling of VESPER to MORFEO capabilities. This article provides an overview of the scientific design drivers, their solutions, and the resulting optical design of the instrument achieving the required optical performance.

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arXiv2023

Cometary dust collected by MIDAS on board Rosetta II. Particle shape descriptors and pristineness evaluation

The MIDAS (Micro-Imaging Dust Analysis System) atomic force microscope on board the Rosetta comet orbiter investigated and measured the 3D topography of a few hundred nm to tens of $μ$m sized dust particles of 67P/Churyumov-Gerasimenko with resolutions down to a few nanometers, giving insights into the physical processes of our early Solar System. We analyze the shapes of the cometary dust particles collected by MIDAS on the basis of a recently updated particle catalog with the aim to determine which structural properties remained pristine. We develop a set of shape descriptors and metrics such as aspect ratio, elongation, circularity, convexity, and particle surface/volume distribution, which can be used to describe the distribution of particle shapes. Furthermore, we compare the structure of the MIDAS dust particles and the clusters in which the particles were deposited to those found in previous laboratory experiments and by Rosetta/COSIMA. Finally, we combine our findings to calculate a pristineness score for MIDAS particles and determine the most pristine particles and their properties. We find that the morphological properties of all cometary dust particles at the micrometer scale are surprisingly homogeneous despite originating from diverse cometary environments (e.g., different collection targets that are associated with cometary activities/source regions and collection velocities/periods). We next find that the types of clusters found by MIDAS show good agreement with those defined by previous laboratory experiments, however, there are some differences to those found by Rosetta/COSIMA. Based on our result, we rate 19 out of 1082 MIDAS particles at least moderately pristine, i.e., they are not substantially flattened by impact, not fragmented, and/or not part of a fragmentation cluster.

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arXiv2023

Cometary dust collected by MIDAS on board Rosetta. I. Dust particle catalog and statistics

We aim to catalog all dust particles collected and analyzed by MIDAS, together with their main statistical properties such as size, height, basic shape descriptors, and collection time. Furthermore, we aim to present the scientific results that can be extracted from the catalog (e.g., the size distribution and statistical characteristics of cometary dust particles). The existing MIDAS particle catalog has been greatly improved by a careful re-analysis of the AFM images, leading to the addition of more dust particles and a detailed description of the particle properties. The catalog documents all images of identified dust particles and includes a variety of derived information tabulated one record per particle. Furthermore, the best image of each particle was chosen for subsequent studies. Finally, we created dust coverage maps and clustering maps of the MIDAS collection targets and traced any possible fragmentation of collected particles with a detailed algorithm. The revised MIDAS catalog includes 3523 MIDAS particles in total, where 1857 particles are expected to be usable for further analysis (418 scans of particles before perihelion + 1439 scans of particles after perihelion, both after the removal of duplicates), ranging from about 40 nm to about 8 $μ$m in size. The mean value of the equivalent radius derived from the 2D projection of the particles is 0.91 ${\pm}$ 0.79 $μ$m. A slightly improved equivalent radius based on the particle's volume coincides in the range of uncertainties with a value of 0.56 ${\pm}$ 0.45 $μ$m. We note that those sizes and all following MIDAS particle size distributions are expected to be influenced by the fragmentation of MIDAS particles upon impact on the collection targets. Furthermore, fitting the slope of the MIDAS particle size distribution with a power law of a r ${^b}$ yields an index b of ${\sim}$ -1.67 to -1.88.

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arXiv2020

Resolved Spectrophotometric Properties of the Ceres Surface from Dawn Framing Camera Images

We present a global spectrophotometric characterization of the Ceres surface using Dawn Framing Camera (FC) images. We identify the photometric model that yields the best results for photometrically correcting images. Corrected FC images acquired on approach to Ceres were assembled into global maps of albedo and color. Generally, albedo and color variations on Ceres are muted. The albedo map is dominated by a large, circular feature in Vendimia Planitia, known from HST images (Li et al., 2006), and dotted by smaller bright features mostly associated with fresh-looking craters. The dominant color variation over the surface is represented by the presence of "blue" material in and around such craters, which has a negative spectral slope over the visible wavelength range when compared to average terrain. We also mapped variations of the phase curve by employing an exponential photometric model, a technique previously applied to asteroid Vesta (Schröder et al., 2013b). The surface of Ceres scatters light differently from Vesta in the sense that the ejecta of several fresh-looking craters may be physically smooth rather than rough. High albedo, blue color, and physical smoothness all appear to be indicators of youth. The blue color may result from the desiccation of ejected material that is similar to the phyllosilicates/water ice mixtures in the experiments of Poch et al. (2016). The physical smoothness of some blue terrains would be consistent with an initially liquid condition, perhaps as a consequence of impact melting of subsurface water ice. We find red terrain (positive spectral slope) near Ernutet crater, where De Sanctis et al. (2017) detected organic material. The spectrophotometric properties of the large Vendimia Planitia feature suggest it is a palimpsest, consistent with the Marchi et al. (2016) impact basin hypothesis. The central bright area in Occator crater, Cerealia...

