Saturn's F Ring: Kinematics and Particle Sizes from Stellar Occultation Studies

The occultation of GSC5249-01240 by Saturn's rings was observed in a spectrally resolved mode using the Faint Object Spectrograph on the Hubble Space Telescope. By combining these data with other occultation data, we have determined the inclination of the F ring to be 0.0065±0.0014 deg. Our inclined F ring orbit model explains an abrupt decrease in flux at the west ansa of the ring that was observed during the November 1995 ring-plane crossing as well as the nondetection of 1995 S5 during one set of observations in November 1995. The F ring's equivalent depth is found to have no significant dependence on wavelength between 0.27 and 0.74 μm, indicating the presence of a population of ring particles larger in size than ∼10 μm. This contrasts with the results from a previous analysis of Voyager images at various phase angles, in which the particles were determined to be predominantly submicron in size. The difference may be due to temporal or longitudinal variability within the ring.     

The Composition of Saturn's Rings

A composite spectrum between 0.30 and 4.05 μm of Saturn's rings is analyzed using the Shkuratov scattering theory (Shkuratov et al. 1999, Icarus137, 235-246). Several types of surface and composition are discussed. We demonstrate that both the strong reddening over the interval 0.3-0.7 μm and the water ice absorption features are well reproduced by an intimate (“salt-and-pepper”) mixture of four coarse particles of two different materials: 93% are grains (typical sizes of 10, 200, and 2000 μm) of water ice containing a few percent of refractory organic solid (tholin) impurities within their bulk, and 7% are coarse grains of a dark material (amorphous carbon). The cosmogenic implications of the inferred composition are discussed.     

Disentangling Saturn's F Ring. I. Clump orbits and lifetimes

A comprehensive analysis of the Voyager images reveals the kinematics and lifetimes of clumps in the F Ring. At any given time, the ring has 2-3 major clumps, each several times brighter than the typical ring, plus numerous smaller features. A total of 34 individual clumps have been tracked over periods of 1-7 weeks. The clumps orbited at measurably different rates, implying a 100-km range of semimajor axes centered on 140,220 km. Most are centered around the nominal mean motion of the ring's core, but a few outliers may be associated with a different strand, or with no strand at all. Most clumps change very little over the ∼30 days that they can be detected; however, no clump persisted for the nine-month interval between the two Voyager encounters. The brightest Voyager 2 clump is unusual in that it travels at a rapid mean motion and seems to be associated with the formation of several other clumps.     

A Study of Saturn's Ring Phase Curves from HST Observations

Solar phase curves between 0.3° and 6.0° and color ratios at wavelengths λ=0.336 μm and λ=0.555 μm for Saturn's rings are presented using recent Hubble Space Telescope observations. We test the hypothesis that the phase reddening of the rings is less due to collective properties of the ring particles than to the individual properties of the ring particles. We use a modified Drossart model, the Hapke model, and the Shkuratov model to model reddening by either intraparticle shadow-hiding on fractal and normal surfaces, multiple scattering, or some combination. The modified Drossart model (including only shadowing) failed to reproduce the data. The Hapke model gives fair fits, except for the color ratios. A detailed study of the opposition effect suggests that coherent backscattering is the principal cause of the opposition surge at very small phase angles. The shape of the phase curve and color ratios of each main ring regions are accurately represented by the Shkuratov model, which includes both a shadow-hiding effect and coherent backscatter enhancement. Our analysis demonstrates that in terms of particle roughness, the C ring particles are comparable to the Moon, but the Cassini division and especially the A and B ring particles are significantly rougher, suggesting lumpy particles such as often seen in models. Another conspicuous difference between ring regions is in the effective size d of regolith grains (d∼λ for the C ring particles, d∼1-10 μm for the other rings).     

