Electrostatic dust transport on Eros: 3-D simulations of pond formation

NEAR-Shoemaker spacecraft images of the surface of the near-Earth Asteroid 433 Eros reveal that more than 200 craters on Eros are partially filled with smooth deposits, termed ponds [Veverka, J., and 32 colleagues, 2001a. Science 292, 484-488]. These ponds appear smooth even at a high resolution of 1.2 cm/pixel and spectral analysis suggests that they may be made up of particles ?50 μm in size [Robinson, M.S., Thomas, P.C., Veverka, J., Murchie, S., Carcish, B., 2001. Nature 413, 396-400; Riner, M.A., Eckart, J.M., Gigilio, J.G., Robinson, M.S., 2006. Lunar Planet. Sci. XXXVII. Abstract 2291]. Coupled with the concentration of ponds at low latitudes, the possible small particle size suggests that these deposits might be related to electrostatic transport of dust near the local terminator [Robinson, M.S., Thomas, P.C., Veverka, J., Murchie, S., Carcish, B., 2001. Nature 413, 396-400]. The work presented here incorporates the precise lighting geometry within a crater at a specified latitude into two models for electrostatic transport of dust grains in order to explore dust deposition and pond formation via this mechanism, particularly as a function of latitude. We find that micrometer-sized dust particles are preferentially transported into craters at latitudes where solar illumination angles are often low. In addition we find that if particles are electrostatically lifted off the surface they are preferentially transported into topographic depressions independent of whether the particles undergo stable levitation. The primary limiting factor for our model is uncertainty concerning the dust launching mechanism. Despite that, and though it does not match the observed north-south asymmetry in pond distribution, our model demonstrates potential for good general agreement between future predictions of pond formation via electrostatic transport of dust and observations of pond locations on the surface of Eros.     

Dust transport near electron beam impact and shadow boundaries

When the moon enters the plasma sheet of the earth, high energy electron fluxes are incident upon the lunar surface. Some regions are in the shadow of these fluxes due to topographic features. Large electric fields were found at similar shadow boundaries created by the electron beams incident upon an obstacle in the laboratory. Potentials on the beam-illuminated surface follow beam energies and were negative relative to potentials on the shadowed surface. Charged dust particles in the beam-illuminated region were observed to move into the shadow due to these electric fields. The oblique incidence of the electron fluxes upon craters can lead to a portion of the crater surface in the beam-illumination and another portion in the shadow. Dust particles on the slopes of the craters can thus experience large electric fields and transport downhill to fill the bottom of the craters. This mechanism may contribute to the formation of dust ponds observed by the NEAR-Shoemaker spacecraft at Eros, and might be at work on the lunar surface as well. In the laboratory, we used electron fluxes with energies up to 90 eV to bombard an insulating half-pipe. An angle of incidence was chosen so that the impact occurred on farside of the slope and left the bottom and the nearside slope in the shadow. Dust particles on the beam-illuminated slope moved down along the surface toward the bottom of the half-pipe and hopped to the bottom as well, while particles on the shadowed slope remained at rest.     

Regolith transport in craters on Eros

Images of Eros from the NEAR Shoemaker spacecraft reveal bright and dark albedo features on steep crater walls unlike markings previously observed on asteroids. These features have been attributed to the downslope movement of space-weathered regolith, exposing less weathered material (Science 292 (2001) 484; Meteor. Planet. Sci. 36 (2001) 1617; Icarus 155 (2002) 145). Here we present observations of the interiors of large craters (>1 km in diameter) to test this hypothesis and constrain the origin of the features. We find that bright regions in these craters correspond to steep slopes, consistent with previous work. The geographic distribution of craters with albedo variations shows no pattern and does not resemble the distribution of ponds, another phenomenon on Eros attributed to regolith movement. Shadows and other indications of topography are not observed at feature boundaries, implying that the transported layer is ?1 m thick. The presence of multiple bright and dark units on long slopes with sharp boundaries between them suggests that mobilized regolith may be halted by frictional or other effects before reaching the foot of the slope. Features on crater walls should darken at the same rate as bright ejecta deposits from crater formation; the lack of observed, morphologically fresh craters with bright interiors or ejecta suggests that the albedo patterns are younger than the most recently formed craters greater than about 100 m in diameter. Smaller or micrometeorite impacts, which would not necessarily leave evident deposits of bright ejecta, remain possible causes of albedo patterns. Although their effectiveness is difficult to assess, electrostatic processes and thermal creep are also candidates.     