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arXiv2020

Spectral investigation of Ceres analogue mixtures: in-depth analysis of crater central peak material (ccp) on Ceres

In order to investigate the causes of different spectral slope in ccps, different grain-sizes of Ceres analogue mixtures were produced, heated to remove absorption of atmospheric water, and spectrally analyzed. First, the end-members which compose the Ceres surface (using the antigorite as Mg-phyllosilicate, the NH4-montmorillonite as NH4-phyllosilicate, the dolomite as carbonate and the graphite as dark component), were mixed, obtaining mixtures with different relative abundance, and identifying the mixture with the reflectance spectrum most similar to the average Ceres spectrum. The mixtures were obtained with grain size of 0-25 μm, 25-50 mic and 50-100 mic, were heated and spectrally analysed at T= 300 K and T=200 K (typical for surface Ceres temperature during VIR observations). The most similar Ceres analogue mixture is composed of dolomite (18%), graphite (27%), antigorite (32%) and NH4-montmorillonite (29%) and the results of this work suggest that this mixture is more similar to the Ceres youngest region than to the Ceres average, in particular for the negative slope of spectrum. Small variation in the composition and grain size of end-members need to be considered, in addition to the occurrence of a dark component dispersed in fine size. Furthermore, the positive spectral slope that characterizes the mean Ceres spectrum can be obtained by the application of some processes simulating the space weathering on Ceres (as micro-meteoritic impacts and solar wind irradiation), i.e. laser and ion irradiation. As conclusion, youngest ccps on Ceresare probably composed by fresher and weakly processed mixture with fine dark material intimately dispersed: as a result, the reflectance spectra of youngest material show a negative slope in the 1.2-1.9 mic range. The redder slope observed in the older ccps is probably the consequence of the space weathering effects on fresher material

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arXiv2020

Infrared detection of aliphatic organics on a cometary nucleus

The ESA Rosetta mission has acquired unprecedented measurements of comet 67/P-Churyumov-Gerasimenko (hereafter 67P) nucleus surface, whose composition, as determined by in situ and remote sensing instruments including VIRTIS (Visible, InfraRed and Thermal Imaging Spectrometer) appears to be made by an assemblage of ices, minerals, and organic material. We performed a refined analysis of infrared observations of the nucleus of comet 67P carried out by the VIRTIS-M hyperspectral imager. We found that the overall shape of the 67P infrared spectrum is similar to that of other carbon-rich outer solar system objects suggesting a possible genetic link with them. More importantly, we are also able to confirm the complex spectral structure of the wide 2.8-3.6 micron absorption feature populated by fainter bands. Among these, we unambiguously identified the presence of aliphatic organics by their ubiquitous 3.38, 3.42 and 3.47 micron bands. This novel infrared detection of aliphatic species on a cometary surface has strong implications for the evolutionary history of the primordial solar system and give evidence that comets provide an evolutionary link between interstellar material and solar system bodies.

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arXiv2020

Ammonium salts are a reservoir of nitrogen on a cometary nucleus and possibly on some asteroids

The measured nitrogen-to-carbon ratio in comets is lower than for the Sun, a discrepancy which could be alleviated if there is an unknown reservoir of nitrogen in comets. The nucleus of comet 67P/Churyumov-Gerasimenko exhibits an unidentified broad spectral reflectance feature around 3.2 micrometers, which is ubiquitous across its surface. On the basis of laboratory experiments, we attribute this absorption band to ammonium salts mixed with dust on the surface. The depth of the band indicates that semivolatile ammonium salts are a substantial reservoir of nitrogen in the comet, potentially dominating over refractory organic matter and more volatile species. Similar absorption features appear in the spectra of some asteroids, implying a compositional link between asteroids, comets, and the parent interstellar cloud.