More Microwave Observations of Saturn: Modeling the Ring with a Monte Carlo Radiative Transfer Code

We present a second epoch of Very Large Array Saturn observations taken in February 1997 spanning wavelengths 1.3-21 cm. These observations complement earlier observations at Saturn's autumnal equinox in November 1995. In this epoch, however, we generally have better signal-to-noise ratios and the ring inclination of the present observations was −5.0°, whereas the previous observations were made with ring inclination +2.7°.Our observations confirm the latitudinal structure on the saturnian disk as seen at 2.0, 3.6, and 6.1 cm. We also see some latitudinal structure at 1.3 cm for the first time. The details of this structure have changed dramatically from those reported by I. de Pater and J. R. Dickel (1991, Icarus94, 474-492) for the 1980s and are consistent with those seen in F. van der Tak et al. (1999, Icarus142, 125-147). The most prominent features are a pair of brightness enhancements just inside the edges of the Equatorial Zone.The rings do not show the east-west asymmetry seen in our previous epoch, perhaps indicative of a viewing angle effect on the scattering properties of the rings. The radial trend in brightness in the ansae is generally consistent with that expected from optical depth variations and increasing distance from the source of scattered light. In particular the increased optical depth towards the center of the C ring is evident. Azimuthal variation in brightness in the C ring shows the forward scattering expected of Mie scattering. By contrast, the A and B rings show little or no azimuthal variation.We present Monte Carlo simulations of the ring brightness under the assumptions of isotropic and Mie scattering. These are the first synthetic maps of Saturn which can be directly compared to the images we obtained. Neither model fits all the data well. However, a hybrid model combining isotropic and Mie scattering does fit well. We interpret the consistency with isotropic scattering in the outer rings as an indication that near-field effects may be important. This in turn implies geometrically thin rings, as predicted by dynamical simulations of these rings.     

Moonlets and clumps in Saturn's F ring

Cassini UVIS star occultations by the F ring detect 13 events ranging from 27 m to 9 km in width. We interpret these structures as likely temporary aggregations of multiple smaller objects, which result from the balance between fragmentation and accretion processes. One of these features was simultaneously observed by VIMS. There is evidence that this feature is elongated in azimuth. Some features show sharp edges. At least one F ring object is opaque and may be a “moonlet.” This possible moonlet provides evidence for larger objects embedded in Saturn's F ring, which were predicted as the sources of the F ring material by Cuzzi and Burns [Cuzzi, J.N., Burns, J.A., 1988. Icarus 74, 284-324], and as an outcome of tidally modified accretion by Barbara and Esposito [Barbara, J.M., Esposito, L.W., 2002. Icarus 160, 161-171]. We see too few events to confirm the bi-modal distribution which Barbara and Esposito [Barbara, J.M., Esposito, L.W., 2002. Icarus 160, 161-171] predict. These F ring structures and other youthful features detected by Cassini may result from ongoing destruction of small parent bodies in the rings and subsequent aggregation of the fragments. If so, the temporary aggregates are 10 times more abundant than the solid objects. If recycling by re-accretion is significant, the rings could be quite ancient, and likely to persist far into the future.     

Saturn's rings, the Yarkovsky effects, and the Ring of Fire

Saturn's icy ring particles, with their low thermal conductivity, are almost ideal for the operation of the Yarkovsky effects (photon thrust due to temperature gradients across the ring particles). An extremely simple case of the Yarkovsky effects is examined here, in which orbital evolution is computed as though each particle travels around Saturn alone in a circular orbit, so that there are no collisions, shadowing, or irradiance from other particles; nor are resonances, tumbling, or micrometeoroid erosion considered. The orbital evolution for random spin orientations appears to be a competition between two effects: the seasonal Yarkovsky effect, which makes orbits contract, and the Yarkovsky-Schach effect, which makes orbits expand. There are values of the far infrared and visible particle albedos for which (working radially out from the planet) the along-track particle acceleration S is negative, then positive, and then negative again; the region for which S>0 is interpreted as a region where stable rings are possible. Typical timescales for centimeter-sized particles to travel half a Saturn radius are ¹⁰⁷-¹⁰⁸ yr. Collisions, shadowing, and resonances may lengthen the timescales, perhaps considerably. It is speculated here that the C ring may be depleted of particles because of the seasonal Yarkovsky effect, and small particles that are present in the C ring ultimately fall on Saturn, possibly creating a “Ring of Fire” as they enter the planet's atmosphere.     

