Density waves in Cassini UVIS stellar occultations: 1. The Cassini Division

We analyze density waves in the Cassini Division of Saturn's rings revealed by multiple stellar occultations by Saturn's rings observed with the Cassini Ultraviolet Imaging Spectrograph. The dispersion and damping of density waves provide information on the local ring surface mass density and viscosity. Several waves in the Cassini Division are on gradients in the background optical depth, and we find that the dispersion of the wave reflects a change in the underlying surface mass density. We find that over most of the Cassini Division the ring opacity (the ratio of optical depth to surface mass density) is nearly constant and is ∼5 times higher than the opacity in the A ring where most density waves are found. However, the Cassini Division ramp, a 1100-km-wide, nearly featureless region of low optical depth that connects the Cassini Division to the inner edge of the A ring, has an opacity like that of the A ring and significantly less than that in the rest of the Cassini Division. This is consistent with particles in the ramp originating in the A ring and being transported into the Cassini Division through ballistic transport processes. Damping of the waves in the Cassini Division suggests a vertical thickness of 3–6 m. Using a mean opacity of 0.1 cm²/g we find the mass of the Cassini Division, excluding the ramp, is 3.1×¹⁰¹⁶ kg while the mass of the Cassini Division ramp, with an opacity of 0.015 cm²/g, is 1.1×¹⁰¹⁷ kg. Assuming a power-law size distribution for the ring particles, the larger opacity of the main Cassini Division is consistent with the largest ring particles there being ∼5 times smaller than the largest particles in the ramp and A ring.     

A close look at Saturn's rings with Cassini VIMS

Soon after the Cassini-Huygens spacecraft entered orbit about Saturn on 1 July 2004, its Visual and Infrared Mapping Spectrometer obtained two continuous spectral scans across the rings, covering the wavelength range 0.35-5.1 μm, at a spatial resolution of 15-25 km. The first scan covers the outer C and inner B rings, while the second covers the Cassini Division and the entire A ring. Comparisons of the VIMS radial reflectance profile at 1.08 μm with similar profiles at a wavelength of 0.45 μm assembled from Voyager images show very little change in ring structure over the intervening 24 years, with the exception of a few features already known to be noncircular. A model for single-scattering by a classical, many-particle-thick slab of material with normal optical depths derived from the Voyager photopolarimeter stellar occultation is found to provide an excellent fit to the observed VIMS reflectance profiles for the C ring and Cassini Division, and an acceptable fit for the inner B ring. The A ring deviates significantly from such a model, consistent with previous suggestions that this region may be closer to a monolayer. An additional complication here is the azimuthally-variable average optical depth associated with “self-gravity wakes” in this region and the fact that much of the A ring may be a mixture of almost opaque wakes and relatively transparent interwake zones. Consistently with previous studies, we find that the near-infrared spectra of all main ring regions are dominated by water ice, with a typical regolith grain radius of 5-20 μm, while the steep decrease in visual reflectance shortward of 0.6 μm is suggestive of an organic contaminant, perhaps tholin-like. Although no materials other than H₂O ice have been identified with any certainty in the VIMS spectra of the rings, significant radial variations are seen in the strength of the water-ice absorption bands. Across the boundary between the C and B rings, over a radial range of ∼7000 km, the near-IR band depths strengthen considerably. A very similar pattern is seen across the outer half of the Cassini Division and into the inner A ring, accompanied by a steepening of the red slope in the visible spectrum shortward of 0.55 μm. We attribute these trends—as well as smaller-scale variations associated with strong density waves in the A ring—to differing grain sizes in the tholin-contaminated icy regolith that covers the surfaces of the decimeter-to-meter sized ring particles. On the largest scale, the spectral variations seen by VIMS suggest that the rings may be divided into two larger ‘ring complexes,’ with similar internal variations in structure, optical depth, particle size, regolith texture and composition. The inner complex comprises the C and B rings, while the outer comprises the Cassini Division and A ring.     

