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This work aims at constraining the size, shape, and geometric albedo of the dwarf planet candidate 2002 MS4 through the analysis of nine stellar occultation events. Using multichord detection, we also studied the object's topography by analyzing the obtained limb and the residuals between observed chords and the best-fitted ellipse. We predicted and organized the observational campaigns of nine stellar occultations by 2002 MS4 between 2019 and 2022, resulting in two single-chord events, four double-chord detections, and three events with three to up to sixty-one positive chords. Using 13 selected chords from the 8 August 2020 event, we determined the global elliptical limb of 2002 MS4. The best-fitted ellipse, combined with the object's rotational information from the literature, constrains the object's size, shape, and albedo. Additionally, we developed a new method to characterize topography features on the object's limb. The global limb has a semi-major axis of 412 $\pm$ 10 km, a semi-minor axis of 385 $\pm$ 17 km, and the position angle of the minor axis is 121 $^\circ$ $\pm$ 16$^\circ$. From this instantaneous limb, we obtained 2002 MS4's geometric albedo and the projected area-equivalent diameter. Significant deviations from the fitted ellipse in the northernmost limb are detected from multiple sites highlighting three distinct topographic features: one 11 km depth depression followed by a 25$^{+4}_{-5}$ km height elevation next to a crater-like depression with an extension of 322 $\pm$ 39 km and 45.1 $\pm$ 1.5 km deep. Our results present an object that is $\approx$138 km smaller in diameter than derived from thermal data, possibly indicating the presence of a so-far unknown satellite. However, within the error bars, the geometric albedo in the V-band agrees with the results published in the literature, even with the radiometric-derived albedo.

Didymos and Dimorphos are primary and secondary, respectively, asteroids who compose a binary system that make up the set of Near Earth Asteroids (NEAs). They are targets of the Double Asteroid Redirection Test (DART), the first test mission dedicated to study of planetary defense, for which the main goal is to measure the changes caused after the secondary body is hit by a kinect impactor. The present work intends to conduct a study, through numerical integrations, on the dynamics of massless particles distributed in the vicinity of the two bodies. An approximate shape for the primary body was considered as a model of mass concentrations (mascons) and the secondary was considered as a massive point. Our results show the location and size of stable regions, and also their lifetime.

A stellar occultation occurs when a Solar System object passes in front of a star for an observer. This technique allows the determination of sizes and shapes of the occulting body with kilometer precision. Also, this technique constrains the occulting body's positions, albedos, densities, etc. In the context of the Galilean moons, these events can provide their best ground-based astrometry, with uncertainties in the order of 1 mas ($\sim$ 3 km at Jupiter's distance during opposition). We organized campaigns and successfully observed a stellar occultation by Io (JI) in 2021, one by Ganymede (JIII) in 2020, and one by Europa (JII) in 2019, with stations in North and South America. Also, we re-analyzed two previously published events, one by Europa in 2016 and another by Ganymede in 2017. Then, we fit the known 3D shape of the occulting satellite and determine its center of figure. That resulted in astrometric positions with uncertainties in the milliarcsecond level. The positions obtained from these stellar occultations can be used together with dynamical models to ensure highly accurate orbits of the Galilean moons. These orbits can help plan future space probes aiming at the Jovian system, such as JUICE by ESA and Europa Clipper by NASA, and allow more efficient planning of flyby maneuvers., Comment: 19 pages, 25 figures, Accepted on March 14, 2022 for publication in The Astronomical Journal

The dynamical evolution of the Prometheus and Pandora pair of satellites is chaotic, with a short 3.3 years Lyapunov time. It is known that the anti-alignment of the apses line of Prometheus and Pandora, which occurs every 6.2 years, is a critical configuration that amplifies their chaotic dynamical evolution. However, the mutual interaction between Prometheus and Pandora is not enough to explain the longitudinal lags observed by the Hubble Space Telescope. The main goal of the current work is to identify the main contributors to the chaotic dynamical evolution of the Prometheus-Pandora pair beyond themselves. Therefore, in this work, we first explore the sensibility of this dynamical system to understand it numerically and then build numerical experiments to reach our goals. We identified that almost all major satellites of the Saturn system play a significant role in the evolution of Prometheus' and Pandora's orbits., Comment: 8 pages, 6 figures