Origin and flatness of ponds on asteroid 433 Eros

NEAR‐Shoemaker Multi‐Spectral Imager data reveal several hundred “ponds” on 433 Eros: smooth deposits that sharply embay the bounding depressions in which they lie, and whose spectra appear blue relative to that of the surrounding terrain. We investigate the topography of these ponds on Eros using a new shape model derived from stereophotoclinometric analysis, and validated against altimetry from the NEAR Laser Rangefinder, to constrain the mode of pond formation from three existing models. We update the locations of 55 pond candidates identified in images registered to the new shape model. We classify the flatness of these features according to the behavior of the first and second derivatives of the topography. We find that less than half of pond candidates have clearly flat floors. Based on the pond topography, we favor an external origin for the ponds' deposits. We suggest that fine dust may be transported into bounding depressions by electrostatic levitation, but may adhere to slopes, and that seismic shaking may not be sufficient to bring the deposits to an equipotential surface. Disaggregation of a central boulder should result in an obvious break in slope, such a variation is only observed in roughly half the pond candidates.     

Ponded deposits on asteroid 433 Eros

Abstract— In late January 2001 the NEAR—Shoemaker spacecraft performed low‐altitude passes over the surface of 433 Eros. Coordinated observations of the asteroid surface were obtained at submeter resolution by the NEAR laser rangefinder and the multispectral imager. This paper presents three independent, coordinated observations of a 90 m pond adjacent to a granular debris flow, including the highest resolution altimetric measurements of ponded deposits on Eros. The ponded deposits appear to have been emplaced by fluid‐like motion of dry asteroidal regolith. A simple model of seismic agitation from impacts is developed to account for pond formation on Eros. The model predicts that ponds should form readily on Eros but not on the Moon, where ponds are not observed. The model also suggests that the absence of observable ponds in the largest craters of Eros, as well as on Phobos and Deimos, may be related to regolith depth.     

Lofted charged dust distribution above the Moon surface

We developed kinetic theory for the charging processes of small dust grains near the lunar surface due to interaction with the anisotropic solar wind plasma. Once charged, these dust grains, which are exposed to the electric field in the sheath region near the lunar surface, could loft and distribute around such heights off the surface where they reach equilibrium with the local gravitational force. Analytical solutions were derived for the charging time, grain floating potential, and grain charge, characterizing the charging processes of small dust grains in a two-component and in a multi-component solar wind plasma, and further highlighting the unique features presented by the high streaming plasma velocity. We have also formulated a novel kinetic theory of sheath formation around an absorbing planar surface immersed in the anisotropic solar wind plasma in the case of a negligible photoelectric effect and presented solutions for the sheath structure. In this study we combined the results from these analyses and provided estimates for the size distribution function of dust that is expected to be lofted in regions dominated by the solar wind plasma, such as near the terminator and in nearby shadowed craters. Corresponding to the two dominant streaming velocity peaks of 300 and 800 km/s, mean dust diameters of 500 and 350 nm, respectively, are expected to be found at equilibrium at heights of relevance to exploration operations, e.g., around 1.5 m height off the lunar surface. In shadowed craters near the terminator region, where isotropic plasma should be dominating, we estimate mean lofted dust diameter of 800 nm around the same 1.5 m height off the lunar surface. The generally applicable solutions could be used to readily calculate the expected lofted size distribution near the lunar surface as a function of plasma parameters, dust grain composition, and other parameters of interest.     