Microwave observations of Saturn's rings: anisotropy in directly transmitted and scattered saturnian thermal emission

We present a new Very Large Array (VLA) image of Saturn, made from data taken in October 1998 at a wavelength of λ3.6 cm. The moderate ring opening angle (B≈15°) allows us to explore direct transmission of microwave photons through the A and C rings. We find a strong asymmetry of photons transmitted through the A ring, but not in the C ring, a new diagnostic of wake structure in the ring particles. We also find a weak asymmetry between east and west for the far side of the ansae. To facilitate quantitative comparison between dynamic models of the A ring and radio observations, we extend our Monte Carlo radiative transfer code (described in Dunn et al., 2002, Icarus 160, 132-160) to include idealized wakes. We show the idealized model can reproduce the properties of dynamic simulations in directly transmitted light. We examine the model behavior in directly transmitted and scattered light over a range of physical and geometric wake parameters. Finally, we present a wake model with a plausible set of physical parameters that quantitatively reproduces the observed intensity and asymmetry of the A ring both across the planet and in the ansae.     

Self-gravity wakes and radial structure of Saturn's B ring

We analyze stellar occultations by Saturn's rings observed with the Cassini Ultraviolet Imaging Spectrograph and find large variations in the apparent normal optical depth of the B ring with viewing angle. The line-of-sight optical depth is roughly independent of the viewing angle out of the ring plane so that optical depth is independent of the path length of the line-of-sight. This suggests the ring is composed of virtually opaque clumps separated by nearly transparent gaps, with the relative abundance of clumps and gaps controlling the observed optical depth. The observations can be explained with a model of self-gravity wakes like those observed in the A ring. These trailing spiral density enhancements are due to the competing processes of self-gravitational accretion of ring particles and Kepler shear. The B ring wakes are flatter and more closely packed than their neighbors in the A ring, with height-to-width ratios <0.1 for most of the ring. The self-gravity wakes are seen in all regions of the B ring that are not opaque. The observed variation in total B ring optical depth is explained by the amount of relatively empty space between the self-gravity wakes. Wakes are more tightly packed in regions where the apparent normal optical depth is high, and the wakes are more widely spaced in lower optical depth regions. The normal optical depth of the gaps between the wakes is typically less than 0.5 and shows no correlation with position or overall optical depth in the ring. The wake height-to-width ratio varies with the overall optical depth, with flatter, more tightly packed wakes as the overall optical depth increases. The highly flattened profile of the wakes suggests that the self-gravity wakes in Saturn's B ring correspond to a monolayer of the largest particles in the ring. The wakes are canted to the orbital direction in the trailing sense, with a trend of decreasing cant angle with increasing orbital radius in the B ring. We present self-gravity wake properties across the B ring that can be used in radiative transfer modeling of the ring. A high radial resolution (∼10 m) scan of one part of the B ring during a grazing occultation shows a dominant wavelength of 160 m due to structures that have zero cant angle. These structures are seen at the same radial wavelength on both ingress and egress, but the individual peaks and troughs in optical depth do not match between ingress and egress. The structures are therefore not continuous ringlets and may be a manifestation of viscous overstability.     

Aggregate impacts in Saturn's rings

Ring particle aggregates are formed in the outer parts of Saturn's main rings. We study how collisions between aggregates can lead to destruction or coalescence of these aggregates, with local N-body simulations taking into account the dissipative impacts and gravitational forces between particles. Impacts of aggregates with different mass ratios are studied, as well as aggregates that consist of particles with different physical properties. We find that the outcome of the collision is very sensitive to the shape of the aggregate, in the sense that more elongated aggregates are more prone to be destroyed. We were interested in testing the accretion criterion Barbara and Esposito [Barbara, J.M., Esposito, L.W., 2002. Icarus 160, 161-171] used in their F ring simulations, according to which accretion requires that the masses of the colliding bodies differ at least by a factor of 100. We confirm that such a critical mass ratio exists. In particular, simulations indicate that the exact critical mass ratio depends on the internal density and elasticity of particles, and the distance from the planet. The zone of transition, defined by the distance where individual particles or small aggregates first start to stick on the larger aggregate, and by the distance where two similar sized aggregates on the average eventually coalesce is only about 5000 km wide, if fixed particle properties are used. The rotational state of the aggregates that form via aggregate collision rapidly reaches synchronous rotation, similarly to the aggregates that form via gradual growth.     

