arXiv subjects

F. Colas

Publications and source records attributed to F. Colas.

At least 37 records · Page 2Linked to original sources

arXiv2020

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

Asteroid (31) Euphrosyne is one of the biggest objects in the asteroid main belt and the Euphrosyne family occupies a highly inclined region in the outer main belt and contains a remarkably large number of members, which is interpreted as an outcome of a disruptive cratering event. The goals of this adaptive-optics imaging study were threefold: to characterize the shape of Euphrosyne, to constrain its density, and to search for the large craters that may be associated with the family formation event. We obtained disk-resolved images of Euphrosyne using SPHERE/ZIMPOL at ESO's 8.2-m VLT as part of our large program (ID: 199.C-0074, PI: Vernazza). We reconstructed its 3D-shape using the adam shape modeling algorithm based on the SPHERE images and the available lightcurves of this asteroid. We analyzed the dynamics of the satellite with the genoid meta-heuristic algorithm. Finally, we studied the shape of Euphrosyne using hydrostatic equilibrium models. Our SPHERE observations show that Euphrosyne has a nearly spherical shape with the sphericity index of 0.9888 and its surface lacks large impact craters. Euphrosyne's diameter is 268+/-6 km, making it one of the top 10 largest main belt asteroids. We detected a satellite of Euphrosyne -- S/2019 (31) 1-- that is about 4 km across, on an circular orbit. The mass determined from the orbit of the satellite together with the volume computed from the shape model imply a density of 1665+/-242 kg/m^3, suggesting that Euphrosyne probably contain a large fraction of water ice in its interior. We find that the spherical shape of Euphrosyne is a result of the reaccumulation process following the impact, as in the case of (10) Hygiea. However, our shape analysis reveals that, contrary to Hygiea, the axis ratios of Euphrosyne significantly differ from the ones suggested by fluid hydrostatic equilibrium following reaccumulation.

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arXiv2020

The size, shape, density and ring of the dwarf planet Haumea from a stellar occultation

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-$σ$ limits), respectively, is detected.

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arXiv2020

The large Trans-Neptunian Object 2002 TC$_{302}$ from combined stellar occultation, photometry and astrometry data

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.

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arXiv2020

A Case Study of the May 30th, 2017 Italian Fireball

On May 30th, 2017 at about 21h 09m 17s UTC a green bright fireball crossed the sky of north-eastern Italy. The fireball path was observed from some all-sky cameras starting from a mean altitude of $81.1 \pm 0.2$ km (Lat. $44.369^{\circ} \pm 0.002^{\circ}$ N; Long. $11.859^{\circ} \pm 0.002^{\circ}$ E) and extinct at $23.3 \pm 0.2$ km (Lat. $45.246^{\circ} \pm 0.002^{\circ}$ N; Long. $12.046^{\circ} \pm 0.002^{\circ}$ E), between the Italian cities of Venice and Padua. In this paper, on the basis of simple physical models, we will compute the atmospheric trajectory, analize the meteoroid atmospheric dynamics, the dark flight phase (with the strewn field) and compute the best heliocentric orbit of the progenitor body. Search for meteorites on the ground has not produced any results so far.

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arXiv2019

Saturn atmospheric dynamics one year after Cassini: Long-lived features and time variations in the drift of the Hexagon