Self-gravity wake parameters in Saturn’s A and B rings

An increasing body of evidence shows that, at the sub-km level, Saturn’s main A and B rings are dominated by an ever-changing pattern of elongated, canted structures known as self-gravity wakes. Best known for causing azimuthal variations in the rings’ reflectivity, these structures also have a profound influence on how the transmission of the rings varies with both longitude and opening angle, B (Colwell et al. [2006] Geophys. Res. Lett. 33, 7201; Colwell et al. [2007] Icarus 190, 127-144; Hedman et al. [2007] Astron. J. 133, 2624-2629). We use data from three stellar occultations observed by Cassini’s Visual and Infrared Mapping Spectrometer (VIMS) to measure the transmission of the rings as a function of B, when viewed parallel to the wakes. These data are used to constrain properties of the self-gravity wakes as a function of radius across the A and B rings: specifically the fractional width of the gaps between the wakes, G/λ, and the average normal optical depth in the gaps, τ_G. We find that the overall normal optical depth of the rings, τ_n is primarily controlled by G/λ, which varies between <0.05 and ∼0.70 in the A and B rings. The gaps, however, are not completely empty, being filled by material — possibly cm-sized ring particles — with an average normal optical depth which varies from 0.12 to ∼0.4. In addition to regional variations, local variations in τ_G are seen in the regular structure which dominates the inner B ring, and in the environs of strong density waves in the A ring. The same model applied to the lower optical depth Cassini Division reveals very little evidence of self-gravity wakes, except where τ_n exceeds ∼0.25.     

Keck observations of the 2002-2003 jovian ring plane crossing

We present new observations of Jupiter's ring system at a wavelength of 2.2 μm obtained with the 10-m W.M. Keck telescopes on three nights during a ring plane crossing: UT 19 December 2002, and 22 and 26 January 2003. We used conventional imaging, plus adaptive optics on the last night. Here we present detailed radial profiles of the main ring, halo and gossamer rings, and interpret the data together with information extracted from radio observations of Jupiter's synchrotron radiation. The main ring is confined to a 800-km-wide annulus between 128,200 and 129,000 km, with a ∼5000 km extension on the inside. The normal optical depth is 8×¹⁰⁻⁶, 15% of which is provided by bodies with radii a?5 cm. These bodies are as red as Metis. Half the optical depth, τ≈4×¹⁰⁻⁶, is attributed to micron-sized dust, and the remaining τ≈3×¹⁰⁻⁶ to grains tens to hundreds of μm in size. The inward extension consists of micron-sized (a?10 μm) dust, which probably migrates inward under Poynting-Robertson drag. The inner limit of this extension falls near the 3:2 Lorentz resonance (at orbital radius r=122,400 km), and coincides with the outer limit of the halo. The gossamer rings appear to be radially confined, rather than broad sheets of material. The Amalthea ring is triangularly shaped, with a steep outer dropoff over ∼5000 km, extending a few 1000 km beyond the orbit of Amalthea, and a more gradual inner dropoff over 15,000-20,000 km. The inner edge is near the location of the synchronous orbit. The optical depth in the Amalthea ring is ∼5×¹⁰⁻⁷, up to 20% of which is comprised of macroscopic material. The optical depth in the Thebe ring is a factor of 3 smaller.     

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.     

