The vertical structure of the F ring of Saturn from ring-plane crossings

We present a photometric model of the rings of Saturn which includes the main rings and an F ring, inclined to the main rings, with a Gaussian vertical profile of optical depth. This model reproduces the asymmetry in brightness between the east and west ansae of the rings of Saturn that was observed by the Hubble Space Telescope (HST) within a few hours after the Earth ring-plane crossing (RPX) of 10 August 1995. The model shows that during this observation the inclined F ring unevenly blocked the east and west ansae of the main rings. The brightness asymmetry produced by the model is highly sensitive to the vertical thickness and radial optical depth of the F ring. The F-ring model that best matches the observations has a vertical full width at half maximum of 13 ± 7 km and an equivalent depth of 10 ± 4 km. The model also reproduces the shape of the HST profiles of ring brightness vs. distance from Saturn, both before and after the time of ring-plane crossing. Smaller asymmetries observed before the RPX, when the Earth was on the dark side of the rings, cannot be explained by blocking of the main rings by the F ring or vice versa and are probably instead due to the intrinsic longitudinal variation exhibited by the F ring.     

Keck near-infrared observations of Saturn's E and G rings during Earth's ring plane crossing in August 1995

We present near-infrared (1.24-2.26 μm) images of Saturn's E and G rings which were taken with the W.M. Keck telescope in 1995 August 9-11, during the period that Earth crossed Saturn's ring plane. Our data confirm that the E ring is very blue. Its radial and vertical structure are found to be remarkably similar to that apparent in the HST ringplane crossing data at visible wavelengths, reinforcing models of the ring's peculiar narrow or very steep particle size distribution. Our data show unambiguously that the satellite Tethys is a secondary source of material for the E ring. The G ring is found to be distinctly red, similar in color to Jupiter's main ring, indicative of a (more typical) broad particle size distribution.     

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.     

Voyager color photometry of Saturn's main rings: a correction

We correct a calibration error in our earlier analysis of Voyager color observations of Saturn's main rings at 14° phase angle (Estrada and Cuzzi, 1996, Icarus 122, 251) and present thoroughly revised and reanalyzed radial profiles of the brightness of the main rings in the Voyager green, violet, and ultraviolet filters and the ratios of these brightnesses. These results are consistent with more recent HST results at 6° phase angle, once allowance is made for plausible phase reddening of the rings (Cuzzi et al., 2002, Icarus 158, 199). Unfortunately, the Voyager camera calibration factors are simply not sufficiently well known for a combination of the Voyager and HST data to be used to constrain the phase reddening quantitatively. However, some interesting radial variations in reddening between 6 and 14° phase angles are hinted at. We update a ring-and-satellite color vs albedo plot from Cuzzi and Estrada (1998, Icarus 132, 1) in several ways. The A and B rings are still found to be in a significantly redder part of color-albedo space than Saturn's icy satellites.     

Photometry of the unlit face of Saturn's rings

From our telescopic observations of Saturn's rings in 1966, 1979, and 1980, the luminance of the unlit face at λ = 0.58 μm is derived as a function of the height B′ of the Sun above the lit face. A maximum is reached at B′ = 1.9° and a decrease is observed for larger values of B′. Ring B is 1.8 time less bright than ring A and Cassini division. The unlit/lit luminances ratios for the two rings merged together is 8% at B′ = 1.0° and 3% at B′ = 2.8°. The larger value at more grazing incidence is related to the photometric “opposition effect” which reflects more of the incident light backward into the ring plane when the height of the sun is small; the light so reflected is again reflected and scattered and a certain flux reaches the unlit face to escape toward the observer. The unlit face luminances for blue and for yellow light indicate a contribution by micron size particles. The Saturn globe produces a ring illumination which, observed from the Earth, amounts to 1.8 × 10^?3 of the disk center reflectance. The rings observed exactly edge-on do not disappear but a faint lineament remains, which produces a flux of (0.30 ± 0.15) 10^?3 times the brightness of a segment of 1 arcsec width at Saturn disk center; illuminations of rings' borders or particles outside the exact ring plane are indicated.     