Detecting crater ejecta‐blanket boundaries and constraining source crater regions for boulder tracks and elongated secondary craters on Eros

Abstract– We present results of a numerical model of the dynamics of ejecta emplacement on asteroid 433 Eros. Ejecta blocks represent the coarsest fraction of Eros’ regolith and are important, readily visible, “tracer particles” for crater ejecta‐blanket units that may be linked back to specific source craters. Model results show that the combination of irregular shape and rapid rotation of an asteroid can result in markedly asymmetric ejecta blankets (and, it follows, ejecta block spatial distribution), with locally very sharp/distinct boundaries. We mapped boulder number densities in NEAR‐Shoemaker MSI images across a portion of a predicted sharp ejecta‐blanket boundary associated with the crater Valentine and confirm a distinct and real ejecta‐blanket boundary, significant at least at the 3‐sigma level. Using our dynamical model, we “back track” the landing trajectories of three ejecta blocks with associated landing tracks in an effort to constrain potential source regions where those blocks were ejected from Eros’ surface in impact events. The observed skip distances of the blocks upon landing on Eros’ surface and the landing speeds and elevation angles derived from our model allow us to estimate the coefficient of restitution, ε, of Eros’ surface for impacts of 10‐m‐scale blocks at approximately 5 m s^?1 impact speeds. We find mean values of ε of approximately 0.09–0.18.     

A model for the formation of spokes in Saturn's ring

We suggest that spokes consist of charged micron-sized dust particles elevated from the rings by radially moving dense plasma columns created by meteor impacts on the ring. Dense plasma causes electrostatic wall-sheaths at the ring and charging of the ring with electric fields strong enough to overcome the gravitational force on small dust particles. Under “ordinary” conditions only very few dust particles will be elevated as the probability of a dust particle having at least one excess electronic charge is very low. Dense plasma raises this probability significantly. The radial motion of the plasma column is due to an azimuthal polarization electric field built up by the relative motion between the corotating plasma and the negatively charged dust particles which move with a Keplerian speed.     

Impact History of Eros: Craters and Boulders

Preliminary measurements of craters and boulders have been made in various locations on Eros from images acquired during the first nine months of NEAR Shoemaker's orbital mission, including the October 2000 low altitude flyover. (We offer some very preliminary, qualitative analysis of later LAF images and very high-resolution images obtained during NEAR's landing on 12 February 2001). Craters on Eros >100 m diameter closely resemble the saturated crater population of Ida; Eros is more heavily cratered than Gaspra but lacks the saturated giant craters of Mathilde. These craters and the other large-scale geological features were formed over a duration of very roughly 2 Gyr while Eros was in the main asteroid belt, between the time when its parent body was disrupted and Eros was injected into an Earth-approaching orbit (probably tens of Myr ago). Saturation equilibrium had been expected to shape Eros' crater population down to very small sizes, as on the lunar maria. However, craters <200 m diameter are instead progressively depleted toward smaller sizes and are a factor of ∼200 below empirical saturation at diameters of 4 m. Conversely, boulders and positive relief features (PRFs) rise rapidly in numbers (differential power-law index ∼−5) and those <10 m in size dominate the landscape at high resolutions. The pervasive boulders and minimal craters on Eros is radically different from the lunar surface at similar scales. This may be partly explained by a major depletion of meter-scale projectiles in the asteroid belt (due to the Yarkovsky Effect: Bell 2001), which thus form few small craters and destroy few boulders. Additionally, the small size and low gravity of Eros may result in redistribution or loss of ejecta due to seismic shaking, thus preferentially destroying small craters formed in such regolith. Possibly Eros has only a patchy, thin regolith of mobile fines; the smaller PRFs may then reflect exposures of fractured bedrock or piles of large ejecta blocks, which might further inhibit formation of craters <10 m in size. Eros may well have been largely detached dynamically and collisionally from the main asteroid belt for the past tens of Myr, in which case its cratering rate would have dropped by two orders of magnitude, perhaps enhancing the relative efficacy of other processes that would normally be negligible in competition with cratering. Such processes include thermal creep, electrostatic levitation and redistribution of fines, and space weathering (e.g., bombardment by micrometeorites and solar wind particles). Combined with other small-body responses to impact cratering (e.g., greater widespread distribution of bouldery ejecta), such processes may also help explain the unexpected small-scale character of geology on Eros. If there was a recent virtual hiatus in cratering of Eros (during which only craters <∼300 m diameter would be expected to have formed), space weathering may have reached maturity, thus explaining Eros' remarkable spectral homogeneity compared with Ida.     