On the damping of the bending waves in Saturn’s ring

We study numerically the motion of a single particle in the bending wave of finite thickness in Saturn’s ring. We include the forcing due to the planet, a moon, the coriolis force and the self gravity of the ring. In particular, we compute the variation of the velocity arising due to the variation of the amplitude and the phase of the epicyclic motion across the local vertical height of the ring. We suggest that the dissipation of energy due to the collision of ring particles in this shear layer damps out the bending wave of Saturn’s ring at the 5:3 vertical resonance of Mimas within a distance of 150 km from the site of its launching as is observed in Voyager data.     

Organizing some very tenuous things: Resonant structures in Saturn's faint rings

Images of the dusty rings obtained by the Cassini spacecraft in late 2006 and early 2007 reveal unusual structures composed of alternating canted bright and dark streaks in the outer G ring (∼170,000 km from Saturn center), the inner Roche Division (∼138,000 km) and the middle D ring (70,000-73,000 km). The morphology, locations and pattern speeds of these features indicate that they are generated by Lindblad resonances. The structure in the G ring appears to be generated by the 8:7 Inner Lindblad Resonance with Mimas. Based in part on the morphology of the G ring structure, we develop a phenomenological model of Lindblad-resonance-induced structures in faint rings, where the observed variations in the rings' optical depth and brightness are due to alignments and trends in the particles' orbital parameters with semi-major axis. To reproduce the canted character of these structures, this model requires a term in the equations of motion that damps eccentricities. Using this model to interpret the structures in the D ring and Roche Division, we find that the D-ring patterns mimic those predicted at 2:1 Inner Lindblad Resonances and the Roche Division patterns look like those expected at 3:4 Outer Lindblad Resonances. As in the G ring, the effective eccentricity-damping timescale is of order 10-100 days, suggesting that free eccentricities are strongly damped by some mechanism that operates throughout all these regions. However, unlike in the G ring, perturbation forces with multiple periods are required to explain the observed patterns in the D ring and Roche Division. The strongest perturbation periods occur at 10.53, 10.56 and 10.74 hours (only detectable in the D ring) and 10.82 hours (detectable in both the D ring and Roche division). These periods are comparable to the rotation periods of Saturn's atmosphere and magnetosphere. The inferred strength of the perturbation forces required to produce these patterns (and the absence of evidence for other resonances driven by these periods in the main rings) suggests that non-gravitational forces are responsible for generating these features in the D ring and Roche Division. If this interpretation is correct, then some of these structures may have some connection with periodic signals observed in Saturn's magnetic field and radio-wave emissions, and accordingly could help clarify the nature and origin(s) of these magnetospheric asymmetries.     

Modeling of global variations and ring shadowing in Saturn's ionosphere

A time-dependent one-dimensional model of Saturn's ionosphere has been developed as an intermediate step towards a fully coupled Saturn Thermosphere-Ionosphere Model (STIM). A global circulation model (GCM) of the thermosphere provides the latitude and local time dependent neutral atmosphere, from which a globally varying ionosphere is calculated. Four ion species are used (H⁺, H⁺₂, H⁺₃, and He⁺) with current cross-sections and reaction rates, and the SOLAR2000 model for the Sun's irradiance. Occultation data from the Voyager photopolarimeter system (PPS) are adapted to model the radial profile of the ultraviolet (UV) optical depth of the rings. Diurnal electron density peak values and heights are generated for all latitudes and two seasons under solar minimum and solar maximum conditions, both with and without shadowing from the rings. Saturn's lower ionosphere is shown to be in photochemical equilibrium, whereas diffusive processes are important in the topside. In agreement with previous 1-D models, the ionosphere is dominated by H⁺ and H⁺₃, with a peak electron density of ∼¹⁰⁴ electrons cm⁻³. At low- and mid-latitudes, H⁺ is the dominant ion, and the electron density exhibits a diurnal maximum during the mid-afternoon. At higher latitudes and shadowed latitudes (smaller ionizing fluxes), the diurnal maximum retreats towards noon, and the ratio of [H⁺]/[H⁺₃] decreases, with H⁺₃ becoming the dominant ion at altitudes near the peak (∼1200-1600 km) for noon-time hours. Shadowing from the rings leads to attenuation of solar flux, the magnitude and latitudinal structure of which is seasonal. During solstice, the season for the Cassini spacecraft's encounter with Saturn, attenuation has a maximum of two orders of magnitude, causing a reduction in modeled peak electron densities and total electron column contents by as much as a factor of three. Calculations are performed that explore the parameter space for charge-exchange reactions of H⁺ with vibrationally excited H₂, and for different influxes of H₂O, resulting in a maximum diurnal variation in electron density much weaker than the diurnal variations inferred from Voyager's Saturn Electrostatic Discharge (SED) measurements. Peak values of height-integrated Pedersen conductivities at high latitudes during solar maximum are modeled to be ∼42 mho in the summer hemisphere during solstice and ∼18 mho during equinox, indicating that even without ionization produced by auroral processes, magnetosphere-ionosphere coupling can be highly variable.     