Infrared observations of Saturn's rings by Cassini CIRS : Phase angle and local time dependence

Since the Saturn orbit insertion (SOI) of the Cassini spacecraft, in July 2004, the Cassini Composite Infrared Spectrometer (CIRS) has obtained a large number of thermal infrared spectra of Saturn's rings. Over the two and a half years of observations to date, ring temperatures were retrieved for a large range of unique geometries, inaccessible from Earth. Understanding their dependencies with phase angle and local time is a clue to understanding the thermal properties and dynamics of Saturn's ring particles.Azimuthal scans of rings, which have been obtained by CIRS at constant radial distance from the planet, have been planned to measure ring temperature variations with local hour angle. Over 47 azimuthal scans for Saturn's main rings (A, B, C and Cassini Division) have been retrieved to date, on both lit and unlit sides, at different phase angles and spacecraft elevations. The first measurements of the transient thermal episode of eclipse cooling in the planetary shadow have also been obtained for all three rings.In this paper, we present an overview of all azimuthal scans obtained by the Cassini/CIRS instrument so far and the dependencies of the temperature and the filling factor with the phase angle and the local hour angle. The ring temperature varies with longitude as the input heating flux coming from Saturn and the Sun changes. The decrease in temperature with the increasing phase angle on both the lit and the unlit sides and for most of the local time also suggests the presence of slowly rotating particles. The crossing of the planet's shadow generates drastic azimuthal variations in temperature, up to 20 K in the C ring. The strong anisotropy of emission observed outside the shadow between low and high phase angles decreases when ring particles cross the shadow, suggesting that particles are almost isothermal in the shadow. This suggests a thermal inertia associated with a rotating rate of particles low enough to have a thermal contrast on their surface.The temperature in the B ring is less sensitive to the phase angle effect on the lit side, suggesting that particles are close enough to form a flat layer at a scale larger than the particle's radius. On the unlit side, particles in the B ring are less sensitive to the lack of solar input than in the C ring or in the A ring. Azimuthal variations of the filling factor in the A ring are also detected with changing ring local time. This effect might be created by the presence of gravitational instabilities (wakes).     

Thermal observations of Saturn's main rings by Cassini CIRS: Phase, emission and solar elevation dependence

Two and a half years after Saturn orbit insertion (SOI) the Cassini composite infrared spectrometer (CIRS) has acquired an extensive set of thermal measurements (including physical temperature and filling factor) of Saturn's main rings for a number of different viewing geometries, most of which are not available from Earth. Thermal mapping of both the lit and unlit faces of the rings is being performed within a multidimensional observation space that includes solar phase angle, spacecraft elevation and solar elevation. Comprehensive thermal mapping is a key requirement for detailed modeling of ring thermal properties.To first order, the largest temperature changes on the lit face of the rings are driven by variations in phase angle while differences in temperature with changing spacecraft elevation are a secondary effect. Ring temperatures decrease with increasing phase angle suggesting a population of slowly rotating ring particles [Spilker, L.J., Pilorz, S.H., Wallis, B.D., Pearl, J.C., Cuzzi, J.N., Brooks, S.M., Altobelli, N., Edgington, S.G., Showalter, M., Michael Flasar, F., Ferrari, C., Leyrat, C. 2006. Cassini thermal observations of Saturn's main rings: implications for particle rotation and vertical mixing. Planet. Space Sci. 54, 1167-1176, doi: 10.1016/j.pss.2006.05.033]. Both lit A and B rings show that temperature decreases with decreasing rings solar elevation while temperature changes in the C ring and Cassini Division are more muted. Variations in the geometrical filling factor, β, are primarily driven by changes in spacecraft elevation. For the optically thinnest region of the C ring, β variations are found to be nearly exclusively determined by spacecraft elevation. Both a multilayer and a monolayer model provide an excellent fit to the data in this region. In both cases, a ring infrared emissivity >0.9 is required, together with a random and homogeneous distribution of the particles. The interparticle shadowing function required for the monolayer model is very well constrained by our data and matches experimental measurements performed by Froidevaux [1981a. Saturn's rings: infrared brightness variation with solar elevation. Icarus 46, 4-17].     