Saturn's dynamic D ring

The Cassini spacecraft has provided the first clear images of the D ring since the Voyager missions. These observations show that the structure of the D ring has undergone significant changes over the last 25 years. The brightest of the three ringlets seen in the Voyager images (named D72), has transformed from a narrow, <40-km wide ringlet to a much broader and more diffuse 250-km wide feature. In addition, its center of light has shifted inwards by over 200 km relative to other features in the D ring. Cassini also finds that the locations of other narrow features in the D ring and the structure of the diffuse material in the D ring differ from those measured by Voyager. Furthermore, Cassini has detected additional ringlets and structures in the D ring that were not observed by Voyager. These include a sheet of material just interior to the inner edge of the C ring that is only observable at phase angles below about 60°. New photometric and spectroscopic data from the ISS (Imaging Science Subsystem) and VIMS (Visual and Infrared Mapping Spectrometer) instruments onboard Cassini show the D ring contains a variety of different particle populations with typical particle sizes ranging from 1 to 100 microns. High-resolution images reveal fine-scale structures in the D ring that appear to be variable in time and/or longitude. Particularly interesting is a remarkably regular, periodic structure with a wavelength of ∼30 km extending between orbital radii of 73,200 and 74,000 km. A similar structure was previously observed in 1995 during the occultation of the star GSC5249-01240, at which time it had a wavelength of ∼60 km. We interpret this structure as a periodic vertical corrugation in the D ring produced by differential nodal regression of an initially inclined ring. We speculate that this structure may have formed in response to an impact with a comet or meteoroid in early 1984.     

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).     

Features around embedded moonlets in Saturn's rings: The role of self-gravity and particle size distributions

This paper presents the results of N-body simulations of moonlets embedded in broad rings, focusing specifically on the saturnian A ring. This work adds to previous efforts by including particle self-gravity and particle size distributions. The discussion here focuses primarily on the features that form in the background particles as a result of the moonlet. Particle self-gravity tends to damp out features produced by embedded moonlets and this damping is enhanced if the moonlet is simply the largest member of a continuous size distribution. Observable features around an embedded moonlet appear to require that the largest ring particles be no more massive than 1/30 the mass of the moonlet. These results, compared with current and future Cassini observations, will provide insight into the nature of the particle population in the saturnian rings. Some time is also spent analyzing the way in which the background particles cluster around the moonlet. The accretion of small particles onto the moonlet can be limited by disruptive collisions with the largest ring particles in the particle size distribution.     

Profiling Saturn's rings by radio occultation

Diffraction of radio waves is a prominent phenomenon in Voyager 1 radio occultation measurements of Saturn's rings. It limits the effective radial resolution of observed signal intensity and phase to the characteristic Fresnel scale F, which is set by the geometry and wavelength, Λ. For the two Voyager wavelengths at Saturn, F ≅ 9–15 km at 3.6 cm Λ, and F ≅ 17–29 km at 13 cm Λ. This limitation can be largely removed by inverse-Fresnel filtering of the complex (i.e., amplitude and phase) observed signals. An Huygens-Fresnel formulation of the diffracted signal in terms of a circularly symmetric, complex gray-screen model of the rings, valid to second order in phase, leads to an exact Fresnel transform solution for the complex transmittance of the screen, which is useful for analysis. Extension of the formulation to fourth order in the phase of the transform kernel provides a practical implementation where the final resolution is limited by uncertainties in system parameters and noise. Consideration of the effects of uncertainties in the geometry, finite width of the data window employed, analytical approximations used, profile reconstruction fidelity required, system thermal noise, and system phase stability shows the phase stability and thermal noise to be the most critical factors for realistic systems. For Voyager at Saturn, phase instability limits radial resolution to values of the order of F/90, or about 200 m for optically thin rings. For more opaque rings, useful signal-to-noise ratios are the limiting factor: the resolution achieved at 3.6 cm Λ is typically 200–400 m over Ring C and the Cassini Division, 1–4 km over Ring A, and is greater than about 4 km over Ring B. For Voyager 2 at Uranus, the achievable resolution at 3.6 cm Λ is set by system phase stability and should approach 30 m as long as the normal opacity does not exceed ∼2. Reconstructed profiles of limited regions of Saturn's rings illustrate the technique. These reveal a remarkable array of small-scale (∼1 km) ring structures, including very sharp edges, narrow ringlets, gaps with distinctive edge profiles, wakes of embedded satellites, bending waves, density waves, and many unidentified wave-like phenomena. Profiles reconstructed over the full extent of the rings are available currently at 4.2 km and 900 m resolutions, and will be available presently at 400 m resolution.     

