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We develop an axisymmetric diffusion model to describe radial density profiles in the vicinity of tiny moons embedded in planetary rings. Our diffusion model accounts for the gravitational scattering of the ring particles by an embedded moon and for the viscous diffusion of the ring matter back into the gap. With test particle simulations, we show that the scattering of the ring particles passing the moon is larger for small impact parameters than estimated by Goldreich & Tremaine and Namouni. This is significant for modeling the Keeler gap. We apply our model to the gaps of the moons Pan and Daphnis embedded in the outer A ring of Saturn with the aim to estimate the shear viscosity of the ring in the vicinity of the Encke and Keeler gap. In addition, we analyze whether tiny icy moons whose dimensions lie below Cassini's resolution capabilities would be able to explain the gap structure of the C ring and the Cassini division.
Airless bodies are directly exposed to ambient plasma and meteoroid fluxes, making them characteristically different from bodies whose dense atmospheres protect their surfaces from such fluxes. Direct exposure to plasma and meteoroids has important consequences for the formation and evolution of planetary surfaces, including altering chemical makeup and optical properties, generating neutral gas and/or dust exospheres, and leading to the generation of circumplanetary and interplanetary dust grain populations. In the past two decades, there have been many advancements in our understanding of airless bodies and their interaction with various dust populations. In this paper, we describe relevant dust phenomena on the surface and in the vicinity of airless bodies over a broad range of scale sizes from to , with a focus on recent developments in this field.
Saturn’s main rings are composed of >95% water ice, and the nature of the remaining few percent has remained unclear. The Cassini spacecraft’s traversals between Saturn and its innermost D ring allowed its cosmic dust analyzer (CDA) to collect material released from the main rings and to characterize the ring material infall into Saturn. We report the direct in situ detection of material from Saturn’s dense rings by the CDA impact mass spectrometer. Most detected grains are a few tens of nanometers in size and dynamically associated with the previously inferred “ring rain.” Silicate and water-ice grains were identified, in proportions that vary with latitude. Silicate grains constitute up to 30% of infalling grains, a higher percentage than the bulk silicate content of the rings.
One of the biggest successes of the Cassini mission is the detection of small moons (moonlets) embedded in Saturns rings that cause S-shaped density structures in their close vicinity, called propellers. Here, we present isothermal hydrodynamic simulations of moonlet-induced propellers in Saturn's A ring that denote a further development of the original model. We find excellent agreement between these new hydrodynamic and corresponding N-body simulations. Furthermore, the hydrodynamic simulations confirm the predicted scaling laws and the analytical solution for the density in the propeller gaps. Finally, this mean field approach allows us to simulate the pattern of the giant propeller Blériot, which is too large to be modeled by direct N-body simulations. Our results are compared to two stellar occultation observations by the Cassini Ultraviolet Imaging Spectrometer (UVIS), which intersect the propeller Blériot. Best fits to the UVIS optical depth profiles are achieved for a Hill radius of 590 m, which implies a moonlet diameter of about 860 m. Furthermore, the model favors a kinematic shear viscosity of the surrounding ring material of ν0 = 340 cm2 s−1, a dispersion velocity in the range of 0.3 cm s−1 < c0 < 1.5 cm s−1, and a fairly high bulk viscosity 7 < ξ0/ν0 < 17. These large transport values might be overestimated by our isothermal ring model and should be reviewed by an extended model including thermal fluctuations.
We summarize the current state of observations of circumplanetary dust populations, including both dilute and dense rings and tori around the giant planets, ejecta clouds engulfing airless moons, and rings around smaller planetary bodies throughout the Solar System. We also discuss the theoretical models that enable these observations to be understood in terms of the sources, sinks and transport of various dust populations. The dynamics and resulting transport of the particles can be quite complex, due to the fact that their motion is influenced by neutral and plasma drag, radiation pressure, and electromagnetic forcesall in addition to gravity. The relative importance of these forces depends on the environment, as well as the makeup and size of the particles. Possible dust sources include the generation of ejecta particles by impacts, active volcanoes and geysers, and the capture of exogenous particles. Possible dust sinks include collisions with moons, rings, or the central planet, erosion due to sublimation and sputtering, even ejection and escape from the circumplanetary environment.