Keck Adaptive Optics Images of Uranus and Its Rings

We present adaptive optic images of Uranus obtained with the 10-m W. M. Keck II telescope in June 2000, at wavelengths between 1 and 2.4 μm. The angular resolution of the images is ∼0.06-0.09″. We identified eight small cloud features on Uranus's disk, four of which were in the northern hemisphere. The latter features are ∼1000-2000 km in extent and located in the upper troposphere, above the methane cloud, at pressures between 0.5 and 1 bar. Our data have been combined with HST data by Hammel et al. (2001, Icarus153, 229-235); the combination of Keck and HST data allowed derivation of an accurate wind velocity profile. Our images further show Uranus's entire ring system: the asymmetric ? ring, as well as the three groups of inner rings (outward from Uranus): the rings 6+5+4, α+β, and the η+γ+δ rings. We derived the equivalent I/F width and ring particle reflectivity for each group of rings. Typical particle albedos are ∼0.04-0.05, in good agreement with HST data at 0.9 μm.     

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.     

Brightness of Saturn's rings with decreasing solar elevation

Early ground-based and spacecraft observations suggested that the temperature of Saturn's main rings (A, B and C) varied with the solar elevation angle, B^′. Data from the composite infrared spectrometer (CIRS) on board Cassini, which has been in orbit around Saturn for more than five years, confirm this variation and have been used to derive the temperature of the main rings from a wide variety of geometries while B^′ varied from near −24^° to 0^° (Saturn's equinox).Still, an unresolved issue in fully explaining this variation relates to how the ring particles are organized and whether even a simple mono-layer or multi-layer approximation describes this best. We present a set of temperature data of the main rings of Saturn that cover the ∼23^°—range of B^′ angles obtained with CIRS at low (α∼30^°) and high (α≥120^°) phase angles. We focus on particular regions of each ring with a radial extent on their lit and unlit sides. In this broad range of B^′, the data show that the A, B and C rings’ temperatures vary as much as 29-38, 22-34 and 18-23 K, respectively. Interestingly the unlit sides of the rings show important temperature variations with the decrease of B^′ as well. We introduce a simple analytical model based on the well known Froidevaux monolayer approximation and use the ring particles’ albedo as the only free parameter in order to fit and analyze this data and estimate the ring particle's albedo. The model considers that every particle of the ring behaves as a black body and warms up due to the direct energy coming from the Sun as well as the solar energy reflected from the atmosphere of Saturn and on its neighboring particles. Two types of shadowing functions are used. One analytical that is used in the latter model in the case of the three rings and another, numerical, that is applied in the case of the C ring alone. The model lit side albedo values at low phase are 0.59, 0.50 and 0.35-0.38 for the A, B and C rings, respectively.     

Near-infrared adaptive optics imaging of the satellites and individual rings of Uranus

We present the first Earth-based images of several of the individual faint rings of Uranus, as observed with the adaptive optics system on the W.M. Keck II telescope on four consecutive days in October 2003. We derive reflectivities based on multiple measurements of 8 minor moons of Uranus as well as Ariel and Miranda in filters centered at wavelengths of 1.25(J), 1.63(H), and 2.1(Kp) μm. These observations have a phase angle of 1.84°-1.96°. We find that the small satellites are somewhat less bright than in observations made by the HST at smaller phase angles, confirming an opposition surge effect. We calculate albedoes for the ring groups and for each ring separately. We find that the ε ring particles, as well as the particles in the three other ring groups, have albedoes near 0.043 at these phase angles. The equivalent depths of some of the individual rings are different than predicted based upon ring widths from occultation measurements (assuming a constant particle ring brightness); in particular the γ ring is fainter and the η ring brighter than expected. Our results indicate that q, the ratio of ε ring intensity at apoapse vs. periapse, is close to 3.2±0.16. This agrees well with a model that has a filling factor for the ε ring of 0.06 (Karkoschka, 2001, Icarus 151, 78-83). We also determine values of the north to south brightness ratio for the individual rings and find that in most cases they are close to unity.     

The jovian rings: new results derived from Cassini, Galileo, Voyager, and Earth-based observations