Small-scale topography of 25143 Itokawa from the Hayabusa laser altimeter

The surface topography of Asteroid 25143 Itokawa is explored using the LIght Detection And Ranging instrument (LIDAR). The data confirm the presence of a rough highland and a smooth lowland. The highland is dominated by boulders, but also possesses topography associated with surface lineaments and broad surface facets. The boulders ensure that the roughness of the highlands over short distances is typically greater relative to most surfaces on 433 Eros. Over larger distances, Itokawa is always smoother than Eros possibly because of its smaller size and weak rubble-pile structure. The lowlands of Itokawa are very smooth, and are typically devoid of boulders. Some transitional regions midway between the highlands and lowlands also exist. In these areas, craters that retain their regolith fill possess flat floors and resemble “ponds” seen on 433 Eros. Analyses of surface elevation, imagery and a quantitative measure of surface roughness are consistent with regolith flowing downhill from the highlands to fill in the low areas of Itokawa, probably covering up any pre-existing rough terrain. Using this interpretation, we find a minimum 2.3±0.4 m thick layer of regolith in the lowlands, which, if spread evenly across the entire asteroid, corresponds to a 42±1 cm thick layer. It is very difficult to generate this amount of regolith with the population of craters seen on Itokawa. However, an Itokawa composed of several large masses may have retained this regolith during its formation. The presence of such large masses could account for the observed lineaments and what appear to be exposures of bedrock on the largest steep slope observed.     

Surveyor observations of lunar horizon-glow

Each of the Surveyor 7, 6, and 5 spacecraft observed a line of light along its western lunar horizon following local sunset. It has been suggested that this horizon-glow (HG) is sunlight, which is forward-scattered by dust grains (~ 10µ in diam, ~ 50 grains cm^?2) present in a tenuous cloud formed temporarily (? 3 h duration) just above sharp sunlight/shadow boundaries in the terminator zone. Electrically charged grains could be levitated into the cloud by intense electrostatic fields (> 500 V cm^?1) extending across the sunlight/shadow boundaries. Detailed analysis of the HG absolute luminance, temporal decay, and morphology confirm the cloud model. The levitation mechanism must eject 10⁷ more particles per unit time into the cloud than could micro meteorites. Electrostatic transport is probably the dominant local transport mechanism of lunar surface fines.     

Perpendicular flow deviation in a magnetized counter-streaming plasma

Charged dust exists in various regions in the Solar System. How this charged dust interacts with the surrounding plasma is not well understood. In this study we neglect the charging process and treat the charged dust as a fluid interacting with the ambient magnetized plasma fluid. The model reproduces the expected plasma deceleration with both positively charged and negatively charged dust, but a new effect arises. Negatively charged dust causes the magnetic field to bend in the direction of the convection electric field, while positively charged dust causes the opposite magnetic field bending. Consequently, the interaction does not only result in a perpendicular shift in the downstream current system, but also a rotation in these currents. We present quantitative results using the multi-fluid MHD code BATSRUS for both subsonic and supersonic interactions. We find that the same perpendicular bending exists for all counter-streaming interaction problems, independent of the shape of the dust cloud. The new model can be applied to plasma interaction studies including, but not limited to, charged dust particles in the solar wind, cometary plasma, the Enceladus plume, and active plasma releases, such as the Active Magnetospheric Particle Tracer Experiment (AMPTE) mission. The predicted behavior is consistent with observations at Enceladus.     

Stochastic forces in space plasmas with ion-acoustic and lower-hybrid-drift turbulence

A Langevin equation for charged particles in a plasma with electrostatic turbulence is developed from first principles and in consistency with the kinetic theory in polarization approximation. For the case of ion-acoustic and electrostatic lower-hybrid-drift turbulence approximate expressions for the space-time spectral density of the wave energy are given and estimates of the intensities of the stochastic wave forces are made. The application is done for the plasmas of the earth's magnetosphere, the solar wind and solar flares. It seems, that ion-acoustic and electrostatic lower-hybrid-drift waves can contribute to electron chaotization in different regions of the space plasma.     