The Centaur (10199) Chariklo has the first rings system discovered around a small object. It was first observed using stellar occultation in 2013. Stellar occultations allow the determination of sizes and shapes with kilometre accuracy and obtain characteristics of the occulting object and its vicinity. Using stellar occultations observed between 2017 and 2020, we aim at constraining Chariklo's and its rings physical parameters. We also determine the rings' structure, and obtain precise astrometrical positions of Chariklo. We predicted and organised several observational campaigns of stellar occultations by Chariklo. Occultation light curves were measured from the data sets, from which ingress and egress times, and rings' width and opacity were obtained. These measurements, combined with results from previous works, allow us to obtain significant constraints on Chariklo's shape and rings' structure. We characterise Chariklo's ring system (C1R and C2R), and obtain radii and pole orientations that are consistent with, but more accurate than, results from previous occultations. We confirmed the detection of W-shaped structures within C1R and an evident variation of radial width. The observed width ranges between 4.8 and 9.1 km with a mean value of 6.5 km. One dual observation (visible and red) does not reveal any differences in the C1R opacity profiles, indicating ring particle's size larger than a few microns. The C1R ring eccentricity is found to be smaller than 0.022 (3-sigma), and its width variations may indicate an eccentricity higher than 0.005. We fit a tri-axial shape to Chariklo's detections over eleven occultations and determine that Chariklo is consistent with an ellipsoid with semi-axes of 143.8, 135.2 and 99.1 km. Ultimately, we provided seven astrometric positions at a milliarcseconds accuracy level, based on Gaia EDR3, and use it to improve Chariklo's ephemeris., Comment: 32 pages, 11 Figures in the main text, paper was accepted for publication in Section 10. Planets and planetary systems of Astronomy and Astrophysics on 12/07/2021

In this work, we study the dynamics of particles around Bennu. The goal is to understand the stability, evolution, and final outcome of the simulated particles around the asteroid. According to the results, the particle sizes can be divided into two main groups depending on their behavior. Particles smaller than a centimeter are quickly removed from the system by solar radiation pressure, while the dynamics of particles larger than a few centimeters is dominated by the gravitational field of Bennu. Because of its shape and spin period, Bennu has eight equilibrium points around it. The structure of the phase space near its equatorial surface is directly connected to these equilibrium points. Therefore, we performed numerical simulations to obtain information about the orbital evolution near the equilibrium points. The results show that most of the particles larger than a few centimeters fall in the equatorial region close to the Kingfisher area or close to the region diametrically opposite to it. In contrast, almost none of these particles fall in the equatorial region close to the Osprey area. In addition, we also performed computational experiments considering a spherical cloud of particles initially orbiting Bennu. Most of the particles in prograde orbits fall on the surface within our integration period, which was limited to 1.14 years. The particles preferentially fall near high-altitude regions at low equatorial latitudes and close to the north pole. The mid-latitudes are those more depleted of falls, as in the Nightingale and Sandpiper areas., Comment: 33 pages, 13 figures and 4 tables. Accepted for publication by "Exploration of the Activity of Asteroid (101955) Bennu", a special edition of the Journal of Geophysical Research: Planets. Simulation codes available on https://github.com/a-amarante. Animated movies of simulation results available from https://www.youtube.com/playlist?list=PLepZc10dZiUouELKD7w-3eZ4XOspuVgnm

Trans-Neptunian objects (TNOs) and Centaurs are remnants of our planetary system formation, and their physical properties have invaluable information for evolutionary theories. Stellar occultation is a ground-based method for studying these small bodies and has presented exciting results. These observations can provide precise profiles of the involved body, allowing an accurate determination of its size and shape. The goal is to show that even single-chord detections of TNOs allow us to measure their milliarcsecond astrometric positions in the reference frame of the Gaia second data release (DR2). Accurated ephemerides can then be generated, allowing predictions of stellar occultations with much higher reliability. We analyzed data from stellar occultations to obtain astrometric positions of the involved bodies. The events published before the Gaia era were updated so that the Gaia DR2 catalog is the reference. Previously determined sizes were used to calculate the position of the object center and its corresponding error with respect to the detected chord and the International Celestial Reference System (ICRS) propagated Gaia DR2 star position. We derive 37 precise astrometric positions for 19 TNOs and 4 Centaurs. Twenty-one of these events are presented here for the first time. Although about 68\% of our results are based on single-chord detection, most have intrinsic precision at the submilliarcsecond level. Lower limits on the diameter and shape constraints for a few bodies are also presented as valuable byproducts. Using the Gaia DR2 catalog, we show that even a single detection of a stellar occultation allows improving the object ephemeris significantly, which in turn enables predicting a future stellar occultation with high accuracy. Observational campaigns can be efficiently organized with this help, and may provide a full physical characterization of the involved object., Comment: 16 pages, 28 figures. The manuscript was accepted and is to be published