Apse Alignment of the Uranian Rings

An explanation of the dynamical mechanism for apse alignment of the eccentric uranian rings is necessary before observations can be used to determine properties such as ring masses, particle sizes, and elasticities. The leading model (P. Goldreich and S. Tremaine 1979, Astron J.84, 1638-1641) relies on the ring self-gravity to accomplish this task, yet it yields equilibrium masses which are not in accord with Voyager radio measurements. We explore possible solutions such that the self-gravity and the collisional terms are both involved in the process of apse alignment. We consider limits that correspond to a hot and a cold ring, and we show that pressure terms may play a significant role in the equilibrium conditions for the narrow uranian rings. In the cold ring case, where the scale height of the ring near periapse is comparable to the ring particle size, we introduce a new pressure correction pertaining to a region of the ring where the particles are locked in their relative positions and jammed against their neighbors and the velocity dispersion is so low that the collisions are nearly elastic. In this case, we find a solution such that the ring self-gravity maintains apse alignment against both differential precession (m=1 mode) and the fluid pressure. We apply this model to the uranian α ring and show that, compared to the previous self-gravity model, the mass estimate for this ring increases by an order of magnitude. In the case of a hot ring, where the scale height can reach a value as much as 50 times the particle size, we find velocity dispersion profiles that result in pressure forces which act in such a way as to alter the ring equilibrium conditions, again leading to a ring mass increase of an order of magnitude. We find that such a velocity dispersion profile would require a different mechanism than is currently envisioned for establishing a heating/cooling balance in a finite-sized, inelastic particle ring. Finally, we introduce an important correction to the model of E. I. Chiang and P. Goldreich (2000, Astrophys. J.540, 1084-1090.). These authors relied on collisional forces in the last ∼100 m of an ∼10 km wide ring to increase ring equilibrium masses by up to a factor of ∼100. However, their treatment of ring edges as one-sided surface density drops leads to a strong dependence of the ring mass on the adjustable parameter λ (the length scale over which the ring's optical depth drops from order unity to zero at the edge). A treatment of the ring edges that takes into account their ridgelike structure retains the increase of ring mass of the order of ∼100 for a 10 km wide ring, while exhibiting weak dependence on λ. We conclude that a modified Chiang-Goldreich model can likely account for the masses of narrow, eccentric planetary rings; however, the role of shepherd satellites both in forming ring edges and in altering the streamline precession conditions near them needs to be explored further. It is also unclear whether a fully self-consistent ring model allows for the possibility of rings with negative eccentricity gradients.     

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.     

Saturn A ring surface mass densities from spiral density wave dispersion behavior

We have undertaken an analysis of the Voyager photopolarimeter (PPS) stellar occultation data of Saturn's A ring. The Voyager PPS observed the bright star δ Scorpii as it was occulted by Saturn's main rings during the spacecraft flyby of the Saturn system in 1981. The occultation measurement produced a ring profile with radial resolution of approximately 100 m, and radial structure is evident in the profile down to the resolution limit. We have applied an autoregressive technique to the data for estimating the power spectrum as a function of radius, which has allowed us to identify 40 spiral density waves in Saturn's A ring, associated with the strongest torques due to forcing from the moons. The majority of the detected waves are observed to disperse linearly in regions beginning a few kilometers from the resonance location. We have used the dispersion behavior for those waves to calculate local surface mass densities in the vicinity of each wave. We find that the inner three-quarters of the A ring (up to the beginning of the Encke gap) has an average surface mass density of , while the outer region has an average surface mass density of . The two regions have different mean surface mass densities with a significance of approximately 0.999993, as estimated with a T-statistic, which corresponds to about 4.5σ. While the mean optical depth of the A ring increases slightly with increasing distance from Saturn, we find that it is not significantly correlated with the surface mass density; the two quantities having a linear Pearson's correlation coefficient of r_corr≈−0.03. The variation of mass density, independent of PPS optical depth, is consistent with previous conjectures that the particle size distribution and composition are not constant across the entire A ring, particularly in the very outer portion. We estimate the mass of Saturn's A ring from our surface mass density estimates as 4.9×10²¹ gm, or 8.61×10⁻⁹ of the mass of Saturn, roughly equivalent to the mass of a 110-km diameter icy satellite. This mass is almost 25% smaller than estimates from previous studies, but is well within the expected errors of the derived mass densities. We also identified three previously unstudied features which exhibit linear dispersion. The strongest of these features is tentatively identified as the Janus 13:11 density wave. The other two features do not fall near any known satellite resonances and may represent density waves created by previously undetected satellites.     

