Saturn's rings: Particle composition and size distribution as constrained by microwave observations: I. Radar observations

We have calculated the radar backscattering characteristics of a variety of compositional and structural models of Saturn's rings and compared them with observations of the absolute value, wavelength dependence, and degree of depolarization of the rings' radar cross section (reflectivity). In the treatment of particles of size comparable to the wavelength of observation, allowance is made for the nonspherical shape of the particles by use of a new semiempirical theory based on laboratory experiments and simple physical principles to describe the particles' single scattering behavior. The doubling method is used to calculate reflectivities for systems that are many particles thick using optical depths derived from observations at visible wavelengths. If the rings are many particles thick, irregular centimeter- to meter-sized particles composed primarily of water ice attain sufficiently high albedos and scattering efficiencies to explain the radar observations. In that case, the wavelength independence of radar reflectivity implies the existence of a broad particle size distribution that is well characterized over the range 1 cm ? r ? m by n(r)dr = n₀r^?3dr. A narrower size distribution with $\text{a}\text{～ 6}\text{cm}$ is also a possibility. Particles of primarily silicate composition are ruled out by the radar observations. Purely metallic particles, either in the above size range and distributed within a many-particle-thick layer or very much larger in size and restricted to a monolayer, may not be ruled out on the basis of existing radar observations. A monolayer of very large ice “particle” that exhibit multiple internal scattering may not yet be ruled out. Observations of the variation of radar reflectivity with the opening angle of the rings will permit further discrimination between ring models that are many particles thick and ring models that are one “particle” thick.     

Saturn's rings: Particle composition and size distribution as constrained by observations at microwave wavelengths: II. Radio interferometric observations

The sizes, composition, and number of particles comprising the rings of Saturn may be meaningfully constrained by a combination of radar- and radio-astronomical observations. In a previous paper, we have discussed constraints obtained from radar observations. In this paper, we discuss the constraints imposed by complementary “passive” radio observations at similar wavelengths. First, we present theoretical models of the brightness of Saturn's rings at microwave wavelengths (0.34–21.0 cm), including both intrinsic ring emission and diffuse scattering by the rings of the planetary emission. The models are accurate simulations of the behavior of realistic ring particles and are parameterized only by particle composition and size distribution, and ring optical depth. Second, we have reanalyzed several previously existing sets of interferometric observations of the Saturn system at 0.83-, 3.71-, 6.0-, 11.1-, and 21.0-cm wavelengths. These observations all have spatial resolution sufficient to resolve the rings and planetary disk, and most have resolution sufficient to resolve the ring-occulted region of the disk as well. Using our ring models and a realistic model of the planetary brightness distribution, we are able to establish improved constraints on the properties of the rings. In particular, we find that: (a) the maximum optical depth in the rings is ～ 1.5 ± 0.3 referred to visible wavelengths; (b) a significant decrease in ring optical depth from λ3.7 to λ21.0 cm allows us to rule out the possibility that more than ～30% of the cross section of the rings is composed of particles larger than a meter or so; this assertion is essentially independent of uncertainties in particle adsorption coefficient; and (c) the ring particles cannot be primarily of silicate composition, independently of particle size, and the particles cannot be primarily smaller than ～0.1 cm, independently of composition.     

Far ultraviolet spectral properties of Saturn’s rings from Cassini UVIS

Spectra taken by the Cassini Ultraviolet Imaging Spectrograph (UVIS) of Saturn’s C ring, B ring, Cassini Division, and A ring have been analyzed in order to characterize ring particle surface properties and water ice abundance in the rings. UVIS spectra sense the outer few microns of the ring particles. Spectra of the normalized reflectance (I/F) in all four regions show a characteristic water ice absorption feature near 165 nm. Our analysis shows that the fractional abundance of surface water ice is largest in the outer B ring and decreases by over a factor of 2 across the inner C ring. We calculate the mean path length of UV photons through icy ring particle regolith and the scattering asymmetry parameter using a Hapke reflectance model and a Shkuratov reflectance model to match the location of the water ice absorption edge in the data. Both models give similar retrieved values of the photon mean length, however the retrieved asymmetry (g) values are different. The photon mean path lengths are nearly uniform across the B and A rings. Shortward of 165 nm the rings exhibit a slope that turns up towards shorter wavelengths, while the UV slope of 180/150 nm (reflectance outside the water absorption ratioed to that inside the absorption band) tracks I/F with maxima in the outer B ring and in the central A ring. Retrieved values of the scattering asymmetry parameter show the regolith grains to be highly backscattering in the FUV spectral regime.     