One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly perturbed regions. In this article we revise the Borderies et al. model using a granular flow model to define the shear and bulk viscosities, ν and ζ, and incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model we developed for gaps in dense planetary rings. Finally, we apply our model to the Encke and Keeler division in order to estimate the shear and bulk viscosities in the vicinity of both gaps
Saturn’s main ring system is associated with a set of small moons that either are embedded within it or interact with the rings to alter their shape and composition. Five close flybys of the moons Pan, Daphnis, Atlas, Pandora, and Epimetheus were performed between December 2016 and April 2017 during the ring-grazing orbits of the Cassini mission. Data on the moons’ morphology, structure, particle environment, and composition were returned, along with images in the ultraviolet and thermal infrared. We find that the optical properties of the moons’ surfaces are determined by two competing processes: contamination by a red material formed in Saturn’s main ring system and accretion of bright icy particles or water vapor from volcanic plumes originating on the moon Enceladus.
The observation of the non-Keplerian behavior of propeller structures in Saturn's outer A ring raises the question: how does the propeller respond to the wandering of the central embedded moonlet? Here, we study numerically how the structural imprint of the propeller changes for a libration of the moonlet. It turns out that the libration induces an asymmetry in the propeller, which depends on the libration period and amplitude of the moonlet. Further, we study the dependence of the asymmetry on the libration period and amplitude for a moonlet with a 400 m Hill radius, which is located in the outer A ring. This allows us to apply our findings to the largest known propeller Blériot, which is expected to be of a similar size. For Blériot, we can conclude that, supposing the moonlet is librating with the largest observed period of 11.1 yr and an azimuthal amplitude of about 1845 km, a small asymmetry should be measurable but depends on the moonlet's libration phase at the observation time. The longitude residuals of other trans-Encke propellers (e.g., Earhart) show amplitudes similar to Blériot, which might allow us to observe larger asymmetries due to their smaller azimuthal extent, allowing us to scan the whole gap structure for asymmetries in one observation. Although the librational model of the moonlet is a simplification, our results are a first step toward the development of a consistent model for the description of the formation of asymmetric propellers caused by a freely moving moonlet.
In July 2004 the Cassini–Huygens mission reached the Saturnian system and started its orbital tour. A total of 75 orbits will be carried out during the primary mission until August 2008. In these four years Cassini crosses the ring plane 150 times and spends approx. 400 h within Titan's orbit. The Cosmic Dust Analyser (CDA) onboard Cassini characterises the dust environment with its extended E ring and embedded moons. Here, we focus on the CDA results of the first year and we present the Dust Analyser (DA) data within Titan's orbit. This paper does investigate High Rate Detector data and dust composition measurements. The authors focus on the analysis of impact rates, which were strongly variable primarily due to changes of the spacecraft pointing. An overview is given about the ring plane crossings and the DA counter measurements. The DA dust impact rates are compared with the DA boresight configuration around all ring plane crossings between June 2004 and July 2005. Dust impacts were registered at altitudes as high as 100 000 km above the ring plane at distances from Saturn between 4 and 10 Saturn radii. In those regions the dust density of particles bigger than 0.5 can reach values of 0.001m-3.
We develop a model of stochastic radiation pressure for rotating non-spherical particles and apply the model to circumplanetary dynamics of dust grains. The stochastic properties of the radiation pressure are related to the ensemble-averaged characteristics of the rotating particles, which are given in terms of the rotational time-correlation function of a grain. We investigate the model analytically and show that an ensemble of particle trajectories demonstrates a diffusion-like behaviour. The analytical results are compared with numerical simulations, performed for the motion of the dusty ejecta from Deimos in orbit around Mars. We find that the theoretical predictions are in a good agreement with the simulation results. The agreement however deteriorates at later time, when the impact of non-linear terms, neglected in the analytic approach, becomes significant. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may in case of some dusty systems noticeably alter an optical depth. (c) 2006 Elsevier Ltd. All rights reserved.