Cassini thermal observations of Saturn's main rings: Implications for particle rotation and vertical mixing

In late 2004 and 2005 the Cassini composite infrared spectrometer (CIRS) obtained spatially resolved thermal infrared radial scans of Saturn's main rings (A, B and C, and Cassini Division) that show ring temperatures decreasing with increasing solar phase angle, α, on both the lit and unlit faces of the ring plane. These temperature differences suggest that Saturn's main rings include a population of ring particles that spin slowly, with a spin period greater than 3.6 h, given their low thermal inertia. The A ring shows the smallest temperature variation with α, and this variation decreases with distance from the planet. This suggests an increasing number of smaller, and/or more rapidly rotating ring particles with more uniform temperatures, resulting perhaps from stirring by the density waves in the outer A ring and/or self-gravity wakes.The temperatures of the A and B rings are correlated with their optical depth, τ, when viewed from the lit face, and anti-correlated when viewed from the unlit face. On the unlit face of the B ring, not only do the lowest temperatures correlate with the largest τ, these temperatures are also the same at both low and high α, suggesting that little sunlight is penetrating these regions.The temperature differential from the lit to the unlit side of the rings is a strong, nearly linear, function of optical depth. This is consistent with the expectation that little sunlight penetrates to the dark side of the densest rings, but also suggests that little vertical mixing of ring particles is taking place in the A and B rings.     

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.     

Waves in Cassini UVIS stellar occultations: 2. The C ring

We performed a complete wavelet analysis of Saturn’s C ring on 62 stellar occultation profiles. These profiles were obtained by Cassini’s Ultraviolet Imaging Spectrograph High Speed Photometer. We used a WWZ wavelet power transform to analyze them. With a co-adding process, we found evidence of 40 wavelike structures, 18 of which are reported here for the first time. Seventeen of these appear to be propagating waves (wavelength changing systematically with distance from Saturn). The longest new wavetrain in the C ring is a 52-km-long wave in a plateau at 86,397 km. We produced a complete map of resonances with external satellites and possible structures rotating with Saturn’s rotation period up to the eighth order, allowing us to associate a previously observed wave with the Atlas 2:1 inner Lindblad resonance (ILR) and newly detected waves with the Mimas 6:2 ILR and the Pandora 4:2 ILR. We derived surface mass densities and mass extinction coefficients, finding σ = 0.22(±0.03) g cm⁻² for the Atlas 2:1 ILR, σ = 1.31(±0.20) g cm⁻² for the Mimas 6:2 ILR, and σ = 1.42(±0.21) g cm⁻² for the Pandora 4:2 ILR. We determined a range of mass extinction coefficients (κ = τ/σ) for the waves associated with resonances with κ = 0.13 (±0.03) to 0.28(±0.06) cm² g⁻¹, where τ is the optical depth. These values are higher than the reported values for the A ring (0.01-0.02 cm² g⁻¹) and the Cassini Division (0.07-0.12 cm² g⁻¹ from Colwell et al. (Colwell, J.E., Cooney, J.H., Esposito, L.W., Srem?evi?, M. [2009]. Icarus 200, 574-580)). We also note that the mass extinction coefficient is probably not constant across the C ring (in contrast to the A ring and the Cassini Division): it is systematically higher in the plateaus than elsewhere, suggesting smaller particles in the plateaus. We present the results of our analysis of these waves in the C ring and estimate the mass of the C ring to be between3.7(±0.9) × 10¹⁶ kg and 7.9(±2.0) × 10¹⁶ kg (equivalent to an icy satellite of radius between 28.0(±2.3) km and 36.2(±3.0) km with a density of 400 kg m⁻³, close to that of Pan or Atlas). Using the ring viscosity derived from the wave damping length, we also estimate the vertical thickness of the C ring between 1.9(±0.4) m and 5.6(±1.4) m, comparable to the vertical thickness of the Cassini Division.     