Gravitational accretion of particles in Saturn's rings

Gravitational accretion in the rings of Saturn is studied with local N-body simulations, taking into account the dissipative impacts and gravitational forces between particles. Common estimates of accretion assume that gravitational sticking takes place beyond a certain distance (Roche distance) where the self-gravity between a pair of ring particles exceeds the disrupting tidal force of the central object, the exact value of this distance depending on the ring particles' internal density. However, the actual physical situation in the rings is more complicated, the growth and stability of the particle groups being affected also by the elasticity and friction in particle impacts, both directly via sticking probabilities and indirectly via velocity dispersion, as well as by the shape, rotational state and the internal packing density of the forming particle groups. These factors are most conveniently taken into account via N-body simulations. In our standard simulation case of identical 1 m particles with internal density of solid ice, ρ=900 kg m⁻³, following the Bridges et al., 1984 elasticity law, we find accretion beyond a=137,000-146,000 km, the smaller value referring to a distance where transient aggregates are first obtained, and the larger value to the distance where stable aggregates eventually form in every experiment lasting 50 orbital periods. Practically the same result is obtained for a constant coefficient of restitution εn=0.5. In terms of rp parameter, the sum of particle radii normalized by their mutual Hill radius, the above limit for perfect accretion corresponds to rp<0.84. Increased dissipation (εn=0.1), or inclusion of friction (tangential force 10% of normal force) shifts the accretion region inward by about 5000 km. Accretion is also more efficient in the case of size distribution: with a q=3 power law extending over a mass range of 1000, accretion shifts inward by almost 10,000 km. The aggregates forming in simulations via gradual accumulation of particles are synchronously rotating.     

Sources and losses of energetic protons in Saturn's magnetosphere

We present Cassini data revealing that protons between a few keV and about 100 keV energy are not stably trapped in Saturn's inner magnetosphere. Instead these ions are present only for relatively short times following injections. Injected protons are lost principally because the neutral gas cloud converts these particles to energetic neutral atoms via charge exchange. At higher energies, in the MeV to GeV range, protons are stably trapped between the orbits of the principal moons because the proton cross-section for charge exchange is very small at such energies. These protons likely result from cosmic ray albedo neutron decay (CRAND) and are lost principally to interactions with satellite surfaces and ring particles during magnetospheric radial diffusion. A main result of this work is to show that the dominant energetic proton loss and source processes are a function of proton energy. Surface sputtering by keV ions is revisited based on the reduced ion intensities observed. Relatively speaking, MeV ion and electron weathering is most important closer to Saturn, e.g. at Janus and Mimas, whereas keV ion weathering is most important farther out, at Dione and Rhea.     

