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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.
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.
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.
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.
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.
Classical methods to analyze the surface composition of atmosphereless planetary objects from an orbiter are IR and gamma ray spectroscopy and neutron backscatter measurements. The idea to analyze surface properties with an in-situ instrument has been proposed by Johnson et al. (1998). There, it was suggested to analyze Europa's thin atmosphere with an ion and neutral gas spectrometer. Since the atmospheric components are released by sputtering of the moon's surface, they provide a link to surface composition. Here we present an improved, complementary method to analyze rocky or icy dust particles as samples of planetary objects from which they were ejected. Such particles, generated by the ambient meteoroid bombardment that erodes the surface, are naturally present on all atmosphereless moons and planets. The planetary bodies are enshrouded in clouds of ballistic dust particles, which are characteristic samples of their surfaces. In situ mass spectroscopic analysis of these dust particles impacting onto a detector of an orbiting spacecraft reveals their composition. Recent instrumental developments and tests allow the chemical characterization of ice and dust particles encountered at speeds as low as 1 km/s and an accurate reconstruction of their trajectories. Depending on the sampling altitude, a dust trajectory sensor can trace back the origin of each analyzed grain with about 10 km accuracy at the surface. Since the detection rates are of the order of thousand per orbit, a spatially resolved mapping of the surface composition can be achieved. Certain bodies (e.g., Europa) with particularly dense dust clouds, could provide impact statistics that allow for compositional mapping even on single flybys. Dust impact velocities are in general sufficiently high at orbiters about planetary objects with a radius > 1000 km and with only a thin or no atmosphere. In this work we focus on the scientific benefit of a dust spectrometer on a spacecraft orbiting Earth's Moon as well as Jupiter's Galilean satellites. This 'dust spectrometer' approach provides key chemical and isotopic constraints for varying provinces or geological formations on the surfaces, leading to better understanding of the body's geological evolution.
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 present a kinetic model of a disk of solid particles, orbiting a primary and experiencing inelastic collisions. In distinction to other collisional models that use a 2D (mass-sernimajor axis) binning and perform a separate analysis of the velocity (eccentricity, inclination) evolution, we choose mass and orbital elements as independent variables of a phase space. The distribution function in this space contains full information on the combined mass, spatial, and velocity distributions of particles. A general kinetic equation for the distribution function is derived, valid for any set of orbital elements and for any collisional outcome, specified by a single kernel function. The first implementation of the model utilizes a 3D phase space (mass-semimajor axis-eccentricity) and involves averages over the inclination and all angular elements. We assume collisions to be destructive, simulate them with available material- and size-dependent scaling laws, and include collisional damping. A closed set of kinetic equations for a mass-semimajor axis-eccentricity distribution is written and transformation rules to usual mass and spatial distributions of the disk material are obtained. The kinetic "core" of our approach is generic. It is possible to add inclination as an additional phase space variable, to include cratering collisions and agglomeration, dynamical friction and viscous stirring, gravity of large perturbers, drag forces, and other effects into the model. As a specific application, we address the collisional evolution of the classical population in the Edgeworth-Kuiper belt (EKB). We run the model for different initial disk's masses and radial profiles and different impact strengths of objects. Our results for the size distribution, collisional timescales, and mass loss are in agreement with previous studies. In particular, collisional evolution is found to be most substantial in the inner part of the EKB, where the separation size between the survivors over EKB ' s age and fragments of earlier collisions lies between a few and several tens of km. The size distribution in the EKB is not a single Dohnanyi-type power law, reflecting the size dependence of the critical specific energy in both strength and gravity regimes. The net mass loss rate of an evolved disk is nearly constant and is dominated by disruption of larger objects. Finally, assuming an initially uniform distribution of orbital eccentricities, we show that an evolved disk contains more objects in orbits with intermediate eccentricities than in nearly circular or more eccentric orbits. This property holds for objects of any size and is explained in terms of collisional probabilities. The effect should modulate the eccentricity distribution shaped by dynamical mechanisms, such as resonances and truncation of perihelia by Neptune. (c) 2004 Elsevier Inc. All rights reserved
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.
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.
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.