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.     

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.     

Saturn's rings: 3-mm low-inclination observations and derived properties

Recent 3-mm observations of Saturn at low ring inclinations are combined with previous observations of E. E. Epstein, M. A. Janssen, J. N. Cuzzi, W. G. Fogarty, and J. Mottmann (Icarus41, 103–118) to determine a much more precise brightness temperature for Saturn's rings. Allowing for uncertainties in the optical depth and uniformity of the A and B rings and for ambiguities due to the C ring, but assuming the ring brightness to remain approximately constant with inclination, a mean brightness temperature for the A and B rings of 17 ± 4°K was determined. The portion of this brightness attributed to ring particle thermal emission is 11 ± 5°K. The disk temperature of Saturn without the rings would be 156 ± 6°K, relative to B. L. Ulich, J. H. Davis, P. J. Rhodes, and J. M. Hollis' (1980, IEEE Trans. Antennas Propag.AP-28, 367–376) absolutely calibrated disk temperature for Jupiter. Assuming that the ring particles are pure water ice, a simple slab emission model leads to an estimate of typical particle sizes of ≈0.3 m. A multiple-scattering model gives a ring particle effective isotropic single-scattering albedo of 0.85 ± 0.05. This albedo has been compared with theoretical Mie calculations of average albedo for various combinations of particle size distribution and refractive indices. If the maximum particle radius (≈5 m) deduced from Voyager bistatic radar observations (E. A. Marouf, G. L. Tyler, H. A. Zebker, V. R. Eshleman, 1983, Icarus54, 189–211) is correct, our results indicate either (a) a particle distribution between 1 cm and several meters radius of the form r^?s with 3.3 ? s ? 3.6, or (b) a material absorption coefficient between 3 and 10 times lower than that of pure water ice Ih at 85°K, or both. Merely decreasing the density of the ice Ih particles by increasing their porosity will not produce the observed particle albedo. The low ring brightness temperature allows an upper limit on the ring particle silicate content of ≈10% by mass if the rocky material is uniformly distributed; however, there could be considerably more silicate material if it is segregated from the icy material.     

Rotation rate and velocity dispersion of planetary ring particles with size distribution II. Numerical simulation for gravitating particles

We examine rotation rates of gravitating particles in low optical depth rings, on the basis of the evolution equation of particle rotational energy derived by Ohtsuki [Ohtsuki, K., 2006. Rotation rate and velocity dispersion of planetary ring particles with size distribution. I. Formulation and analytic calculation. Icarus 183, 373-383]. We obtain the rates of evolution of particle rotation rate and velocity dispersion, using three-body orbital integration that takes into account distribution of random velocities and rotation rates. The obtained stirring and friction rates are used to calculate the evolution of velocity dispersion and rotation rate for particles in one- and two-size component rings as well as those with a narrow size distribution, and agreement with N-body simulation is confirmed. Then, we perform calculations to examine equilibrium rotation rates and velocity dispersion of gravitating ring particles with a broad size distribution, from 1 cm up to 10 m. We find that small particles spin rapidly with 〈ω²〉^1/2/Ω?¹⁰²-¹⁰³, where ω and Ω are the particle rotation rate and its orbital angular frequency, respectively, while the largest particles spin slowly, with 〈ω²〉^1/2/Ω?1. The vertical scale height of rapidly rotating small particles is much larger than that of slowly rotating large particles. Thus, rotational states of ring particles have vertical heterogeneity, which should be taken into account in modeling thermal infrared emission from Saturn's rings.     

Infrared brightness temperature of Saturn's rings based on the inhomogeneous multilayer assumption