Context. Most theoretical investigations of dust charging processes in space have treated the current balance condition as independent of grain size. However, for small grains, since they are often observed in space environments, a dependence on grain size is expected owing to secondary electron emission (SEE). Here, by the term "small" we mean a particle size comparable to the typical penetration depth for given primary electron energy. The results are relevant for the dynamics of small, charged dust particles emitted by the volcanic moon Io, which forms the Jovian dust streams. Aims. We revise the theory of charging of small (submicron sized) micrometeoroids to take into account a high production of secondary electrons for small grains immersed in an isotropic flux of electrons. We apply our model to obtain an improved estimate for the charge of the dust streams leaving the Jovian system, detected by several spacecraft. Methods. We apply a continuum model to describe the penetration of primary electrons in a grain and the emission of secondary electrons along the path. Averaging over an isotropic flux of primaries, we derive a new expression for the secondary electron yield, which can be used to express the secondary electron current on a grain. Results. For the Jupiter plasma environment we derive the surface potential of grains composed of NaCl (believed to be the major constituent of Jovian dust stream particles) or silicates. For small particles, the potential depends on grain size and the secondary electron current induces a sensitivity to material properties. As a result of the small particle effect, the estimates for the charging times and for the fractional charge fluctuations of NaCl grains obtained using our general approach to SEE give results qualitatively different from the analogous estimates derived from the traditional approach to SEE. We find that for the charging environment considered in this paper field emission does not limit the charging of NaCl grains.
In this paper, the dynamical analysis of the Jovian dust originating from the four Galilean moons is presented. High-accuracy orbital integrations of dust particles are used to determine their dynamical evolution. A variety of forces are taken into account, including the Lorentz force, solar radiation pressure, Poynting-Robertson drag, solar gravity, the satellites' gravity, plasma drag, and gravitational effects due to nonsphericity of Jupiter. More than 20,000 dust particles from each source moon in the size range from 0.05 μm to 1 cm are simulated over 8000 (Earth) years until each dust grain hits a sink (moons, Jupiter, or escape from the system). Configurations of dust number density in the Jovicentric equatorial inertial frame are calculated and shown. In a Jovicentric frame rotating with the Sun the dust distributions are found to be asymmetric. For certain small particle sizes, the dust population is displaced towards the Sun, while for certain larger sizes, the dust population is displaced away from the Sun. The average lifetime as a function of particle size for ejecta from each source moon is derived, and two sharp jumps in the average lifetime are analyzed. Transport of dust between the Galilean moons and to Jupiter is investigated. Most of the orbits for dust particles from Galilean moons are prograde, while, surprisingly, a small fraction of orbits are found to become retrograde mainly due to solar radiation pressure and Lorentz force. The distribution of orbital elements is also analyzed.
We investigate the influence of the Coriolis force on mass motion related to the Rheasilvia impact on asteroid Vesta. Observations by the NASA Dawn mission revealed a pattern of curved radial ridges, which are related to Coriolis-deflected mass-wasting during the initial modification stage of the crater. Utilizing the projected curvature of the mass-wasting trajectories, we developed a method that enabled investigation of the initial mass wasting of the Rheasilvia impact by observational means. We demonstrate that the Coriolis force can strongly affect the crater formation processes on rapidly rotating objects, and we derive the material's velocities (28.9 ± 22.5 m/s), viscosities (1.5–9.0 × 106 Pa s) and coefficients of friction (0.02–0.81) during the impact modification stage. The duration of the impact modification stage could be estimated to (1.1 ± 0.5) h. By analyzing the velocity distribution with respect to the topography, we deduce that the Rheasilvia impactor hit a heterogeneous target and that the initial crater walls were significantly steeper during the modification stage.