The (153591) 2001 SN263 asteroid system, target of the first Brazilian interplanetary space mission, is one of the known three triple systems within the population of NEAs. One of the mission objectives is to collect data about the formation of this system. The analysis of these data will help in the investigation of the physical and dynamical structures of the components (Alpha, Beta and Gamma) of this system, in order to find vestiges related to its origin. In this work, we assume the irregular shape of the 2001 SN263 system components as uniform density polyhedra and computationally investigate the gravitational field generated by these bodies. The goal is to explore the dynamical characteristics of the surface and environment around each component. Then, taking into account the rotational speed, we analyze their topographic features through the quantities geometric altitude, tilt, geopotential, slope, surface accelerations, among others. Additionally, the investigation of the environment around the bodies made it possible to construct zero-velocity curves, which delimit the location of equilibrium points. The Alpha component has a peculiar number of 12 equilibrium points, all of them located very close to its surface. In the cases of Beta and Gamma, we found four equilibrium points not so close to their surfaces. Then, performing numerical experiments around their equilibrium points, we identified the location and size of just one stable region, which is associated with an equilibrium point around Beta. Finally, we integrated a spherical cloud of particles around Alpha and identified the location on the surface of Alpha were the particles have fallen., Comment: 22 pages, 16 figures

Radar observations show that (16) Psyche is one of the largest and most massive asteroids of the M-class located in the main belt, with a diameter of approximately 230 km. This fact makes Psyche a unique object since observations indicated an iron-nickel composition. It is believed that this body may be what was left of a metal core of an early planet that would have been fragmented over millions of years due to violent collisions. In this work we study a variety of dynamical aspects related to the surface, as well as, the environment around this asteroid. We use computational tools to explore the gravitational field generated by this body, assuming constant values for its density and rotation period. We then determine a set of physical and dynamical characteristics over its entire surface. The results include the geometric altitude, geopotential altitude, tilt, slope, among others. We also explore the neighborhood around the asteroid (16) Psyche, so that the location and linear stability of the equilibrium points were found. We found four external equilibrium points, two of them linearly stable. We confirmed the stability of these points by performing numerical simulations of massless particles around the asteroid, which also showed an asymmetry in the size of the stable regions. In addition, we integrate a cloud of particles in the vicinity of (16) Psyche in order to verify in which regions of its surface the particles are most likely to collide., Comment: 19 pages

In this paper, we present the cosmological scenario obtained from $f(R,T)$ gravity by using an exponential dependence on the trace of the energy-momentum tensor. With a numerical approach applied to the equations of motion, we show several precise fits and the respective cosmological consequences. As a matter of completeness, we also analyzed cosmological scenarios where this new version of $f(R,T)$ is coupled with a real scalar field. In order to find analytical cosmological parameters, we used a slow-roll approximation for the evolution of the scalar field. This approximation allowed us to derived the Hubble and the deceleration parameters whose time evolutions describe the actual phase of accelerated expansion, and corroborate with our numerical investigations. Therefore, the analytical parameters unveil the viability of this proposal for $f(R,T)$ in the presence of an inflaton field., Comment: 7 pages, 9 figures

Progress in astrometry and orbital modelling of planetary moons in the last decade enabled better determinations of their orbits. These studies need accurate positions spread over extended periods. We present the results of the 2014-2015 Brazilian campaign for 40 mutual events from 47 observed light curves by the Galilean satellites plus one eclipse of Amalthea by Ganymede. We also reanalysed and updated results for 25 mutual events observed in the 2009 campaign. All telescopes were equipped with narrow-band filters centred at 889 nm with a width of 15 nm to eliminate the scattered light from Jupiter. The albedos' ratio was determined using images before and after each event. We simulated images of moons, umbra, and penumbra in the sky plane, and integrated their fluxes to compute albedos, simulate light curves and fit them to the observed ones using a chi-square fitting procedure. For that, we used the complete version of the Oren-Nayer reflectance model. The relative satellite positions mean uncertainty was 11.2 mas ($\sim$35 km) and 10.1 mas ($\sim$31 km) for the 2014-2015 and 2009 campaigns respectively. The simulated and observed \textsc{ascii} light curve files are freely available in electronic form at the \textit{Natural Satellites DataBase} (NSDB). The 40/25 mutual events from our 2014-2015/2009 campaigns represent a significant contribution of 17%/15% in comparison with the PHEMU campaigns lead by the IMCCE. Besides that, our result for the eclipse of Amalthea is only the 4$^{th}$ such measurement ever published after the three ones observed by the 2014-2015 international PHEMU campaign. Our results are suitable for new orbital/ephemeris determinations for the Galilean moons and Amalthea., Comment: 14 pages, 8 figures and 5 tables