A procedure to analyze nonlinear density waves in Saturn's rings using several occultation profiles

Cassini radio science experiments have provided multiple occultation optical depth profiles of Saturn's rings that can be used in combination to analyze density waves. This paper establishes an accurate procedure of inversion of the wave profiles to reconstruct the wave kinematic parameters as a function of semi-major axis, in the nonlinear regime. This procedure is established using simulated data in the presence of realistic noise perturbations, to control the reconstruction error. It is then applied to the Mimas 5:3 density wave. There are two important concepts at the basis of this procedure. The first one is that it uses the nonlinear representation of density waves, and the second one is that it relies on a combination of optical depth profiles instead of just one profile. A related method to analyze density waves was devised by Longaretti and Borderies [Longaretti, P.-Y., Borderies, N., 1986. Icarus 67, 211-223] to study the nonlinear density wave associated with the Mimas 5:3 resonance, but the single photopolarimetric profile provided limited constraints. Other studies of density waves analyzing Cassini data [Colwell, J.E., Esposito, L.W., 2007. Bull. Am. Astron. Soc. 39, 461; Tiscareno, M.S., Burns, J.A., Nicholson, P.D., Hedman, M.M., Porco, C.C., 2007. Icarus 189, 14-34] are based on the linear theory and find inconsistent results from profile to profile. Multiple cuts of the rings are helpful in a fundamental way to ensure the accuracy of the procedure by forcing consistency among the various optical depth profiles. By way of illustration we have applied our procedure to the Mimas 5:3 density wave. We were able to recover precisely the kinematic parameters from the radio experiment occultation data in most of the propagation region; a preliminary analysis of the pressure-corrected dispersion allowed us to determine new but still uncertain values for the opacity (K?0.02 cm²/g) and velocity dispersion of (c₀?0.6 cm/s) in the wave region. Our procedure constitutes the first step in our planned analysis of the density waves of Saturn's rings. It is very accurate and efficient in the far-wave region. However, improvements are required within the first wavelength. The ways in which this method can be used to establish diagnostics of ring physics are outlined.     

Energetic electron signatures of Saturn's smaller moons: Evidence of an arc of material at Methone

We present several energetic charged particle microsignatures of two Lagrange moons, Telesto and Helene, measured by the MIMI/LEMMS instrument. These small moons absorb charged particles but their effects are usually obscured by Tethys and Dione, the two larger saturnian satellites that occupy the same orbits. The scales and structures of these microsignatures are consistent with standard models for electron absorption from asteroid-sized moons in Saturn's radiation belts. In the context of these observations, we also examine the possibility that the 3 km Satellite Methone is responsible for two electron microsignatures detected by Cassini close to this moon's orbit. We infer that a previously undetected arc of material exists at Methone's orbit (R/2006 S5), we speculate how such a structure could form and what its physical characteristics and location could be. The origin of this arc could be linked to a possible presence of a faint ring produced by micrometeoroid impacts on Methone's surface, to E-ring dust clump formation at that distance or to temporary dust clouds produced by enceladian activity that spiral inwards under the effect of non-gravitational forces.     

HST observations of azimuthal asymmetry in Saturn's rings

From 378 Hubble Space Telescope WFPC2 images obtained between 1996-2004, we have measured the detailed nature of azimuthal brightness variations in Saturn's rings. The extensive geometric coverage, high spatial resolution (), and photometric precision of the UBVRI images have enabled us to determine the dependence of the asymmetry amplitude and longitude of minimum brightness on orbital radius, ring elevation, wavelength, solar phase angle, and solar longitude. We explore a suite of dynamical models of self-gravity wakes for two particle size distributions: a single size and a power law distribution spanning a decade in particle radius. From these N-body simulations, we calculate the resultant wake-driven brightness asymmetry for any given illumination and viewing geometry. The models reproduce many of the observed properties of the asymmetry, including the shape and location of the brightness minimum and the trends with ring elevation and solar longitude. They also account for the “tilt effect” in the A and B rings: the change in mean ring brightness with effective ring opening angle, |Beff|. The predicted asymmetry depends sensitively on dynamical ring particle properties such as the coefficient of restitution and internal mass density, and relatively weakly on photometric parameters such as albedo and scattering phase function. The asymmetry is strongest in the A ring, reaching a maximum amplitude A∼25% near a=128,000 km. Here, the observations are well-matched by an internal particle density near 450 kg m⁻³ and a narrow particle size distribution. The B ring shows significant asymmetry (∼5%) in regions of relatively low optical depth (τ∼0.7). In the middle and outer B ring, where τ?1, the asymmetry is much weaker (∼1%), and in the C ring, A<0.5%. The asymmetry diminishes near opposition and at shorter wavelengths, where the albedo of the ring particles is lower and multiple-scattering effects are diminished. The asymmetry amplitude varies strongly with ring elevation angle, reaching a peak near |Beff|=10° in the A ring and at |Beff|=15-20° in the B ring. These trends provide an estimate of the thickness of the self-gravity wakes responsible for the asymmetry. Local radial variations in the amplitude of the asymmetry within both the A and B rings are probably caused by regional differences in the particle size distribution.     