We examine Saturn's atmosphere with observations from ground-based telescopes and Hubble Space Telescope (HST). We present a detailed analysis of observations acquired during 2018. A system of polar storms that appeared in the planet in March 2018 and remained active with a complex phenomenology at least until Sept. is analyzed elsewhere (Sanchez-Lavega et al., in press , 2019). Many of the cloud features in 2018 are long-lived and can be identified in images in 2017, and in some cases, for up to a decade using also Cassini ISS images. Without considering the polar storms, the most interesting long-lived cloud systems are: i) A bright spot in the EZ that can be tracked continuously since 2014 with a zonal velocity of 444 m/s in 2014 and 452 m/s in 2018. This velocity is different from the zonal winds at the cloud level at its latitude during the Cassini mission, and is closer to zonal winds obtained at the time of the Voyager flybys and zonal winds from Cassini VIMS infrared images of the lower atmosphere. ii) A large Anticyclone Vortex, here AV, that formed after the GWS of 2010-2011. This vortex has changed significantly in visual contrast, drift rate and latitude with minor changes in size over the last years. iii) A system of subpolar vortices present at least since 2011. These vortices follow drift rates consistent with zonal winds obtained by Cassini. We also present the positions of the vertices of the North polar hexagon from 2015 to 2018 compared with previous analyses during Cassini (2007-2014), observations with HST, and Voyager data in 1980-1981 to explore the long-term hexagon's drift rate. Variations in the drift rate cannot be fit by seasonal changes. Instead, the different drift rates reinforce the role of the North Polar Spot that was present in the Voyager epoch to cause a faster drift rate of the hexagon at that time compared with the current one.

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arXiv2019

A new non-convex model of the binary asteroid (809) Lundia obtained with the SAGE modelling technique

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 - $λ=122^{\circ}$, $β=22^{\circ}$, $σ=\pm5^{\circ}$ - 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.

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arXiv2019

Precise determination of stellar parameters of the ZZ Ceti and DAZ white dwarf GD 133 through asteroseismology

An increasing number of white dwarf stars show atmospheric chemical composition polluted by heavy elements accreted from debris disk material. The existence of such debris disks strongly suggests the presence of one or more planet(s) whose gravitational interaction with rocky planetesimals is responsible for their disruption by tidal effect. The ZZ Ceti pulsator and polluted DAZ white dwarf GD 133 is a good candidate for searching for such a potential planet. We started in 2011 a photometric follow-up of its pulsations. As a result of this work in progress, we used the data gathered from 2011 to 2015 to make an asteroseismological analysis of GD 133, providing the star parameters from a best fit model with $M$/$M_{\odot}$ = 0.630 $\pm$ 0.002, $T_{\rm eff}$ = 12400 K $\pm$ 70 K, log($M_{\rm He}/M$) = -2.00 $\pm$ 0.02, log($M_{\rm H}/M$) = -4.50 $\pm$ 0.02 and determining a rotation period of $\approx$ 7 days.

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arXiv2019

Pluto's lower atmosphere and pressure evolution from ground-based stellar occultations, 1988-2016

Context. Pluto's tenuous nitrogen (N2) atmosphere undergoes strong seasonal effects due to high obliquity and orbital eccentricity, and has been recently (July 2015) observed by the New Horizons spacecraft. Goals are (i) construct a well calibrated record of the seasonal evolution of surface pressure on Pluto and (ii) constrain the structure of the lower atmosphere using a central flash observed in 2015. Method: eleven stellar occultations by Pluto observed between 2002 and 2016 are used to retrieve atmospheric profiles (density, pressure, temperature) between $\sim$5 km and $\sim$380 km altitude levels (i.e. pressures from about 10 microbar to 10 nanobar). Results: (i) Pressure has suffered a monotonic increase from 1988 to 2016, that is compared to a seasonal volatile transport model, from which tight constraints on a combination of albedo and emissivity of N2 ice are derived; (ii) A central flash observed on 2015 June 29 is consistent with New Horizons REX profiles, provided that (a) large diurnal temperature variations (not expected by current models) occur over Sputnik Planitia and/or (b) hazes with tangential optical depth of about 0.3 are present at 4-7 km altitude levels and/or (c) the nominal REX density values are overestimated by an implausibly large factor of about 20% and/or (d) higher terrains block part of the flash in the Charon facing hemisphere.

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arXiv2019

The shape of (7) Iris as evidence of an ancient large impact?

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 $ρ$=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.

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arXiv2019

Closing the gap between Earth-based and interplanetary mission observations: Vesta seen by VLT/SPHERE

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.