We study the vertical extent of propeller structures in Saturn's rings (i) by extending the model of Spahn and Sremcevic (Spahn, F., Sremcevic, M. [2000]. Astron. Astrophys., 358, 368-372) to include the vertical direction and (ii) by performing N-body box simulations of a perturbing moonlet embedded into the rings. We find that the gravitational interaction of ring particles with a non-inclined moonlet does not induce considerable vertical excursions of ring particles, but causes a considerable thermal motion in the ring plane. We expect ring particle collisions to partly convert the lateral induced thermal motion into vertical excursions of ring particles in the course of a quasi-thermalization. The N-body box simulations lead to maximal propeller heights of about 0.6-0.8 Hill radii of the embedded perturbing moonlet. Moonlet sizes estimated by this relation are in good agreement with size estimates from radial propeller scalings for the propellers Bleriot and Earhart. For large propellers, the extended hydrodynamical propeller model predicts an exponential propeller height relaxation, confirmed by N-body box simulations of non-self gravitating ring particles. Exponential cooling constants, calculated from the hydrodynamical propeller model agree fairly well with values from fits to the tail of the azimuthal height decay of the N-body box simulations. From exponential cooling constants, determined from shadows cast by the propeller Earhart and imaged by the Cassini spacecraft, we estimate collision frequencies of about 6 collisions per particle per orbit in the propeller gap region and about 11 collisions per particle per orbit in the propeller wake region. (C) 2015 Elsevier Inc. All rights reserved.
Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, similar to r(-q) with q approximate to 3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75 <= q <= 3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn's rings.
Charges dropped
(2015)
It is found that for objects possessing small surface structures with differing radii of curvature the secondary electron emission (SEE) yield may be significantly higher than for objects with smooth surfaces of the same material. The effect is highly pronounced for surface structures of nanometer scale, often providing a more than 100% increase of the SEE yield. The results also show that the SEE yield from surfaces with structure does not show a universal dependence on the energy of the primary, incident electrons as it is found for flat surfaces in experiments. We derive conditions for the applicability of the conventional formulation of SEE using the simplifying assumption of universal dependence. Our analysis provides a basis for studying low-energy electron emission from nanometer structured surfaces under a penetrating electron beam important in many technological applications.
Modeling the total dust production of Enceladus from stochastic charge equilibrium and simulations
(2015)
A statistical model of fragmentation of aggregates is proposed, based on the stochastic propagation of cracks through the body. The propagation rules are formulated on a lattice and mimic two important features of the process-a crack moves against the stress gradient while dissipating energy during its growth. We perform numerical simulations of the model for two-dimensional lattice and reveal that the mass distribution for small-and intermediate-size fragments obeys a power law, F(m) proportional to m(-3/2), in agreement with experimental observations. We develop an analytical theory which explains the detected power law and demonstrate that the overall fragment mass distribution in our model agrees qualitatively with that one observed in experiments.
Giant planets helped to shape the conditions we see in the Solar System today and they account for more than 99% of the mass of the Sun's planetary system. They can be subdivided into the Ice Giants (Uranus and Neptune) and the Gas Giants (Jupiter and Saturn), which differ from each other in a number of fundamental ways. Uranus, in particular is the most challenging to our understanding of planetary formation and evolution, with its large obliquity, low self-luminosity, highly asymmetrical internal field, and puzzling internal structure. Uranus also has a rich planetary system consisting of a system of inner natural satellites and complex ring system, five major natural icy satellites, a system of irregular moons with varied dynamical histories, and a highly asymmetrical magnetosphere. Voyager 2 is the only spacecraft to have explored Uranus, with a flyby in 1986, and no mission is currently planned to this enigmatic system. However, a mission to the uranian system would open a new window on the origin and evolution of the Solar System and would provide crucial information on a wide variety of physicochemical processes in our Solar System. These have clear implications for understanding exoplanetary systems. In this paper we describe the science case for an orbital mission to Uranus with an atmospheric entry probe to sample the composition and atmospheric physics in Uranus' atmosphere. The characteristics of such an orbiter and a strawman scientific payload are described and we discuss the technical challenges for such a mission. This paper is based on a white paper submitted to the European Space Agency's call for science themes for its large-class mission programme in 2013.