HST observations of spokes in Saturn's B ring

As part of a long-term study of Saturn's rings, we have used the Hubble Space Telescope's (HST) Wide Field and Planetary Camera (WFPC2) to obtain several hundred high resolution images from 1996 to 2004, spanning the full range of ring tilt and solar phase angles accessible from the Earth. Using these multiwavelength observations and HST archival data, we have measured the photometric properties of spokes in the B ring, visible in a substantial number of images. We determined the spoke particle size distribution by fitting the wavelength-dependent extinction efficiency of a prominent, isolated spoke, using a Mie scattering model. Following Doyle and Grün (1990, Icarus 85, 168-190), we assumed that the spoke particles were sub-micron size spheres of pure water ice, with a Hansen-Hovenier size distribution (Hansen and Hovenier, 1974, J. Atmos. Sci. 31, 1137-1160). The WFPC2 wavelength coverage is broader than that of the Voyager data, resulting in tighter constraints on the nature of spoke particles. The effective particle size was reff=0.57±0.05 μm, and the size distribution was quite narrow with a variance of b=0.09±0.03, very similar to the results of Doyle and Grün (1990, Icarus 85, 168-190), and consistent with predictions of plasma cloud models for spoke production from meteoritic impacts (Goertz and Morfill, 1983, Icarus 53, 219-229; Goertz, 1984, Adv. Space Res. 4, 137-141). In all, we identified 36 spokes or spoke complexes, predominantly on the morning (east) ansa. The photometric contrast of the spokes is strongly dependent on effective ring opening angle, Beff. Spokes were clearly visible on the north face of the rings in 1994, just prior to the most recent ring plane crossing (RPX) epoch, and on the south face shortly after RPX. However, spokes were both less abundant and fainter as the rings opened up, and no spokes were detected after 18 October 1998 (Beff=−15.43°), when a single faint spoke was seen on the morning ansa. The high resolution and photometric quality of the WFPC2 images enabled us to set a detection limit of ?1% in fractional brightness contrast for spokes for the post-1998 observations. We compare the observed trend of spoke contrast with Beff to radiative transfer calculations based on three models of the distribution of spoke material. In the first, the spoke “haze” is uniformly mixed with macroscopic B ring particles. No variation in spoke contrast is predicted for single-scattering, in this case, and only a modest decrease in contrast with Beff is predicted when multiple scattering is taken into account. In the second model, the spoke dust occupies an extended layer that is thicker than the B ring, which gives virtually identical results to a third case, when the haze layer lies exclusively above the ring. Multiple-scattering Monte Carlo calculations for these two extended haze models match the trend of spoke contrast exceptionally well. We compute the predicted spoke contrast for a wide variety of viewing geometries, including forward- and backscattering. Based on these results, spokes should be easily detectable during the Cassini mission when the rings are viewed at relatively small (|B|?10°) ring opening angles.     

The influence of particle adhesion on the stability of agglomerates in Saturn's rings

In planetary rings, binary collisions and mutual gravity are the predominant particle interactions. Based on a viscoelastic contact model we implement the concept of static adhesion. We discuss the collision dynamics and obtain a threshold velocity for restitution or agglomeration to occur. The latter takes place within a range of a few cm s⁻¹ for icy grains at low temperatures. The stability of such two-body agglomerates bound by adhesion and gravity in a tidal environment is discussed and applied to the saturnian system. A maximal agglomerate size for a given orbit location is obtained. In this way we are able to resolve the borderline of the zone where agglomerates can exist as a function of the agglomerate size and thus gain an alternative to the classical Roche limit. An increasing ring grain size with distance to Saturn as observed by the VIMS-experiment on board the Cassini spacecraft can be found by our estimates and implications for the saturnian system will be addressed.