Electrostatic solitons in rotating dusty plasmas with anisotropic ion pressure

The Zakharov-Kuznetsov (ZK) equation is derived for electrostatic wave in a rotating magnetoplasma with anisotropic ion pressure and in the presence of stationary charged dust particles. The anisotropic ion pressure is defined using double adiabatic Chew-Golberger-Low (CGL) theory. The reductive perturbation method is employed to study the dynamics of obliquely propagating low frequency ion acoustic wave with adiabatic ions. It is found that the ion pressure anisotropy, polarity, density of the dust particles and rotational frequency have significant effects on the formation nonlinear structures in rotating magnetized dusty plasmas. The numerical results are also presented for illustration.     

Electrostatic charging and motion of dust near the surface of an asteroid

The electrostatic charging and motion of dust near the surface of an asteroid is analyzed. It is shown that, despite the weak gravity, strong electric fields are needed to lift charged dust particles from the surface. The mechanism of generation of such fields, and the results of calculations of the motion of particles with various diameters in the electric fields near the dark side of the asteroid surface, is discussed. It is noted that the dust particle motion should be the most pronounced, as happens in the case of the Moon, in a certain neighborhood of the terminator.     

Hyperbolic cosmic dust: Its origin and its astrophysical significance

The heliocentric radial distribution of the flux of hyperbolic cosmic dust particles, as measured by the Pioneer 8 and 9 spacecraft, is closely related to the radial variation of the spatial density of source or “parent” meteoroids. Within the limits of the experimental and theoretical uncertainties the spatial density of parent meteoroids, as deduced from the hyperbolic cosmic dust data, is found to be increasing with increasing heliocentric distance in the neighborhood of one a.u. Other recent experimental evidence confirms this result. The new results also suggest that the ratio of the areal density of submicron sized craters to the areal density of millimeter sized craters will be less on the north-south faces of lunar rocks than on the east-west faces of the same rocks. The changeinratio is not as large as previously thought, however. Finally it is noted that the solar system is not presently contributing significant amounts of dust to the interstellar medium though it may once have done so.     

The geology of 433 Eros

Abstract— The global high‐resolution imaging of asteroid 433 Eros by the Near‐Earth Asteroid Rendezvous (NEAR) Shoemaker spacecraft has made it possible to develop the first comprehensive picture of the geology of a small S‐type asteroid. Eros displays a variety of surface features, and evidence of a substantial regolith. Large scale facets, grooves, and ridges indicate the presence of at least one global planar structure. Directional and superposition relations of smaller structural features suggest that fracturing has occurred throughout the object. As with other small objects, impact craters dominate the overall shape as well as the small‐scale topography of Eros. Depth/diameter ratios of craters on Eros average ～0.13, but the freshest craters approach lunar values of ～0.2. Ejecta block production from craters is highly variable; the majority of large blocks appear to have originated from one 7.6 km crater (Shoemaker). The interior morphology of craters does not reveal the influence of discrete mechanical boundaries at depth in the manner of craters formed on lunar mare regolith and on some parts of Phobos. This lack of mechanical boundaries, and the abundant evidence of regolith in nearly every high‐resolution image, suggests a gradation in the porosity and fracturing with depth. The density of small craters is deficient at sizes below ～200 m relative to predicted slopes of empirical saturation. This characteristic, which is also found on parts of Phobos and lunar highland areas, probably results from the efficient obliteration of small craters on a body with significant topographic slopes and a thick regolith. Eros displays a variety of regolith features, such as debris aprons, fine‐grained “ponded” deposits, talus cones, and bright and dark streamers on steep slopes indicative of efficient downslope movement of regolith. These processes serve to mix materials in the upper loose fragmental portion of the asteroid (regolith). In the instance of “ponded” materials and crater wall deposits, there is evidence of processes that segregate finer materials into discrete deposits. The NEAR observations have shown us that surface processes on small asteroids can be very complex and result in a wide variety of morphologic features and landforms that today seem exotic. Future missions to comets and asteroids will surely reveal still as yet unseen processes as well as give context to those discovered by the NEAR Shoemaker spacecraft.     