Saturn's rings: Particle size distributions for thin layer models

The small physical thickness of Saturn's rings requires that radio occultation observations be interpreted using scattering models with limited amounts of multiple scatter. A new model in which the possible order of near-forward scatter is strictly limited allows for the small physical thickness, and can be used to relate Voyager 1 observations of 3.6-and 13-cm wavelength microwave scatter from Saturn's rings to the ring particle size distribution function n(a), for particles with radius 0.001 ≤ a ≤ 20 m. This limited-scatter model yields solutions for particle size distribution functions for eight regions in Saturn's rings, which exhibit approximately inverse-cubic power-law behavior, with large-size cutoffs in particle radius ranging from about 5 m in ring C to about 10 m in parts of ring A. The power-law index is about 3.1 in ring C, about 2.8 in the Cassini division, and increases systematically with radial location in ring A from 2.7 at 2.10R_s to slightly more than 3.0 at 2.24R_s. Corresponding mass densities are 32–43 kg/m² in ring C, 188 kg/m² in the Cassini division, and 244–344 kg/m² in ring A, under the assumption that the material density of the particles is 0.9 g/cm³. These values are a factor of 1 to 2 lower than first-order mass loading estimates derived from resonance phenomena. In view of the uncertainties in the measurements and in the linear density wave model, and the strong arguments for icy particles with specific gravity not greater than about 1, we interpret this discrepancy as being indicative of possible differences in the regions studied, or systematic errors in the interpretation of the scattering results, the density wave phenomena, or some combination of the above.     

Aperture synthesis observations of Saturn and its rings at 2.7-mm wavelength

We present 2.7-mm interferometric observations of Saturn made near opposition in June 1984 and June 1985, when the ring opening angle was 19° and 23°, respectively. By combining the data sets we produce brightness maps of Saturn and its rings with a resolution of 6″. The maps show flux from the ring ansae, and are the first direct evidence of ring flux in the 3-mm wavelength region. Modelfits to the visibility data yield a disk brightness temperature of 156 ± 5°K, a combined A, B, and C ring brightness temperature of 19 ± 3°K, and a combined a ring cusp (region of the rings which block the planet's disk) brightness temperature of 85 ± 5°K. These results imply a normal-to-the-ring optical depth for the combined ABC ringof 0.31 ± 0.04, which is nearly the same value found for wavelenghts from the UV to 6 cm. About 6°K of the ring flux is attributed to scattered planetary emission, leaving an intrinsic thermal component of ∼13°K. These results, together with the ring particle size distributions found by the Voyager radio occultation experiments, are consistent with the idea that the ring particles are composed chiefly of water ice.     

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

We have used 3-mm Saturn observations, obtained from 1965 through 1977 and with Jupiter as a reference, to derive a ring brightness temperature of 18 ± 8°K. Thebrightness temperature of the disk of Saturn is 156 ± 9° K. Part of the ring brightness (≈62K) may be accounted for as disk emission which is scattered from the rings; the remainder (12 ± 8° K we attributed to ring particle thermal emission. Because this thermal component brightness temperatures is so much less than the particle physical temperature, limits are placed on the mean size and composition of the ring particles. In particular, as found by others, the particles cannot be rocky, but must be either metallic or composed of extremely low-loss dielectric material such as water ice. If the particles are pure water ice, for example, then a simple slab model and a multiple-scattering model both give upper limits to the particle sizes of ≈ 1 m, a value three times smaller than previously available. The multiple-scattering model gives a particle single-scattering albedo at 3 mm of 0.83±0.13.     