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arXiv2019

Asteroid pairs: a complex picture

We studied 93 asteroid pairs. We estimated times elapsed since separation of pair members that are between 7*10^3 and a few 10^6 yr. We derived the rotation periods for all the primaries and a sample of secondaries. We derived the absolute magnitude differences of the asteroid pairs that provide their mass ratios. We refined their WISE geometric albedos and estimated their taxonomic classifications. For 17 pairs, we determined their pole positions. In 2 pairs where we obtained the spin poles for both components, we saw the same sense of rotation for both components and constrained the angles between their original spin vectors at the time of their separation. We found that the primaries of 13 pairs are actually binary or triple systems, i.e., they have one or two bound secondaries (satellites). As by-product, we found 3 new young asteroid clusters (each of them consisting of three known asteroids on highly similar orbits). We compared the obtained asteroid pair data with theoretical predictions and discussed their implications. We found that 86 of the 93 studied pairs follow the trend of primary rotation period vs mass ratio that was found by Pravec et al. (2010). Of the 7 outliers, 3 appear insignificant (may be due to our uncertain or incomplete knowledge), but 4 are high mass ratio pairs that were unpredicted by the theory of asteroid pair formation by rotational fission. We discuss a (remotely) possible way that they could be created by rotational fission of flattened parent bodies followed by re-shaping of the formed components. The 13 pairs with binary primaries are particularly interesting systems that place important constraints on formation and evolution of asteroid pairs. We present two hypotheses for their formation: The pairs having both bound and unbound secondaries could be `failed asteroid clusters', or they could be formed by a cascade primary spin fission process.

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arXiv2019

The homogeneous internal structure of CM-like asteroid (41) Daphne

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 σ). 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.

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arXiv2018

(16) Psyche: A mesosiderite-like asteroid?

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

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arXiv2018

(121514) 1999 UJ7: A primitive, slow-rotating Martian Trojan

Aims. The goal of this investigation is to determine the origin and surface composition of the asteroid (121514) 1999 UJ7, the only currently known L4 Martian Trojan asteroid. Methods. We have obtained visible reflectance spectra and photometry of 1999 UJ7 and compared the spectroscopic results with the spectra of a number of taxonomic classes and subclasses. A light curve was obtained and analysed to determine the asteroid spin state. Results. The visible spectrum of 1999 UJ7 exhibits a negative slope in the blue region and the presence of a wide and deep absorption feature centred around ~0.65 microns. The overall morphology of the spectrum seems to suggest a C-complex taxonomy. The photometric behaviour is fairly complex. The light curve shows a primary period of 1.936 d, but this is derived using only a subset of the photometric data. The asteroid may be in a non-principal axis rotational state, but our observational coverage is insufficient to draw definitive conclusions. Conclusions. Although the observed spectral absorption is wider and deeper, this finding may be compatible with the 0.7 microns spectral feature exhibited by some Ch-type asteroids and could possibly be interpreted as diagnostic of the presence of hydrated minerals. The inferred composition of 1999 UJ7 as a primitive object can be consistent with a volatile-rich object originally accreted beyond the snow line of the solar system and subsequently evolved to reach the inner regions of the solar system.

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arXiv2018

Photometry of asteroids (5141), (43032), (85953), (259221), and (363599) observed at Pic du Midi Observatory

These are the first results of an observational program devoted to the complete physical data of asteroids that could produce or feed meteoroid streams. Our results are based on the optical observation at Pic du Midi observatory in April 6-7, 2016 and January 17-18, 2018. We will present the light curve of asteroid (259221) 2003 BA21, associated with Daytime Sextantids (221 DSX) and November theta Aurigids (390 THA); the light curves and colors of asteroid (363599) 2004 FG11, associated with Daytime zeta Perseids (172 ZPE) as well as g-r and g-i; and the corresponding reflectances for the (85953) 1999 FK21, associated with Daytime eta Sagittariids (100 XSA). We will also present the colors for two additional objects, namely, (5141) Tachibana and (43032) 1999 VR26.