We present results from three world-wide campaigns that resulted in the detections of two single-chord and one multi-chord stellar occultations by the Plutino object (84922) 2003~VS$_2$. From the single-chord occultations in 2013 and 2014 we obtained accurate astrometric positions for the object, while from the multi-chord occultation on November 7th, 2014, we obtained the parameters of the best-fitting ellipse to the limb of the body at the time of occultation. We also obtained short-term photometry data for the body in order to derive its rotational phase during the occultation. The rotational light curve present a peak-to-peak amplitude of 0.141 $\pm$ 0.009 mag. This allows us to reconstruct the three-dimensional shape of the body, with principal semi-axes $a = 313.8 \pm 7.1$ km, $b = 265.5^{+8.8}_{-9.8}$ km, and $c = 247.3^{+26.6}_{-43.6}$ km, which is not consistent with a Jacobi triaxial equilibrium figure. The derived spherical volume equivalent diameter of $548.3 ^{+29.5}_{-44.6}$ km is about 5\% larger than the radiometric diameter of 2003~VS$_2$ derived from Herschel data of $523 \pm 35$ km, but still compatible with it within error bars. From those results we can also derive the geometric albedo ($0.123 ^{+0.015}_{-0.014}$) and, under the assumption that the object is a Maclaurin spheroid, the density $\rho = 1400^{+1000}_{-300}$ for the plutino. The disappearances and reappearances of the star during the occultations do not show any compelling evidence for a global atmosphere considering a pressure upper limit of about 1 microbar for a pure nitrogen atmosphere, nor secondary features (e.g. rings or satellite) around the main body., Comment: 22 pages, 14 figures, 1 appendix

Context. Bright stellar positions are now known with an uncertainty below 1 mas thanks to Gaia DR2. Between 2019-2020, the Galactic plane will be the background of Jupiter. The dense stellar background will lead to an increase in the number of occultations, while the Gaia DR2 catalogue will reduce the prediction uncertainties for the shadow path. Aims. We observed a stellar occultation by the Galilean moon Europa (J2) and propose a campaign for observing stellar occultations for all Galilean moons. Methods. During a predicted period of time, we measured the light flux of the occulted star and the object to determine the time when the flux dropped with respect to one or more reference stars, and the time that it rose again for each observational station. The chords obtained from these observations allowed us to determine apparent sizes, oblatness, and positions with kilometre accuracy. Results. We present results obtained from the first stellar occultation by the Galilean moon Europa observed on 2017 March 31. The apparent fitted ellipse presents an equivalent radius of 1561.2 $\pm$ 3.6 km and oblatenesses 0.0010 $\pm$ 0.0028. A very precise Europa position was determined with an uncertainty of 0.8 mas. We also present prospects for a campaign to observe the future events that will occur between 2019 and 2021 for all Galilean moons. Conclusions. Stellar occultation is a suitable technique for obtaining physical parameters and highly accurate positions of bright satellites close to their primary. A number of successful events can render the 3D shapes of the Galilean moons with high accuracy. We encourage the observational community (amateurs included) to observe the future predicted events., Comment: 10 pages, 16 figures, 4 tables, A&A Letter doi:10.1051/0004-6361/201935500