Models of Saturn's rings based on the classical multilayer assumption have been studied in the infrared. Thermal energy balance of Saturn's rings is treated rigorously by solving the infrared radiative transfer equations. It was found that a homogeneous multilayer model is incompatible with the observed infrared brightness variation of the A and B rings, although it can fit that of the C ring. The alternative inhomogeneous multilayer model with dark particles within a bright haze of small icy particles is presented in order to satisfy the available infrared data of the A, B, and C rings. The results based on the inhomogeneous multilayer model may be summarized as follows: The observed infrared brightness data of the three rings are explained in terms of the different optical thickness without having significant differences in the ring-particle properties, such as albedo, spin rate, and sizes. But each ring contains a different amount of bright haze particles and their concentration within the rings depends on whether or not dark particles emit radiation mostly from one hemisphere (slow rotator and/or low thermal inertia). If a dark particle is an isothermal radiator, the possible ranges of A₁ and A₂ for all three rings are given by 0.9 ? A₁ ? 0.95 and 0.0 ? A₂ ? 0.15, where A₁ and A₂ are the bolometric bond albedos of a bright haze and a dark particle, respectively. The possible ranges of the optical thickness ratio X of the dark particle layer to the total ring layer for the rings A, B, and C are given by 0.65 ? X ? 0.75, 0.8 ? X ? 0.9, and 0.8 ? X ? 1.0, respectively. If a dark particle is a slow rotator, we obtain 0.9 ? A₁ ? 0.95 and 0.0 ? A₂ ? 0.4 for all three rings. The ranges of X for the rings A, B, and C are given by 0.35 ? X ? 0.7, 0.65 ? X ? 0.9, and 0.35 ? X ? 1.0, respectively. In this paper, for the first time, a consistent model is presented which is applicable to all three rings from the multilayer point of view.     

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.     

The brightness temperatures of Saturn and its rings at 39 microns

We have resolved the relative rings-to-disk brightness (specific intensity) of Saturn at 39 μm (δλ ? 8 μm) using the 224-cm telecscope at Mauna Kea Oservatory, and have also measured the total flux of Saturn relative to Jupiter in the same bandpass from the NASA Learjet Observatory. These two measurements, which were made in early 1975 with Saturn's rings near maximum inclination (b′ ? 25°), determine the disk and average ring (A and B) brightness in terms of an absolute flux calibration of Jupiter in the same bandpass. While present uncertainties in Jupiter's absolute calibration make it possible to compare existing measurementsunambiguously, it is nevertheless possible to conclude the following: (1) observations between 20 and 40 μm are all compatible (within 2σ) of a disk brightness temperature of 94°K, and do not agree with the radiative equilibrium models of Trafton; (2) the rings at large tilt contribute a flux component comparable to that of the planet itself for λ ? 40 μm and (3) there is a decrease of ～22% in the relative ring: disk brightness between effective wavelengths of 33.5 and 39 μm.     

The color of the Uranian rings

Observations of the Uranian rings were made in several color filters by the Voyager Imaging Science experiment in January 1986 for the purpose of determining the color of the rings. Selected images were taken through the Violet (λ = 0.41 μm), Clear (λ = 0.48 μm), and Green (λ = 0.55 μm) filters of the Voyager 2 narrow angle camera. The results of the analysis are consistent with the α, β, η, γ, δ, and ϵ rings being very dark, with flat spectra throughout the visible, and are comparable to the latest Voyager results showing a lack of color for the Uranian satellites. The general lack of color in the ring/satellite system of Uranus is remarkably different than the case of the distinctly reddish systems of Jupiter and Saturn. The unique combination of low absolute reflectivity and flat spectrum which characterizes the Uranian rings supports the concept that the Uranian ring material is compositionally distinct from either the Si- and S-rich Jovian ring and inner satellites, or the water-ice-rich rings and inner satellites of Saturn. Of all cosmically abundant materials, the candidate which best matches the low brightness and flat spectrum of the Uranian rings is carbon.     

On the rotation of a moonlet embedded in planetary rings

We examine the rotation of a small moonlet embedded in planetary rings caused by impacts of ring particles, using analytic calculation and numerical orbital integration for the three-body problem. Taking into account the Rayleigh distribution of particles' orbital eccentricities and inclinations, we evaluate both systematic and random components of rotation, where the former arises from an average of a large number of small impacts and the latter is contribution from large impacts. Calculations for parameter values corresponding to inner parts of Saturn's rings show that a moonlet would spin slowly in the prograde direction if most impactors are small particles whose velocity dispersion is comparable to or smaller than the moonlet's escape velocity. However, we also find that the effect of the random component can be significant, if the velocity dispersion of particles is larger and/or impacts of large particles comparable to the moonlet's size are common: in this case, both prograde and retrograde rotations can be expected. In the case of a small moonlet embedded in planetary rings of equal-sized particles, we find that the systematic component dominates the moonlet rotation when m/M?0.1 (m and M are the mass of a particle and a moonlet, respectively), while the random component is dominant when m/M?0.3. We derive the condition for the random component to dominate moonlet rotation on the basis of our results of three-body orbital integration, and confirm agreement with N-body simulation.     