N-body simulations of cohesion in dense planetary rings: A study of cohesion parameters

We present results from a large suite of simulations of Saturn’s dense A and B rings using a new model of particle sticking in local simulations (Perrine, R.P., Richardson, D.C., Scheeres, D.J. [2011]. Icarus 212, 719–735). In this model, colliding particles can be incorporated into or help fragment rigid aggregations on the basis of certain user-specified parameters that can represent van der Waals forces or interlocking surface frost layers.Our investigation is motivated by laboratory results that show that interpenetration of surface layers can allow impacting frost-covered ice spheres to stick together. In these experiments, cohesion only occurs below specific impact speeds, which happen to be characteristic of impact speeds in Saturn’s rings. Our goal is to determine if weak bonding is consistent with ring observations, to constrain cohesion parameters in light of existing ring observations, to make predictions about particle populations throughout the rings, and to discover other diagnostics that may constrain bonding parameters.We considered the effects of five parameters on the equilibrium characteristics of our ring simulations: speed-based merge and fragmentation limits, bond strength, ring surface density, and patch orbital distance (i.e., the A or B ring), some with both monodisperse and polydisperse comparison cases. In total, we present data from 95 simulations.We find that weak cohesion is consistent with observations of the A and B rings (e.g., French, R.G., Nicholson, P.D. [2000]. Icarus 145, 502–523), and we present a range of simulation parameters that reproduce the observed size distribution and maximum particle size. It turns out that the parameters that match observations differ between the A and B rings, and we discuss the potential implications of this result. We also comment on other observable consequences of cohesion for the rings, such as optical depth and scale height effects, and discuss whether very large objects (e.g., “propeller” source objects) are grown bottom-up from cohesion of smaller ring particles.     

The 2–4-μm spectrum of Saturn's rings

Observations of the rings of Saturn at 2–4 μm reveal the presence of a 3.6-μm peak in the infrared reflectivity. This peak is consistent with a particle size of ? 50 μm, and a composition of pure H₂O ice. The quoted size may only be indicative of the textural scale of frost on the surface of larger particles. The presence of small amounts of CH₄ in the form of a clathrate, however, cannot be ruled out by our measurements.     

Rings of Uranus: Not so thick,not so black

The optical thickness of the rings of Uranus has been thoroughly measured by many stellar occultations. However, we show that the optical thickness so obtained is larger by an extinction efficiency factor of 2 than the fractional area physically filled by particles which is commonly used to infer both particle reflectivity and particle size. By neglecting this factor, previous work has overestimated particle packing density and therefore underestimated individual particle reflectances and sizes (as well as overestimated collision frequencies). This has led to concern as to why the ring particles seemed unusually black and small. We present new estimates of particle reflectance which include both this effect and an improved radiative transfer treatment, and show that the ring particles, while still quite dark, are no longer mysteriously so. Particle sizes, while not strongly constrained, could easily lie in the macroscopic size range characteristic of other planetary rings.     

International conference on planetary satellites

Further analysis of visual (V) wavelength photometric function data for Saturn's ring is presented. Evidence indicating both that primary scattering dominates, and that mutual shadowing is an irrelevant concept, is reviewed. Simple anisotropic scattering radiative transfer models are used to define the probable ranges in the single scattering albedo, and in the general shape of the scattering phase function of the individual particles. Limitations on the mean perpendicular optical thickness of the ring are also obtained. Results indicate that the ring particles are highly efficient back-scatterers of visual radiation. Macroscopic particles account for the basic shape of the scattering phase function. Based on an infinite optical thickness for the ring, a minimum single scattering albedo ≈0.75 is found. Use of conservative scattering leads to a minimum optical thickness ≈0.7. The analysis is consistent with the ring particles being centimeter-size pieces of ice.     

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.     

The rings of saturn: A frost-coated semiconductor?

Optical complex indices of refraction for the iron-sulfur semiconductors troilite and pyrrhotite have been measured between 0.3 and 1.1 μm, and at 1.5 and 3.0 cm in the microwave region. The behavior of the absorptive and refractive components of the index in the visual and ultraviolet regions suggests a reasonable match to published data on Saturn's rings. A combination of the iron sulfur with water ice and the orthopyroxene enstatite is consistent with an equilibrium condensation model for the formation of the solar system; the water ice and an orthopyroxene are also suggested by near-infrared observational data. A combination of these materials could explain all spectral features seen in the ring spectra to date. The microwave behavior of a small quantity of troilite embedded in water ice at low temperatures is consistent with the radar reflectivity and radio emissivity data.     

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.     

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.     