The technique of mutual approximations accurately gives the central instant at the maximum apparent approximation of two moving natural satellites in the sky plane. This can be used in ephemeris fitting to infer the relative positions between satellites with high precision. Only the mutual phenomena -- occultations and eclipses -- may achieve better results. However, mutual phenomena only occur every six years in the case of Jupiter. Mutual approximations do not have this restriction and can be observed at any time along the year as long as the satellites are visible. In this work, we present 104 central instants determined from the observations of 66 mutual approximations between the Galilean moons carried out at different sites in Brazil and France during the period 2016--2018. For 28 events we have at least two independent observations. All telescopes were equipped with a narrow-band filter centred at 889 nm with a width of 15 nm to eliminate the scattered light from Jupiter. The telescope apertures ranged between 25--120 cm. For comparison, the precision of the positions obtained with classical CCD astrometry is about 100 mas, for mutual phenomena it can achieve 10 mas or less and the average internal precision obtained with mutual approximations was 11.3 mas. This new kind of simple, yet accurate observations can significantly improve the orbits and ephemeris of Galilean satellites and thus be very useful for the planning of future space missions aiming at the Jovian system., Comment: 12 pages, 7 figures

In 2014, the discovery of two well-defined rings around the Centaur (10199) Chariklo were announced. This was the first time that such structures were found around a small body. In 2015, it was proposed that the Centaur (2060) Chiron may also have a ring. In a previous study, we analyzed how close encounters with giant planets would affect the rings of Chariklo. The most likely result is the survival of the rings. In the present work, we broaden our analysis to (2060) Chiron. In addition to Chariklo, Chiron is currently the only known Centaur with a presumed ring. By applying the same method as \cite{araujo2016}, we performed numerical integrations of a system composed of 729 clones of Chiron, the Sun, and the giant planets. The number of close encounters that disrupted the ring of Chiron during one half-life of the study period was computed. This number was then compared to the number of close encounters for Chariklo. We found that the probability of Chiron losing its ring due to close encounters with the giant planets is about six times higher than that for Chariklo. Our analysis showed that, unlike Chariklo, Chiron is more likely to remain in an orbit with a relatively low inclination and high eccentricity. Thus, we found that the bodies in Chiron-like orbits are less likely to retain rings than those in Chariklo-like orbits. Overall, for observational purposes, we conclude that the bigger bodies in orbits with high inclinations and low eccentricities should be prioritized., Comment: 8 pages, 3 figures, accepted for publication in MNRAS

Among the current population of the 81 known trans-Neptunian binaries (TNBs), only two are in orbits that cross the orbit of Neptune. These are (42355) Typhon-Echidna and (65489) Ceto-Phorcys. In the present work, we focused our analyses on the temporal evolution of the Typhon-Echidna binary system through the outer and inner planetary systems. Using numer- ical integrations of the N-body gravitational problem, we explored the orbital evolutions of 500 clones of Typhon, recording the close encounters of those clones with planets. We then analysed the effects of those encounters on the binary system. It was found that only 22% of the encounters with the giant planets were strong enough to disrupt the binary. This binary system has an ~3.6% probability of reaching the terrestrial planetary region over a time scale of approximately 5.4 Myr. Close encounters of Typhon-Echidna with Earth and Venus were also registered, but the probabilities of such events occurring are low (~0.4%). The orbital evolution of the system in the past was also investigated. It was found that in the last 100 Myr, Typhon might have spent most of its time as a TNB crossing the orbit of Neptune. Therefore, our study of the Typhon-Echidna orbital evolution illustrates the possibility of large cometary bodies (radii of 76 km for Typhon and 42 km for Echidna) coming from a remote region of the outer Solar System and that might enter the terrestrial planetary region preserving its binarity throughout the journey., Comment: 10 pages, 8 figures

The G ring arc hosts the smallest satellite of Saturn, Aegaeon, observed with a set of images sent by Cassini spacecraft. Along with Aegaeon, the arc particles are trapped in a 7:6 corotation eccentric resonance with the satellite Mimas. Due to this resonance, both Aegaeon and the arc material are confined to within sixty degrees of corotating longitudes. The arc particles are dust grains which can have their orbital motions severely disturbed by the solar radiation force. Our numerical simulations showed that Aegaeon is responsible for depleting the arc dust population by removing them through collisions. The solar radiation force hastens these collisions by removing most of the 10$~\mu$m sized grains in less than 40 years. Some debris released from Aegaeon's surface by meteoroid impacts can populate the arc. However, it would take 30,000 years for Aegaeon to supply the observed amount of arc material, and so it is unlikely that Aegaeon alone is the source of dust in the arc.