Saturn's rings: II. Condensations of light and optical thickness of Cassini's division

“Condensations” of light have been observed when Saturn's rings are seen almost edge on, and the Sun and the Earth are on opposite sides of the ring plane. These condensations are associated with ring C and Cassini's division. If the relative brightness between the two condensations and the optical thickness of ring C are known, we can calculate the optical thickness of Cassini's division, τ_CASS. Using Barnard's and Sekiguchi's measurements, we have obtained 0.01 ? τ_CASS ? 0.05. A brightness profile of the condensations which agrees well with visual observations is also presented.We are able to set an upper limit of about 0.01 for the optical thickness of any hypothetical outer ring. This rules out a ring observed by C. Cragg in 1954, but does not eliminate the D′ ring observed by Feibelman in 1967.It is known that the outer edge of ring B is almost at the position of the 1/2 resonance with Mimas. Franklin, Colombo, and Cook explained this fact in 1971, postulating a total mass of ring B of 10^?6M_SATURN. We have derived a formula for the mass of the rings, which is a linear function of the mean particle size. We find that 10^?6M_SATURN implies large particles (～70m). If the particles are small (～10cm), as currently believed, the total mass of ring B is not enough to shift the outer edge. We conclude that the above explanation and current size estimates are inconsistent.     

Infrared radiometry of the rings of Saturn

Broad-band radiometry with a spatial resolution of 5 arc sec is presented of Saturn and its rings. The brightness temperature of the B ring is 96 ± 3°K at 20 μm and 91 ± 3°K at 11 μm. These values constrain the bolometric Bond albedo of the ring particles to be less than 0.6, thus requiring a phase integral of less than unity. From differences in the thermal emission of the ansae, I suggest that the leading side of the particles has higher albedo than the trailing side. A measured drop in temperature of the B ring following eclipse of 2.0 ± 0.5°K is consistent with radii for the ring particles of 2 cm or larger.     

Particle size distributions in Saturn's rings from voyager 1 radio occultation

Observations of microwave opacity τ[λ] and near forward scatter from Saturn's rings at wavelengths λ of 3.6 and 13 cm from the Voyager 1 ring occultation experiment contain information regarding ring particle sizes in the range of about a = 0.01 to 15 m radius. The opacity measurements τ[3.6] and τ[13] are sufficient to constrain the scale factor n(a₀) and index q of a power law incremental size distribution n(a) = n(a₀)[a₀/a]^q, assuming known minimum and maximum sizes and a many-particle-thick model. The families of such distributions are highly convergent in the centimeter-size range. Forward scatter at 3.6 cm can be used to solve for a general distribution over the radius range $\text{1 ? a ? 15}\text{m}$ by integral inversion and inverse scattering methods, again assuming a many-particle-thick slab-type radiative transfer model. Distributions n(a) valid over $\text{0.01 ? a ? 15}\text{m}$ are obtained by combining the results from the two types of measurements above. Mass distributions may be computed directly from n(a). Such distributions, partly measured and partly synthesized, have been obtained for four features in the ring system centered at 1.35, 1.51, 2.01, and 2.12 Saturn radii (R_s). The size and mass distributions both cut off sharply at a ? 4–5 m; the mass distribution peaks over the narrow size range $\text{3 ? a ? 4}\text{m}$ for all four locations. No single power law distribution is consistent with the data over the entire interval $\text{0.01 ? a ? 5}\text{m}$, although a power law-type model is consistent with the data over a limited size range of $\text{0.01 ? a ? 1}\text{m}$, where the indices q = 3.4 and 3.3 are obtained from the slab model for the features located at 1.51 and 2.01 R_s. The fractional contribution of the suprameter particles to the microwave opacity in each feature appears to be about $\text{1}\text{3}\text{,}\text{1}\text{3}\text{,}\text{2}\text{3}\text{,}\text{and}\text{1}$, respectively, with the fraction at 2.12 R_s being the least certain. The cumulative surface mass per unit area obtained for the classical slab model is approximately 11, 16, 41, and 132 g/cm² for the four features, respectively, if the particles are solid H₂O ice. Both the fractional opacity and the mass density estimates represent upper bounds implied by the assumption of a uniformly mixed set of particles in a many-particle-thick vertical profile; lower estimates would result if the rings were assumed to be nearly a monolayer or if the vertical distribution of particles were size dependent.     