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.     

Keck and VLT AO observations and models of the uranian rings during the 2007 ring plane crossings

We present observations of the uranian ring system at a wavelength of 2.2 μm, taken between 2003 and 2008 with NIRC2 on the W.M. Keck telescope in Hawaii, and on 15–17 August 2007 with NaCo on the Very Large Telescope (VLT) in Chile. Of particular interest are the data taken around the time of the uranian ring plane crossing with Earth on 16 August 2007, and with the Sun (equinox) on 7 December 2007. We model the data at the different viewing aspects with a Monte Carlo model to determine: (1) the normal optical depth τ₀, the location, and the radial extent of the main rings, and (2) the parameter Aτ₀ (A is the particle geometric albedo), the location, and the radial plus vertical extent of the dusty rings. Our main conclusions are: (i) The brightness of the ? ring is significantly enhanced at small phase and ring inclination angles; we suggest this extreme opposition effect to probably be dominated by a reduction in interparticle shadowing. (ii) A broad sheet of dust particles extends inwards from the λ ring almost to the planet itself. This dust sheet has a vertical extent of ∼140 km, and Aτ₀ = 2.2 × 10⁻⁶. (iii) The dusty rings between ring 4 and the α ring and between the α and β rings are vertically extended with a thickness of ∼300 km. (iv) The ζ ring extends from ∼41,350 km almost all the way inwards to the planet. The main ζ ring, centered at ∼39,500 km from the planet, is characterized by Aτ₀ = 3.7 × 10⁻⁶; this parameter decreases closer to the planet. The ζ ring has a full vertical extent of order 800–900 km, with a pronounced density enhancement in the mid-plane. (v) The η_c ring is optically thin and less than several tens of km in the vertical direction. This ring may be composed of macroscopic material, surrounded by clumps of dust.     

Morphology and variability of the Titan ringlet and Huygens ringlet edges

We present a forward modeling approach for determining, in part, the ring particle spatial distribution in the vicinity of sharp ring or ringlet edges. Synthetic edge occultation profiles are computed based on a two-parameter particle spatial distribution model. One parameter, h, characterizes the vertical extent of the ring and the other, δ, characterizes the radial scale over which the ring optical depth transitions from the background ring value to zero. We compare our synthetic occultation profiles to high resolution stellar occultation light curves observed by the Cassini Ultraviolet Imaging Spectrograph (UVIS) High Speed Photometer (HSP) for occultations by the Titan ringlet and Huygens ringlet edges.More than 100 stellar occultations of the Huygens ringlet and Titan ringlet edges were studied, comprising 343 independent occultation cuts of the edges of these two ringlets. In 237 of these profiles the measured light-curve was fit well with our two-parameter edge model. Of the remaining edge occultations, 69 contained structure that could only be fit with extremely large values of the ring-plane vertical thickness (h > 1 km) or by adopting a different model for the radial profile of the ring optical depth. An additional 37 could not be fit by our two-parameter model.Certain occultations at low ring-plane incidence angles as well as occultations nearly tangent to the ring edge allow the direct measurement of the radial scale over which the particle packing varies at the edge of the ringlet. In 24 occultations with these particular viewing geometries, we find a wide variation in the radial scale of the edge. We are able to constrain the vertical extent of the rings at the edge to less than ∼300 m in the 70% of the occultations with appropriate viewing geometry, however tighter constraints could not be placed on h due to the weaker sensitivity of the occultation profile to vertical thickness compared to its sensitivity to δ.Many occultations of a single edge could not be fit to a single value of δ, indicating large temporal or azimuthal variability, although the azimuthal variation in δ with respect to the longitudes of various moons in the system did not show any discernible pattern.     