Cassini's Imaging Science Subsystem (ISS) instrument took nearly 1200 images of the Jupiter ring system during the spacecraft's 6-month encounter with Jupiter (Porco et al., 2003, Science 299, 1541-1547). These observations constitute the most complete data set of the ring taken by a single instrument, both in phase angle (0.5°-120° at seven angles) and wavelength (0.45-0.93 μm through eight filters). The main ring was detected in all targeted exposures; the halo and gossamer rings were too faint to be detected above the planet's stray light. The optical depth and radial profile of the main ring are consistent with previous observations. No broad asymmetries within the ring were seen; we did identify possible hints of 1000 km-scale azimuthal clumps within the ring. Cassini observations taken within 0.02° of the ring plane place an upper limit on the ring's full thickness of 80 km at a phase angle of 64°. We have combined the Cassini ISS and VIMS (Visible and Infrared Mapping Spectrometer) observations with those from Voyager, HST (Hubble Space Telescope), Keck, Galileo, Palomar, and IRTF (Infrared Telescope Facility). We have fit the entire suite of data using a photometric model that includes microscopic silicate dust grains as well as larger, long-lived ‘parent bodies’ that engender this dust. Our best-fit model to all the data indicates an optical depth of small particles of τ_s=4.7×10⁻⁶ and large bodies τ_l=1.3×10⁻⁶. The dust's cross-sectional area peaks near 15 μm. The data are fit significantly better using non-spherical rather than spherical dust grains. The parent bodies themselves must be very red from 0.4-2.5 μm, and may have absorption features near 0.8 and 2.2 μm.     

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.     

Photometric modeling of Saturn's rings. II. Azimuthal asymmetry in reflected and transmitted light

Dynamical N-body simulations (Salo, 992, Nature 359, 619) suggest the formation of trailing density enhancements in the outer portions of Saturn's rings, due to local gravitational instabilities. These Julian-Toomre type wakes, having a pitch angle of about 20°-25° with respect to the local tangential direction, seem to provide a plausible explanation for the observed quadrupole brightness variation in Saturn's A ring (Salo and Karjalainen, 1999, Bull. Am. Astron. Soc. 31, 1160; French et al., 2000, Bull. Am. Astron. Soc. 32, 806; Porco et al., 2001, Bull. Am. Astron. Soc. 33, 1091). We have carried out systematic photometric modeling of gravitational wake structures seen in dynamical simulations, performed for the parameter values of the A ring, using the Monte Carlo radiative transfer code described in Salo and Karjalainen (2003, Icarus 164, 428). Comparisons to the observed asymmetry in various cases are presented (asymmetry in reflected and transmitted light, ring longitude and opening angle dependence), in all cases confirming the applicability of the wake model. Typically, minimum brightness corresponds to viewing/illumination along the long axis of wakes; however, the sense of modeled asymmetry reverses at small tilt angles in diffuse transmission. Implications of wakes on the occultation optical depth profiles and the A ring overall brightness behavior are also discussed: it is shown that the wake structure needs to be taken into account when the Cassini occultation profiles for the A ring are interpreted in terms of variations in surface density. Also, the presence of wakes offers a plausible explanation for the inverse tilt effect seen in the mid A-ring.     

Observation and photometry of an outer ring of saturn

A faint outer ring (E ring), which lies outside the classical rings A, B, C, and F, has been detected out to eight Saturn radii. We first observed it on November 1, 1979, and thereby confirmed the 1966 observation by Feibelman. Our plates were taken with a coronographic design and are specially intended for photometry. They are directly scaled in reflectance by reference to the Saturn disk which is properly attenuated. Photometry of the edge-on ring E lineament shows a strong brightness increase at small phase angles, which is compatible with scattering by particles of several microns in radius. The excess reflectivity in blue compared to the B ring implies a significant contribution of small particles in the scattering process. The E ring shows brightness and radial gradient changes, with condensations, which differ between east and west limbs and are not always the same from night to night. The E ring is probably a flat structure with a condensation centered at a distance of 4 R_s, but without a simple axial symmetry. It is probably shaped by segments or lumps and may have streamerlike structures.     

Bar-driven evolution of S0s: the edge-on galaxy NGC 4570

We present circumstantial evidence that the central region of the edge-on S0 galaxy NGC 4570, which harbours a 150-pc scale nuclear disc in addition to its main outer disc, has been shaped under the influence of a small (∼ 500 pc) bar. This is based on the discovery of two edge-on rings, the locations of which are consistent with the inner Lindblad and ultraharmonic resonances of a rapidly tumbling triaxial potential. Observed features in the photometry and rotation curve correspond nicely with the positions of the main resonances, strengthening the case for a tumbling bar potential. The relative blue colour of the ILR ring, and the complete absence of any detected ISM, indicates that the nuclear ring is made of relatively young (≲ 2 Gyr) stars. We discuss a possible secular evolution scenario for this complex multicomponent galaxy, which may also apply to many other S0 galaxies with observed rings and/or multiple disc components.     