The space missions Voyager and Cassini together with earthbound observations revealed a wealth of structures in Saturn's rings. There are, for example, waves being excited at ring positions which are in orbital resonance with Saturn's moons. Other structures can be assigned to embedded moons like empty gaps, moon induced wakes or S-shaped propeller features. Furthermore, irregular radial structures are observed in the range from 10 meters until kilometers. Here some of these structures will be discussed in the frame of hydrodynamical modeling of Saturn's dense rings. For this purpose we will characterize the physical properties of the ring particle ensemble by mean field quantities and point to the special behavior of the transport coefficients. We show that unperturbed rings can become unstable and how diffusion acts in the rings. Additionally, the alternative streamline formalism is introduced to describe perturbed regions of dense rings with applications to the wake damping and the dispersion relation of the density waves.
We propose a simple theoretical model for aggregative and fragmentative collisions in Saturn's dense rings. In this model the ring matter consists of a bimodal size distribution: large (meter sized) boulders and a population of smaller particles (tens of centimeters down to dust). The small particles can adhesively stick to the boulders and can be released as debris in binary collisions of their carriers. To quantify the adhesion force we use the JKR theory (Johnson, K., Kendall, K., Roberts, A. [1971]. Proc. R. Soc. Lond. A 324, 301-313). The rates of release and adsorption of particles are calculated, depending on material parameters, sizes, and plausible velocity dispersions of carriers and debris particles. In steady state we obtain an expression for the amount of free debris relative to the fraction still attached to the carriers. In terms of this conceptually simple model a paucity of subcentimeter particles in Saturn's rings (French, R.G., Nicholson, P.D. [2000]. Icarus 145, 502-523; Marouf, E. et al. [2008]. Abstracts for "Saturn after Cassini-Huygens" Symposium, Imperial College London, UK, July 28 to August 1, p. 113) can be understood as a consequence of the increasing strength of adhesion (relative to inertial forces) for decreasing particle size. In this case particles smaller than a certain critical radius remain tightly attached to the surfaces of larger boulders, even when the boulders collide at their typical speed. Furthermore, we find that already a mildly increased velocity dispersion of the carrier-particles may significantly enhance the fraction of free debris particles, in this way increasing the optical depth of the system.
We present a toy-model for an ensemble of adhering mesoscopic constituents in order to estimate the effect of the granular temperature on the sizes of embedded aggregates. The major goal is to illustrate the relation between the mean aggregate size and the granular temperature in dense planetary rings. For sake of simplicity we describe the collective behavior of the ensemble by means of equilibrium statistical mechanics, motivated by the stationary temperature established by the balance between a Kepler-shear driven viscous heating and inelastic cooling in these cosmic granular disks. The ensemble consists of N' equal constituents which can form cluster(s) or move like a gas-or both phases may coexist-depending on the (granular) temperature of the system. We assume the binding energy levels of a cluster E-c = -N-c gamma a to be determined by a certain contact number N-c, given by the configuration of N constituents of the aggregate (energy per contact: -gamma a). By applying canonical and grand-canonical ensembles, we show that the granular temperature T of a gas of constituents (their mean kinetic energy) controls the size distribution of the aggregates. They are the smaller the higher the granular temperature T is. A mere gas of single constituents is sustained for T >> gamma a. In the case of large clusters (low temperatures T << gamma a) the size distribution becomes a Poissonian.
The discovery of volcanic activity on Enceladus stands out amongst the long list of findings by the Cassini mission to Saturn. In particular the compositional analysis of Enceladus ice particles by Cassini's Cosmic Dust Analyser (CDA) (Srama et al., 2004) has proven to be a powerful technique for obtaining information about processes below the moon's ice crust. Small amounts of sodium salts embedded in the particles' ice matrices provide direct evidence for a subsurface liquid water reservoir, which is, or has been, in contact with the moon's rocky core (Postberg et al., 2009, 2011b).