The effect of surface topography on the lunar photoelectron sheath and electrostatic dust transport

The dayside near-surface lunar plasma environment is electrostatically complex, due to the interaction between solar UV-induced photoemission, the collection of ambient ions and electrons, and the presence of micron and sub-micron sized dust grains. Further complicating this environment, although less well understood in effect, is the presence of surface relief, typically in the form of craters and/or boulders. It has been suggested that such non-trivial surface topography can lead to complex electrostatic potentials and fields, including “mini-wakes” behind small obstacles to the solar wind flow and “supercharging” near sunlit-shadowed boundaries (Criswell, D.R., De, B.R. [1977]. J. Geophys. Res. 82 (7); De, B.R., Criswell, D.R. [1977]. J. Geophys. Res. 82 (7); Farrell, W.M., Stubbs, T.J., Vondrak, R.R., Delory, G.T., Halekas, J.S. [2007]. Geophys. Res. Lett. 34; Wang, X., Horányi, M., Sternovsky, Z., Robertson, S., Morfill, G.E. [2007]. Geophys. Res. Lett. 34, L16104). In this paper, we present results from a three-dimensional, self-consistent, electrostatic particle-in-cell code used to model the dayside near-surface lunar plasma environment over a variety of local times with the presence of a crater. Additionally, we use the particle-in-cell model output to study the effect of surface topography on the dynamics of electrostatic dust transport, with the goal of understanding previous observations of dust dynamics on the Moon and dust ponding on various asteroids.     

Packing effect of fluffy particles

Packing forces, produced by an anisotropic sublimation of mantle material of grains located at the surface layer of loosely conglomerated fluffy particles, move the grains towards the center of the fluffy particles. This leads to a reduction of the empty space inside the fluffy particle and consequently to an increase of the mass density of the fluffy particle with time.As observed by the Helios dust experiment, fluffy particles of low density are ejected by comets with high eccentricity e and large semimajor axis a Since e and a of fluffy particles decrease with time due to the Poynting-Robertson effect, the accompanying increase of the density of fluffy particles seems to explain the existence of normal dense particles in quasi-circular orbits as detected during in situ measurements. It also explains that the majority of lunar craters have been produced by normal dense particles rather than by low density particles.     

The lunar dust environment

Each year the Moon is bombarded by about 10⁶ kg of interplanetary micrometeoroids of cometary and asteroidal origin. Most of these projectiles range from 10 nm to about 1 mm in size and impact the Moon at 10–72 km/s speed. They excavate lunar soil about 1000 times their own mass. These impacts leave a crater record on the surface from which the micrometeoroid size distribution has been deciphered. Much of the excavated mass returns to the lunar surface and blankets the lunar crust with a highly pulverized and “impact gardened” regolith of about 10 m thickness. Micron and sub-micron sized secondary particles that are ejected at speeds up to the escape speed of 2300 m/s form a perpetual dust cloud around the Moon and, upon re-impact, leave a record in the microcrater distribution. Such tenuous clouds have been observed by the Galileo spacecraft around all lunar-sized Galilean satellites at Jupiter. The highly sensitive Lunar Dust Experiment (LDEX) onboard the LADEE mission will shed new light on the lunar dust environment. LADEE is expected to be launched in early 2013.Another dust related phenomenon is the possible electrostatic mobilization of lunar dust. Images taken by the television cameras on Surveyors 5, 6, and 7 showed a distinct glow just above the lunar horizon referred to as horizon glow (HG). This light was interpreted to be forward-scattered sunlight from a cloud of dust particles above the surface near the terminator. A photometer onboard the Lunokhod-2 rover also reported excess brightness, most likely due to HG. From the lunar orbit during sunrise the Apollo astronauts reported bright streamers high above the lunar surface, which were interpreted as dust phenomena. The Lunar Ejecta and Meteorites (LEAM) Experiment was deployed on the lunar surface by the Apollo 17 astronauts in order to characterize the lunar dust environment. Instead of the expected low impact rate from interplanetary and interstellar dust, LEAM registered hundreds of signals associated with the passage of the terminator, which swamped any signature of primary impactors of interplanetary origin. It was suggested that the LEAM events are consistent with the sunrise/sunset-triggered levitation and transport of charged lunar dust particles. Currently no theoretical model explains the formation of a dust cloud above the lunar surface but recent laboratory experiments indicate that the interaction of dust on the lunar surface with solar UV and plasma is more complex than previously thought.