The Centaur population is composed by minor bodies wandering between the giant planets and that frequently perform close gravitational encounters with these planets, which leads to a chaotic orbital evolution. Recently, the discovery of two well-defined narrow rings was announced around the Centaur 10199 Chariklo. The rings are assumed to be in the equatorial plane of Chariklo and to have circular orbits. The existence a well-defined system of rings around a body in such perturbed orbital region poses an interesting new problem. Are the rings of Chariklo stable when perturbed by close gravitational encounters with the giant planets? Our approach to address this question consisted of forward and backward numerical simulations of 729 clones of Chariklo, with similar initial orbits, for a period of 100 Myrs. We found, on average, that each clone suffers along its lifetime more than 150 close encounters with the giant planets within one Hill radius of the planet in question. We identified some extreme close encounters able to significantly disrupt or to disturb the rings of Chariklo. About 3% of the clones lose the rings and about 4% of the clones have the ring significantly disturbed. Therefore, our results show that in most of the cases (more than 90%) the close encounters with the giant planets do not affect the stability of the rings in Chariklo-like systems. Thus, if there is an efficient mechanism that creates the rings, then these structures may be common among these kinds of Centaurs., Comment: 11 pages. Accepted for publication in APj

Until now, rings have been detected in the Solar System exclusively around the four giant planets. Here we report the discovery of the first minor-body ring system around the Centaur object (10199) Chariklo, a body with equivalent radius 124$\pm$9 km. A multi-chord stellar occultation revealed the presence of two dense rings around Chariklo, with widths of about 7 km and 3 km, optical depths 0.4 and 0.06, and orbital radii 391 and 405 km, respectively. The present orientation of the ring is consistent with an edge-on geometry in 2008, thus providing a simple explanation for the dimming of Chariklo's system between 1997 and 2008, and for the gradual disappearance of ice and other absorption features in its spectrum over the same period. This implies that the rings are partially composed of water ice. These rings may be the remnants of a debris disk, which were possibly confined by embedded kilometre-sized satellites.

The $\mu$ and $\nu$ rings of Uranus form a secondary ring-moon system with the satellites Puck, Mab,Portia, and Rosalind. These rings are tenuous and dominated by micrometric particles, which can be strongly disturbed by the solar radiation pressure. We performed a numerical analysis of the orbital evolution of a sample of particles under the influence of the solar radiation force and the planetary oblateness, combined with the gravitational interaction with the close satellites. The most likely result is a collisions and the deposition of particles onto the surface of these satellites. Since this mechanism tends to cause a depletion of material of the rings, we investigate additional sources for these dust particles. Adopting a rough estimative of the flux of interplanetary meteoroids, we found that the ejections from Mab could generate a ring with optical depth comparable with the observations. A similar analysis was carried out for the F-ring dust band. The damping due to the Saturn's oblateness prevents the overstated changes of the eccentricity and increases in the lifetime of the particles. Therewithal photometric study of the F-ring using Cassini images revealed that substantial secular increase in the brightness of Saturn's F ring has occurred in the last 25 years. The shapes of the phase curves from Cassini and Voyager are similar, suggesting that although the number of dust particles has increased, the overall distribution of sizes is unchanged. The dust bands that permeate the rings of Uranus were observed late in 2007 during the equinox, when the Sun crossed the ring plane. Images taken with the VLT were processed and then combined to result in long-exposure frames. For each frame, the north and south radial profiles were extracted. They will be used to develop a photometric model., Comment: PhD thesis. 159 pages. Language: Portuguese

Impacts of micrometeoroids on the surfaces of Nix and Hydra can produced dust particles and form a ring around Pluto. However, dissipative forces, such as the solar radiation pressure, can lead the particles into collisions in a very short period of time. In this work we investigate the orbital evolution of escaping ejecta under the effects of the radiation pressure force combined with the gravitational effects of Pluto,Charon, Nix and Hydra. The mass production rate from the surfaces of Nix and Hydra was obtained from analytical models. By comparing the lifetime of the survived particles, derived from our numerical simulations, and the mass of a putative ring mainly formed by the particles released from the surfaces of Nix and Hydra we could estimate the ring normal optical depth. The released particles, encompassing the orbits of Nix and Hydra, temporarily form a 16000 km wide ring. Collisions with the massive bodies, mainly due to the effects of the radiation pressure force, remove about 50% of the $1\mu$m particles in 1 year. A tenuous ring with a normal optical depth of $6 \times 10^{-11}$ can be maintained by the dust particles released from the surfaces of Nix and Hydra., Comment: This paper has been withdrawn by the author and will be replaced by an updated version