Jupiter's Galilean satellites Ganymede, Europa, and Callisto are also believed to have subsurface oceans and are therefore prime targets for future NASA and ESA outer Solar System missions. The Galilean moons are engulfed in tenuous dust clouds consisting of tiny pieces of the moons' surfaces (Kruger et al., 1999), released by hypervelocity impacts of micrometeoroids, which steadily bombard the surfaces of the moons. In situ chemical analysis of these grains by a high resolution dust spectrometer will provide spatially resolved mapping of the surface composition of Europa. Ganymede, and Callisto, meeting key scientific objectives of the planned missions. However, novel high-resolution reflectron-type dust mass spectrometers (Sternovsky et al., 2007; Srama et al., 2007) developed for dust astronomy missions (Gran et al., 2009) are probably not robust enough to be operated in the energetic radiation environment of the inner Jovian system. In contrast, CDA's linear spectrometer is much less affected by harsh radiation conditions because its ion detector is not directly facing out into space. The instrument has been continuously operated on Cassini for 11 years. In this paper we investigate the possibility of operating a CDA-like instrument as a high resolution impact mass spectrometer. We show that such an instrument is capable of reliably identifying traces of organic and inorganic materials in the ice matrix of ejecta expected to be generated from the surfaces of the Galilean moons. These measurements are complementary, and in some cases superior, compared to other traditional techniques such as infrared remote sensing or in situ ion or neutral mass spectrometers.
Particles in Saturn's main rings range in size from dust to kilometer-sized objects. Their size distribution is thought to be a result of competing accretion and fragmentation processes. While growth is naturally limited in tidal environments, frequent collisions among these objects may contribute to both accretion and fragmentation. As ring particles are primarily made of water ice attractive surface forces like adhesion could significantly influence these processes, finally determining the resulting size distribution. Here, we derive analytic expressions for the specific self-energy Q and related specific break-up energy Q(star) of aggregates. These expressions can be used for any aggregate type composed of monomeric constituents. We compare these expressions to numerical experiments where we create aggregates of various types including: regular packings like the face-centered cubic (fcc), Ballistic Particle Cluster Aggregates (BPCA), and modified BPCAs including e.g. different constituent size distributions. We show that accounting for attractive surface forces such as adhesion a simple approach is able to: (a) generally account for the size dependence of the specific break-up energy for fragmentation to occur reported in the literature, namely the division into "strength" and "gravity" regimes and (b) estimate the maximum aggregate size in a collisional ensemble to be on the order of a few tens of meters, consistent with the maximum particle size observed in Saturn's rings of about 10 m.
Two images, taken by the Cassini spacecraft near Saturn's equinox in 2009 August, show the Earhart propeller casting a 350 km long shadow, offering the opportunity to watch how the ring height, excited by the propeller moonlet, relaxes to an equilibrium state. From the shape of the shadow cast and a model of the azimuthal propeller height relaxation, we determine the exponential cooling constant of this process to be lambda = 0.07 +/- 0.02 km(-1), and thereby determine the collision frequency of the ring particles in the vertically excited region of the propeller to be omega(c)/Omega = 0.9 +/- 0.2.
We propose a new mechanism which explains the existence of enormously sharp edges in the rings of Saturn. This mechanism is based on the synchronization phenomenon due to which the epicycle rotational phases of particles in the ring, under certain conditions, become synchronized with the phase of external satellite, e. g. with the phase of Mimas in the case of the outer B ring edge. This synchronization eliminates collisions between particles and suppresses the diffusion induced by collisions by orders of magnitude. The minimum of the diffusion is reached at the centre of the synchronization regime corresponding to the ratio 2:1 between the orbital frequency at the edge of B ring and the orbital frequency of Mimas. The synchronization theory gives the sharpness of the edge in a few tens of meters that is in agreement with available observations.
Viscous overstability in Saturn's B ring : II. Hydrodynamic theory and comparison to simulations
(2001)
Planetary rings
(2002)