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arXiv2019

Diurnal variation of dust and gas production in comet 67P/Churyumov-Gerasimenko at the inbound equinox as seen by OSIRIS and VIRTIS-M on board Rosetta

On 27 Apr 2015, when 67P/C-G was at 1.76 au from the Sun and moving towards perihelion, the OSIRIS and VIRTIS-M instruments on Rosetta observed the evolving dust and gas coma during a complete rotation of the comet. We aim to characterize the dust, H2O and CO2 gas spatial distribution in the inner coma. To do this we performed a quantitative analysis of the release of dust and gas and compared the observed H2O production rate with the one calculated using a thermo-physical model. For this study we selected OSIRIS WAC images at 612 nm (dust) and VIRTIS-M image cubes at 612 nm, 2700 nm (H2O) and 4200 nm (CO2). We measured the average signal in a circular annulus, to study spatial variation around the comet, and in a sector of the annulus, to study temporal variation in the sunward direction with comet rotation, both at a fixed distance of 3.1 km from the comet centre. The spatial correlation between dust and water, both coming from the sun-lit side of the comet, shows that water is the main driver of dust activity in this time period. The spatial distribution of CO2 is not correlated with water and dust. There is no strong temporal correlation between the dust brightness and water production rate as the comet rotates. The dust brightness shows a peak at 0deg sub-solar longitude, which is not pronounced in the water production. At the same epoch, there is also a maximum in CO2 production. An excess of measured water production, with respect to the value calculated using a simple thermo-physical model, is observed when the head lobe and regions of the Southern hemisphere with strong seasonal variations are illuminated. A drastic decrease in dust production, when the water production (both measured and from the model) displays a maximum, happens when typical Northern consolidated regions are illuminated and the Southern hemisphere regions with strong seasonal variations are instead in shadow.

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arXiv2019

Synthesis of the Morphological Description of Cometary Dust at Comet 67P

Before Rosetta, the space missions Giotto and Stardust shaped our view on cometary dust, supported by plentiful data from Earth based observations and interplanetary dust particles collected in the Earth's atmosphere. The Rosetta mission at comet 67P/Churyumov-Gerasimenko was equipped with a multitude of instruments designed to study cometary dust. While an abundant amount of data was presented in several individual papers, many focused on a dedicated measurement or topic. Different instruments, methods, and data sources provide different measurement parameters and potentially introduce different biases. This can be an advantage if the complementary aspect of such a complex data set can be exploited. However, it also poses a challenge in the comparison of results in the first place. The aim of this work therefore is to summarise dust results from Rosetta and before. We establish a simple classification as a common framework for inter-comparison. This classification is based on a dust particle's structure, porosity, and strength as well as its size. Depending on the instrumentation, these are not direct measurement parameters but we chose them as they were the most reliable to derive our model. The proposed classification already proved helpful in the Rosetta dust community and we propose to take it into consideration also beyond. In this manner we hope to better identify synergies between different instruments and methods in the future.

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arXiv2019

VIRTIS-H observations of comet 67P's dust coma: spectral properties and color temperature variability with phase and elevation

We analyze 2-5 micrometre spectroscopic observations of the dust coma of comet 67P/Churyumov-Gerasimenko obtained with the VIRTIS-H instrument onboard Rosetta from 3 June to 29 October 2015 at heliocentric distances r_h = 1.24-1.55 AU. The 2-2.5 micrometre color, bolometric albedo, and color temperature are measured using spectral fitting. Data obtained at alpha = 90° solar phase angle show an increase of the bolometric albedo (0.05 to 0.14) with increasing altitude (0.5 to 8 km), accompanied by a possible marginal decrease of the color and color temperature. Possible explanations include the presence in the inner coma of dark particles on ballistic trajectories, and radial changes in particle composition. In the phase angle range 50-120°, phase reddening is significant (0.031 %/100 nm/°), for a mean color of 2 %/100 nm at alpha = 90°, that can be related to the roughness of the dust particles. Moreover, a decrease of the color temperature with decreasing phase angle is also observed at a rate of ~ 0.3 K/°, consistent with the presence of large porous particles, with low thermal inertia, and showing a significant day-to-night temperature contrast. Comparing data acquired at fixed phase angle (alpha = 90°), a 20% increase of the bolometric albedo is observed near perihelion. Heliocentric variations of the dust color are not significant in the analyzed time period. Measured color temperatures are varying from 260 to 320 K, and follow a r^0.6 variation in the r_h = 1.24-1.5 AU range, close to the expected r_h^0.5 value.