HST observations of spokes in Saturn's B ring

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

The vertical structure and thickness of Saturn's rings

We have considered the steady state vertical structure of Saturn's rings with regard to whether collapse to a monolayer due to collisions between particles, the end state predicted by Jeffreys (1947a), may be prevented by any of a variety of mechanisms. Given a broad distribution of particle sizes such as a typical power law n(R) = n₀R^?3, it is found that gravitational scattering of small particles by large particles maintains a true ring thickness of several times the radius of the largest particles, or many times the radius of the smallest particles. Thus the “many-particle-thick” condition which best satisfies optical observations, such as the opposition effect, may be reconciled with ongoing particle collisions. If we consider the obvious sources of energy available for such a process, we find that a ring thickness of only tens of meters may be sustained over the lifetime of the solar system. This implies a maximum particle size on the order of a few meters.     

Radar imaging of Saturn's rings

We present delay-Doppler images of Saturn's rings based on radar observations made at Arecibo Observatory between 1999 and 2003, at a wavelength of 12.6 cm and at ring opening angles of 20.1°?|B|?26.7°. The average radar cross-section of the A ring is ∼77% relative to that of the B ring, while a stringent upper limit of 3% is placed on the cross-section of the C ring and 9% on that of the Cassini Division. These results are consistent with those obtained by Ostro et al. [1982, Icarus 49, 367-381] from radar observations at |B|=21.4°, but provide higher resolution maps of the rings' reflectivity profile. The average cross-section of the A and B rings, normalized by their projected unblocked area, is found to have decreased from 1.25±0.31 to 0.74±0.19 as the rings have opened up, while the circular polarization ratio has increased from 0.64±0.06 to 0.77±0.06. The steep decrease in cross-section is at variance with previous radar measurements [Ostro et al., 1980, Icarus 41, 381-388], and neither this nor the polarization variations are easily understood within the framework of either classical, many-particle-thick or monolayer ring models. One possible explanation involves vertical size segregation in the rings, whereby observations at larger elevation angles which see deeper into the rings preferentially see the larger particles concentrated near the rings' mid-plane. These larger particles may be less reflective and/or rougher and thus more depolarizing than the smaller ones. Images from all four years show a strong m=2 azimuthal asymmetry in the reflectivity of the A ring, with an amplitude of ±20% and minima at longitudes of 67±4° and 247±4° from the sub-Earth point. We attribute the asymmetry to the presence of gravitational wakes in the A ring as invoked by Colombo et al. [1976, Nature 264, 344-345] to explain the similar asymmetry long seen at optical wavelengths. A simple radiative transfer model suggests that the enhancement of the azimuthal asymmetry in the radar images compared with that seen at optical wavelengths is due to the forward-scattering behavior of icy ring particles at decimeter wavelengths. A much weaker azimuthal asymmetry with a similar orientation may be present in the B ring.     

Saturn's rings in the thermal infrared

This paper reviews our current knowledge of Saturn's rings’ physical properties as derived from thermal infrared observations. Ring particle composition, surface structure and spin as well as the vertical structure of the main rings can be determined. These properties are the key to understand the origin and evolution of Saturn's rings. Ring composition is mainly constrained by observations in the near-infrared but the signature of some probable contaminants present in water ice may also be found at mid-infrared wavelengths. The absence of the silicate signature limits nowadays their mass fraction to 10^−7±1. Recent measurements on the thermal inertia of the ring particle surface show it is very low, of the order of 5±2 Jm⁻² K⁻¹ s^−1/2. New models and observations of the complete crossing of the planetary shadow are needed to attribute this low value either to compact regoliths covered by cracks due to collisions and thermal stresses or to large fluffy and irregular surfaces. Studies of the energy balance of ring particles show a preference for slowly spinning particles in the main rings. Supplementary observations at different phase angles, showing the temperature contrast between night and day sides of particles, and new models including finite spin and thermal inertia, are needed to constrain the actual spin distribution of ring particles. These results can then be compared to numerical simulations of ring dynamics. Many thermal models have been proposed to reproduce observations of the main rings, including alternative mono- or many-particles-thick layers or vertical heterogeneity, with no definitive answer. Observations on the lit and dark faces of rings as a function of longitude, at many incidence and emission angles, would provide prime information on the vertical thermal gradient due to interparticle shadowing from which constraints on the local vertical structure and dynamics can be produced. Future missions such as Cassini will provide new information to further constrain the ring thermal models.     

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

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