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.     

A multilayer model for thermal infrared emission of Saturn's rings: Basic formulation and implications for Earth-based observations

We present our new model for the thermal infrared emission of Saturn's rings based on a multilayer approximation. In our model, (1) the equation of classical radiative transfer is solved directly for both visible and infrared light, (2) the vertical heterogeneity of spin frequencies of ring particles is taken into account, and (3) the heat transport due to particles motion in the vertical and azimuthal directions is taken into account. We adopt a bimodal size distribution, in which rapidly spinning small particles (whose spin periods are shorter than the thermal relaxation time) with large orbital inclinations have spherically symmetric temperatures, whereas non-spinning large particles (conventionally called slow rotators) with small orbital inclinations are heated up only on their illuminated sides. The most important physical parameters, which control ring temperatures, are the albedo in visible light, the fraction of fast rotators (ffast) in the optical depth, and the thermal inertia. In the present paper, we apply the model to Earth-based observations. Our model can well reproduce the observed temperature for all the main rings (A, B, and C rings), although we cannot determine exact values of the physical parameters due to degeneracy among them. Nevertheless, the range of the estimated albedo is limited to 0-0.52±0.05, 0.55±0.07-0.74±0.03, and 0.51±0.07-0.74±0.06 for the C, B, and A rings, respectively. These lower and upper limits are obtained assuming all ring particles to be either fast and slow rotators, respectively. For the C ring, at least some fraction of slow rotators is necessary (ffast?0.9) in order for the fitted albedo to be positive. For the A and B rings, non-zero fraction of fast rotators (ffast?0.1-0.2) is favorable, since the increase of the brightness temperature with increasing solar elevation angle is enhanced with some fraction of fast rotators.     

The wake model for azimuthal brightness variations in Saturn's A-ring

A dynamical model offering a possible explanation for azimuthal brightness variations in Saturn's ring A is considered. The orbits of ring particles encountering a massive moonlet (radius～100m) are integrated numerically. It is seen that a density wake is produced if the random velocities of the ring particles are much smaller than 1 cm s^?1.     

The 15 August 1980 occultation by the Uranian system: Structure of the rings and temperature of the upper atmosphere

A stellar occultation by Uranus and its rings was observed on August 15, 1980, from the European Southern Observatory (Chile), at the 3.6-m telescope equipped with an infrared (2.2 μm) photometer. The recording presents the best signal-to-noise ratio obtained since the discovery of the Uranian rings in March 1977. The nine rings were observed, and the profiles of rings α, β, and ? were resolved, the ring α exhibiting a double structure. Strong diffraction peaks are visible in the γ ring profile suggesting an opaque ring with very sharp edges. A broad and faint structure extends outward from the η ring, on a radial scale of about 55 km. Apart from the ring occultations, unexplained sharp and deep events were recorded, and no interpretation is possible until future observations are made. Furthermore, the stellar light curve during the immersion of the star behind the planet provides (via an inversion computation) the temperature profile of the upper atmosphere of Uranus. The temperature is close to 145 ± 10°K at the 3 × 10^?2-mbar pressure level and is nearly constant (155 ± 15°K) in the pressure interval from 10^?2 to 10^?3 mbar. The thermal inversion is as strong as the inversion on Neptune but is located at higher altitudes. This high stratospheric temperature is consistent with the upper limit of the brightness temperature at 8 μm only if CH₄ follows its saturation law.     