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arXiv2018

Solar system science with the Wide-Field InfraRed Survey Telescope (WFIRST)

We present a community-led assessment of the solar system investigations achievable with NASA's next-generation space telescope, the Wide Field InfraRed Survey Telescope (WFIRST). WFIRST will provide imaging, spectroscopic, and coronagraphic capabilities from 0.43-2.0 $μ$m and will be a potential contemporary and eventual successor to JWST. Surveys of irregular satellites and minor bodies are where WFIRST will excel with its 0.28 deg$^2$ field of view Wide Field Instrument (WFI). Potential ground-breaking discoveries from WFIRST could include detection of the first minor bodies orbiting in the Inner Oort Cloud, identification of additional Earth Trojan asteroids, and the discovery and characterization of asteroid binary systems similar to Ida/Dactyl. Additional investigations into asteroids, giant planet satellites, Trojan asteroids, Centaurs, Kuiper Belt Objects, and comets are presented. Previous use of astrophysics assets for solar system science and synergies between WFIRST, LSST, JWST, and the proposed NEOCam mission are discussed. We also present the case for implementation of moving target tracking, a feature that will benefit from the heritage of JWST and enable a broader range of solar system observations.

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arXiv2017

Comet 67P outbursts and quiescent coma at 1.3 AU from the Sun: dust properties from Rosetta/VIRTIS-H observations

We present 2-5 $μ$m spectroscopic observations of the dust coma of 67P/Churyumov-Gerasimenko obtained with the VIRTIS-H instrument onboard Rosetta during two outbursts that occurred on 2015, 13 September 13.6 h UT and 14 September 18.8 h UT at 1.3 AU from the Sun. Scattering and thermal properties measured before the outburst are in the mean of values measured for moderately active comets. The colour temperature excess (or superheat factor) can be attributed to submicrometre-sized particles composed of absorbing material or to porous fractal-like aggregates such as those collected by the Rosetta in situ dust instruments. The power law index of the dust size distribution is in the range 2-3. The sudden increase of infrared emission associated to the outbursts is correlated with a large increase of the colour temperature (from 300 K to up to 630 K) and a change of the dust colour at 2-2.5 $μ$m from red to blue colours, revealing the presence of very small grains ($\leq$ 100 nm) in the outburst material. In addition, the measured large bolometric albedos ($\sim$ 0.7) indicate bright grains in the ejecta, which could either be silicatic grains, implying the thermal degradation of the carbonaceous material, or icy grains. The 3-$μ$m absorption band from water ice is not detected in the spectra acquired during the outbursts, whereas signatures of organic compounds near 3.4 $μ$m are observed in emission. The H$_2$O 2.7-$μ$m and CO$_2$ 4.3-$μ$m vibrational bands do not show any enhancement during the outbursts.

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arXiv2017

VESPA: a community-driven Virtual Observatory in Planetary Science

The VESPA data access system focuses on applying Virtual Observatory (VO) standards and tools to Planetary Science. Building on a previous EC-funded Europlanet program, it has reached maturity during the first year of a new Europlanet 2020 program (started in 2015 for 4 years). The infrastructure has been upgraded to handle many fields of Solar System studies, with a focus both on users and data providers. This paper describes the broad lines of the current VESPA infrastructure as seen by a potential user, and provides examples of real use cases in several thematic areas. These use cases are also intended to identify hints for future developments and adaptations of VO tools to Planetary Science.

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arXiv2017

Spectrophotometric properties of dwarf planet Ceres from the VIR spectrometer on board the Dawn mission