Evolution of the dusty rings of Uranus

We present high quality images of the uranian ring system, obtained in August 2002, October 2003, and July 2004 at 2.2 μm with the adaptive optics camera NIRC2 on the Keck II telescope. Using these data, we report the first detection in backscattered light of a ring (which we refer to as the ζ ring) interior to Uranus' known rings. This ring consists of a generally uniform sheet of dust between 37,850 and 41,350 km with an equivalent width (in 2004; or ), and extends inward to 32,600 km at a gradually decreasing brightness. This ring might be related to the Voyager ring R/1986 U 2, although both its location and extent differ. This could be attributed to a difference in observing wavelength and/or solar phase angle, or perhaps to temporal variations in the ring. Through careful modeling of the I/F of the individual rings at each ansa, we reveal the presence of narrow (few 100 km wide) sheets of dust between the δ and ε rings, and between rings 4 and α. We derived a typical anisotropy factor g≈0.7 in the scattering behavior of these particles. The spatial distribution and relative intensity of these dust sheets is different than that seen in Voyager images taken in forward scattered light, due either to a difference in observing wavelength, and/or solar phase angle or to changes over time. We may have detected the λ ring in one scan at , but other scans provided upper limits below this value. A single detection, however, would be consistent with azimuthal asymmetries known to exist in this ring. We further demonstrate the presence of azimuthal asymmetries in all rings. We confirm the eccentricity of ∼0.001 in rings 4, 5, 6, which in 2004 are ∼70 km closer to Uranus in the north (near periapse; lower I/F) than in the south. We find a global optical depth of τ∼0.3 in the main rings, and of τ=0.25±0.05 in the ε ring.     

Solar infrared occultation observations by SPICAM experiment on Mars-Express: Simultaneous measurements of the vertical distributions of H2O, CO2 and aerosol

The infrared AOTF spectrometer is a part of the SPICAM experiment onboard the Mars-Express ESA mission. The instrument has a capability of solar occultations and operates in the spectral range of 1-1.7 μm with a spectral resolution of ∼3.5 cm⁻¹. We report results from 24 orbits obtained during MY28 at Ls 130°-160°, and the latitude range of 40°-55° N. For these orbits the atmospheric density from 1.43 μm CO₂ band, water vapor mixing ratio based on 1.38 μm absorption, and aerosol opacities were retrieved simultaneously. The vertical resolution of measurements is better than 3.5 km. Aerosol vertical extinction profiles were obtained at 10 wavelengths in the altitude range from 10 to 60 km. The interpretation using Mie scattering theory with adopted refraction indices of dust and H₂O ice allows to retrieve particle size (reff∼0.5-1 μm) and number density (∼1 cm⁻³ at 15-30 km) profiles. The haze top is generally below 40 km, except the longitude range of 320°-50° E, where high-altitude clouds at 50-60 km were detected. Optical properties of these clouds are compatible with ice particles (effective radius reff=0.1-0.3 μm, number density N∼10 cm−3) distributed with variance νeff=0.1-0.2 μm. The vertical optical depth of the clouds is below 0.001 at 1 μm. The atmospheric density profiles are retrieved from CO₂ band in the altitude range of 10-90 km, and H₂O mixing ratio is determined at 15-50 km. Unless a supersaturation of the water vapor occurs in the martian atmosphere, the H₂O mixing ratio indicates ∼5 K warmer atmosphere at 25-45 km than predicted by models.