Photometric modeling of Saturn's rings: I. Monte Carlo method and the effect of nonzero volume filling factor

The scattering properties of particulate rings with volume filling factors in the interval D=0.001-0.3 are studied, with photometric Monte Carlo ray tracing simulations combining the advantages of direct (photons followed from the source) and indirect methods (brightness as seen from the observing direction). Besides vertically homogeneous models, ranging from monolayers to classical many-particle thick rings, particle distributions obtained from dynamical simulations are studied, possessing a nonuniform vertical profile and a power law distribution of particle sizes. Self-gravity is not included to assure homogeneity in planar directions. Our main goal is to check whether the moderately flattened ring models predicted by dynamical simulations (with central plane D>0.1) are consistent with the basic photometric properties of Saturn's rings seen in ground-based observations, including the brightening near zero phase angle (opposition effect), and the brightening of the B-ring with increasing elevation angle (tilt effect). Our photometric simulations indicate that dense rings are typically brighter in reflected light than those with D→0, due to enhanced single scattering. For a vertically illuminated layer of identical particles this enhancement amounts at intermediate viewing elevations to roughly 1+2D. Increased single scattering is also obtained for low elevation illumination, further augmented at low phase angles α by the opposition brightening when D increases: the simulated opposition effect agrees very well with the Lumme and Bowell (1981, Astron. J. 86, 1694-1704) theoretical formula. For large α the total intensity may also decrease, due to reduced amount of multiple scattering. For the low (α=13°) and high (α=155°) phase angle geometries analyzed in Dones et al. (1993, Icarus 105, 184-215) the brightness change for D=0.1 amounts to 20% and −17%, respectively. In the case of an extended size distribution, dynamical simulations indicate that the smallest particles typically occupy a layer several times thicker than the largest particles. Even if the large particles form a dynamically dense system, a narrow opposition peak can arise due to mutual shadowing among the small particles: for example, a size distribution extending about two decades can account for the observed about 1° wide opposition peak, solely in terms of mutual shadowing. The reduced width of the opposition peak for extended size distribution is in accordance with Hapke's (1986, Icarus 67, 264-280) treatment for semi-infinite layers. Due to vertical profile and particle size distribution, the photometric behavior is sensitive to the viewing elevation: this can account for the tilt-effect of the B-ring, as dense and thus bright central parts of the ring become better visible for larger elevation, whereas in the case of smaller elevation, mainly low volume density upper layers are visible. Since multiple scattering is not involved, the explanation works also for albedo well below unity. Inclusion of nonzero volume density helps also to model some of the Voyager observations. For example, the discrepancy between predicted and observed brightness at large phase angles for much of the A-ring (Dones et al., 1993, Icarus 105, 184-215) is removed when the enhanced low α single scattering and reduced large α multiple scattering is allowed for. Also, a model with vertical thickness increasing with saturnocentric distance offers at least a qualitative explanation for the observed contrast reversal between the inner and outer A-ring in low and high phase Voyager images. Differences in local size distribution and thus on the effective D may also account for the contrast reversal in resonance sites.     

The 1 May 1982 stellar occultation by Uranus and the rings: Observations from Mount Stromlo Observatory

The 1 May 1982 occultation of KME 15 by Uranus and its rings was observed at λ = 2.2 μm using the 1.9-m telescope of the Mount Stromlo Observatory. From model fits to the immersion and emersion ring profiles, accurate midtimes for rings 6, 5, 4, α, β, η, γ, σ, and ϵ, and ring widths, equivalent widths, and normal optical depths for all but ring 6 were obtained. The recently discovered ring 1986 U1R is not detectable in the data, setting an upper limit on the product of ring width and normal optical depth of ≤0.4 km at λ = 2.2 μm. From the immersion and emersion atmosphere occultations, vertical temperature profiles were obtained by numerical inversion. Both profiles show mean temperatures near 130°K and a local maximum near the 8-μbar pressure level.     

On the structure of Saturn's rings and the ‘real’ rotational period for the planet

An analysis of the Lowell Observatory photographic plates of Saturn gave the following results: (1) ring A and B show peculiar brightness distributions around the planet, from which we conclude that both are composed of particles in synchronous rotation. (2) The leading side of the particles in ring A is brighter than the trailing side by about 4%, which may indicate an interaction between such particles and the interplanetary medium. (3) Scans of the rings across the major axis show a small (～0.3″) region of enhanced brightness, from which we derive a value ofT _s =10^h13 _. ^m 8±5 _. ^m 4 for the actual planetary rotational period of Saturn. (4) In order to explain the synchronous rotation, the particles in ring A have to be at least 42 m in diameter.     

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.