We study the spectrophotometric properties of dwarf planet Ceres in the VIS-IR spectral range by means of hyper-spectral images acquired by the VIR imaging spectrometer on board the NASA Dawn mission. Disk-resolved observations with a phase angle within the $7^{\circ}<α<132^{\circ}$ interval were used to characterize Ceres' phase curve in the 0.465-4.05 $μ$m spectral range. Hapke's model was applied to perform the photometric correction of the dataset, allowing us to produce albedo and color maps of the surface. The $V$-band magnitude phase function of Ceres was fitted with both the classical linear model and H-G formalism. The single-scattering albedo and the asymmetry parameter at 0.55$μ$m are $w=0.14\pm0.02$ and $ξ=-0.11\pm0.08$, respectively (two-lobe Henyey-Greenstein phase function); the modeled geometric albedo is $0.094\pm0.007$; the roughness parameter is $\barθ=29^{\circ}\pm6^{\circ}$. Albedo maps indicate small variability on a global scale with an average reflectance of $0.034 \pm 0.003$. Isolated areas such as the Occator bright spots, Haulani, and Oxo show an albedo much higher than average. We measure a significant spectral phase reddening, and the average spectral slope of Ceres' surface after photometric correction is $1.1\%kÅ^{-1}$ and $0.85\%kÅ^{-1}$ at VIS and IR wavelengths, respectively. Broadband color indices are $V-R=0.38\pm0.01$ and $R-I=0.33\pm0.02$. H-G modeling of the $V$-band magnitude phase curve for $α<30^{\circ}$ gives $H=3.14\pm0.04$ and $G=0.10\pm0.04$, while the classical linear model provides $V(1,1,0^{\circ})=3.48\pm0.03$ and $β=0.036\pm0.002$. The comparison with spectrophotometric properties of other minor bodies indicates that Ceres has a less back-scattering phase function and a slightly higher albedo than comets and C-type objects. However, the latter represents the closest match in the usual asteroid taxonomy.

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arXiv2016

The temporal evolution of exposed water ice-rich areas on the surface of 67P/Churyumov-Gerasimenko: spectral analysis

Water ice-rich patches have been detected on the surface of comet 67P/Churyumov-Gerasimenko by the VIRTIS hyperspectral imager on-board the Rosetta spacecraft, since the orbital insertion in late August 2014. Among those, three icy patches have been selected, and VIRTIS data are used to analyse their properties and their temporal evolution while the comet was moving towards the Sun. We performed an extensive analysis of the spectral parameters, and we applied the Hapke radiative transfer model to retrieve the abundance and grain size of water ice, as well as the mixing modalities of water ice and dark terrains on the three selected water ice rich areas. Study of the spatial distribution of the spectral parameters within the ice-rich patches has revealed that water ice follows different patterns associated to a bimodal distribution of the grains: ~50 μm sized and ~2000 μm sized. In all three cases, after the first detections at about 3.5 AU heliocentric distance, the spatial extension and intensity of the water ice spectral features increased, it reached a maximum after 60-100 days at about 3.0 AU, and was followed by an approximately equally timed decrease and disappearanceat about ~2.2 AU, before perihelion. The behaviour of the analysed patches can be assimilated to a seasonal cycle. In addition we found evidence of short-term variability associated to a diurnal water cycle. The similar lifecycle of the three icy regions indicates that water ice is uniformly distributed in the subsurface layers, and no large water ice reservoirs are present.

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arXiv2014

The contamination of the surface of Vesta by impacts and the delivery of the dark material

The Dawn spacecraft observed the presence of dark material, which in turn proved to be associated with OH and H-rich material, on the surface of Vesta. The source of this dark material has been identified with the low albedo asteroids, but it is still a matter of debate whether the delivery of the dark material is associated with a few large impact events, to micrometeorites or to the continuous, secular flux of impactors on Vesta. The continuous flux scenario predicts that a significant fraction of the exogenous material accreted by Vesta should be due to non-dark impactors likely analogous to ordinary chondrites, which instead represent only a minor contaminant in the HED meteorites. We explored the continuous flux scenario and its implications for the composition of the vestan regolith, taking advantage of the data from the Dawn mission and the HED meteorites. We used our model to show that the stochastic events scenario and the micrometeoritic flux scenario are natural consequences of the continuous flux scenario. We then used the model to estimate the amounts of dark and hydroxylate materials delivered on Vesta since the LHB and we showed how our results match well with the values estimated by the Dawn mission. We used our model to assess the amount of Fe and siderophile elements that the continuous flux of impactors would mix in the vestan regolith: concerning the siderophile elements, we focused our attention on the role of Ni. The results are in agreement with the data available on the Fe and Ni content of the HED meteorites and can be used as a reference frame in future studies of the data from the Dawn mission and of the HED meteorites. Our model cannot yet provide an answer to the fate of the missing non-carbonaceous contaminants, but we discuss possible reasons for this discrepancy.

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