Thermal response of Saturn's ring particles during and after eclipse

We present infrared (20 μm) observations of Saturn's rings for a solar elevation angle of 10° and phase angle of 6°. Scans across the rings yield information about the cooling of particles during eclipse and the subsequent heating along their orbits. All three rings exhibit significant cooling during eclipse, as well as a 20-μm brightness asymmetry between east and west ansae, the largest asymmetry occuring in the C ring (the brightest ring). The eclipse cooling is a simple and adequate explanation for 20-μm brightness asymmetries between the ansae of Saturn's rings. The relatively large C ring asymmetry is thought to be primarily due to the short travel time of the particles in that ring from eclipse exit to east ansa. We compare the B ring data to the theoretical models of H.H. Aumann and H.H. Kieffer (1973, Astrophys. J.186, 305–311) in order to set constraints on the average particle size and thermal inertia. The rather rapid heating after exit from eclipse points to low-conductivity-particle surfaces, similar to the water frost surfaces of Galilean satellites. If the surface conductivity is indeed low, one cannot determine an upper limit for the particle size through such infrared observations, since only the uppermost millimeters experience a thermal response during eclipse. However, based on these infrared data alone, it is clear that particles of radius equal to a few millimeters or less cannot occupy a significant fraction of the ring surface area, because-regardless of thermal inertia-their thermal response is much faster than observed.     

A deep search for Martian dust rings and inner moons using the Hubble Space Telescope

It has long been suspected that Mars might be encircled by two faint rings, one originating from each of its moons Phobos and Deimos. Meteoroid impacts into these moons should release clouds of dust that quickly spread out to become rings; similar dust rings have been associated with several small inner moons of the gas giants. On May 28, 2001 Mars’ hypothetical ring plane appeared edge-on to Earth within weeks of its opposition, providing the best Earth-based opportunity to detect these rings in several decades. Using the Wide Field/Planetary Camera 2 (WFPC2) on the Hubble Space Telescope, we obtained a set of deep exposures off the east and west limbs of Mars to search for these hypothetical rings. No rings were detected. This result limits normal optical depths to ∼3×10⁻⁸ for the Phobos ring and ∼10⁻⁷ for the Deimos ring. These limits fall at the low end of prior dynamical predictions and a factor of 1000 below previous observational limits. However, our limit for the Deimos ring is more tentative because of large uncertainties about this ring's expected shape, size and orientation. Our data set is also sensitive to small, previously undetected inner moons. No moons were detected down to a radius limit of 75–125 m. Longitudinal coverage of the region near and between Phobos and Deimos is 40–80% complete. We conclude by describing a promising opportunity for further Martian ring viewing in December 2007.     

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.     

Saturn's rings: Infrared brightness variation with solar elevation

The variation in infrared equilibrium brightness temperature of Saturn's A, B, and C rings is modeled as a function of solar elevation B′ with respect to the ring plane. The basic model includes estimates of minimum and maximum interparticle shadowing in a monolayer approximation. Simple laboratory observations of random particle distributions at various illumination angles provide more realistic shadowing functions. Radiation balance calculations yield the physical (kinetic) temperature of particles in equilibrium with radiation from the Sun, Saturn, and neighboring particles. Infrared brightness temperatures as a function of B′ are then computed and compared to the available 20-μm data (Pioneer results are also briefly discussed). The A and B rings are well modeled by an optically thick monolayer, or equivalently, a flat sheet, radiating from one side only. This points to a temperature contrast between the two sides, possibly due to particles with low thermal inertia. Other existing models for the B ring are discussed. The good fit for the monolayer model does not rule out the possibility that the A and B rings are many particles thick. It could well be that a multilayer ring produces an infrared behavior (as a function of tilt angle) similar to that of a monolayer. The C ring brightness increases as B′ decreases. This contrast in behavior can be understood simply in terms of the low C ring optical depth and small amount of interparticle shadowing. High-albedo particles (A?0.5) can fit the C ring infrared data if they radiate mostly from one hemisphere due to slow rotation or low thermal inertia (or both). Alternatively, particles isothermal over their surface (owing to a rapid spin, high inertia, or small size), and significantly darker (A?0.3) than the A and B ring particles, can produce a similar brightness variation with ring inclination. In any case, the C ring particles have significantly hotter physical temperatures than the particles in the A and B rings, whether or not the rings form a monolayer.