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arXiv2018

Probing the use of spectroscopy to determine the meteoritic analogues of meteors

Determining the source regions of meteorites is one of the major goals of current research in planetary science. Whereas asteroid observations are currently unable to pinpoint the source regions of most meteorite classes, observations of meteors with camera networks and the subsequent recovery of the meteorite may help make progress on this question. The main caveat of such an approach, however, is that the recovery rate of meteorite falls is low, implying that the meteoritic analogues of at least 80% of the observed falls remain unknown. Aims: Spectroscopic observations of bolides may have the potential to mitigate this problem by classifying the incoming material. Methods: To probe the use of spectroscopy to determine the meteoritic analogues of bolides, we collected emission spectra in the visible range (320-880nm) of five meteorite types (H,L,LL,CM,eucrite) acquired in atmospheric entry-like conditions in a plasma wind tunnel at the University of Stuttgart (Germany). A detailed spectral analysis including line identification and mass ratio determinations (Mg/Fe,Na/Fe) was subsequently performed on all spectra. Results: Spectroscopy, via a simple line identification, allows us to distinguish the main meteorite classes (chondrites, achondrites and irons) but does not have the potential to distinguish for example an H from a CM chondrite. Conclusions: The source location within the main belt of the different meteorite classes (H, L, LL, CM, etc.) should continue to be investigated via fireball observation networks. Spectroscopy of incoming bolides only marginally helps precisely classify the incoming material (iron meteorites only). To reach a statistically significant sample of recovered meteorites along with accurate orbits (>100) within a reasonable time frame (10-20 years), the optimal solution may be the spatial extension of existing fireball observation networks.

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arXiv2017

Neptune long-lived atmospheric features in 2013-2015 from small (28-cm) to large (10-m) telescopes

Since 2013, observations of Neptune with small telescopes have resulted in several detections of long-lived bright atmospheric features that have also been observed by large telescopes such as Keck II or Hubble. The combination of both types of images allows the study of the long term evolution of major cloud systems in the planet. In 2013 and 2014 two bright features were present on the planet at southern mid latitudes. These may have merged in late 2014, possibly leading to the formation of a single bright feature observed during 2015 at the same latitude. This cloud system was first observed in January 2015 and nearly continuously from July to December 2015 in observations with telescopes in the 2 to 10 meter class and in images from amateur astronomers. These images show the bright spot as a compact feature at 40.1 deg South planetographic latitude well resolved from a nearby bright zonal band that extended from 42 deg South to 20 deg South. Tracking its motion from July to November 2015 suggests a longitudinal oscillation of 16 deg in amplitude with a 90 day period, typical of dark spots on Neptune and similar to the Great Red Spot oscillation in Jupiter. The limited time covered by high-resolution observations only covers one full oscillation and other interpretations of the changing motions could be possible. HST images in September 2015 show the presence of a dark spot at short wavelengths in the southern flank of the bright cloud observed throughout 2015.

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arXiv2017

The structure of Chariklo's rings from stellar occultations

Two narrow and dense rings (called C1R and C2R) were discovered around the Centaur object (10199) Chariklo during a stellar occultation observed on 2013 June 3. Following this discovery, we planned observations of several occultations by Chariklo's system in order to better characterize the physical properties of the ring and main body. Here, we use 12 successful occulations by Chariklo observed between 2014 and 2016. They provide ring profiles (physical width, opacity, edge structure) and constraints on the radii and pole position. Our new observations are currently consistent with the circular ring solution and pole position, to within the $\pm 3.3$ km formal uncertainty for the ring radii derived by Braga-Ribas et al. The six resolved C1R profiles reveal significant width variations from $\sim 5$ to 7.5 km. The width of the fainter ring C2R is less constrained, and may vary between 0.1 and 1 km. The inner and outer edges of C1R are consistent with infinitely sharp boundaries, with typical upper limits of one kilometer for the transition zone between the ring and empty space. No constraint on the sharpness of C2R's edges is available. A 1$σ$ upper limit of $\sim 20$ m is derived for the equivalent width of narrow (physical width <4 km) rings up to distances of 12,000 km, counted in the ring plane.

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