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.     

VLA observations of Saturn at 1.3, 2, and 6 cm

Radio maps with a resolution of 1″.5 were made of Saturn at 1.3, 2, and 6 cm. The inclination of the ring plane was ?5°.4. A fraction of 0.49 ± 0.08 of Saturn's emitted light is transmitted through the rings at λ2 and λ6 cm. This value converts to an effective head-on or normal optical depth of 0.07 ± 0.02. The transparency at this small inclination angle must be provided entirely by the regions of very low optical depth, e.g., the Cassini and Encke's Divisions, and to achieve our number this requires either a relatively large fraction of gaps or a strong forward scattering by the ring particles. The planetary disk appears to be much less limb darkened in the N-S than the E-W direction, while cuts across the planet, averaged over all directions, agree with the theoretical limb-darkening curves for a planet with a uniform atmosphere and solar abundances for all chemical elements.     

Interferometric observations of Saturn and its rings at a wavelength of 3 3.71 cm

Interferometric observations of Saturn and its rings made at the Owens Valley Radio Observatory at a wavelength of 3.71 cm ar fit to models of the Saturn brightness structure. The models have allowed us to estimate the brightness temperatures and optical thicknesses of the A, B, and C rings as well as the brightness temperature of the planetary disk. The most accurate results are the ratios of the ring temperatures to the planet temperature of 0.030 ± 0.012, 0.050 ± 0.010, and 0.040 ± 0.014 for the A, B, and C rings, respectively. The best estimates of the ring optical thicknesses are τ_A = 0.2 ± 0.1, τ_B = 0.9 ± 0.2, and τ_C = 0.1 ± 0.1. The actual brightness temperatures, which are affected by the absolute calibration errors, are T_planet = 178 ± 8, T_A = 5.2 ± 2.0, T_B = 9.1 ± 1.8, and T_C = 7.1 ± 2.6°K. The particle single-scattering albedo that would be most consistent with the observations is slightly less than one, but probably greater than 0.95. The observations are consistent with particles which conservatively scatter the thermal emission from Saturn to the Earth and emit no thermal emission of their own. The 3.71-cm optical depths which we have estimated are very close to the visible wavelength optical depths. This similarity indicates that the ring particles must be at least a few centimeters in size, although we feel that the particles may well be much larger than this in view of the closeness of the visible and microwave optical depths. Particles which are nearly conservative scatterers at our wavelength and at least a few centimeters in size must be composed of a material which is either a very good reflector of microwaves or a very poor absorber of them. At this time, water ice seems to be the most likely candidate since it is a very poor absorber of microwaves and has been detected in the rings spectroscopically.     

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.     

Interferometry of Saturn and its rings at 1.30-cm wavelength

We present interferometric observations of Saturn and its ring system made at the Hat Creek Radio Astronomy Observatory at a wavelength of 1.30 cm. The data have been analyzed by both model-fitting and aperture synthesis techniques to determine the brightness temperature and optical thickness of the ring system and estimate the amount of planetary limb darkening. We find that the ring optical depth is close to that observed at visible wavelenghts, while the ring brightness temperature is only 7 ± 1°K. These observational constraints require the ring particles to be nearly conservative scatterers at this wavelength. A conservative lower limit to the single-scattering albedo of the particles at 1.30-cm wavelength is 0.95, and if their composition is assumed to be water ice, then this lower limit implies an upper limit of 2.4 m for the radius of a typical ring particle. The aperture synthesis maps show evidence for a small offset in the position of Saturn from that given in the American Ephemeris and Nautical Almanac. The direction and magnitude of this offset are consistent with that found from a similar analysis of 3.71-cm interferometric data which we have previously presented (F.P. Schloerb, D.O. Muhleman, and G.L. Berge, 1979b, Icarus39, 232–250). Limb darkening of the planetary disk has been estimated by solving for the best-fitting disk radius in the models. The best-fitting radius is 0.998 ± 0.004 times the nominal Saturn radius and indicates that the planet is not appreciably limb dark at 1.30 cm. Since our previous 3.71-cm data also indicated that the planet was not strongly limb dark (F.P. Schloerb, D. O. Muhleman, and G.L. Berge, 1979a, Icarus39, 214–230), we feel that the limb darkening is not strongly wavelength dependent between 1.30 and 3.71 cm. The difference between the best-fitting disk radii at 3.71 and 1.30 cm is +0.007 ± 0.007 times the nominal Saturn radius and suggests that the planet is more limb dark at 1.30 cm than at 3.71 cm. Models of the atmosphere which have NH₃ as the principal source of microwave opacity predict that the planet will be less limb dark at 1.30 cm. However, the magnitude of the effect predicted by the NH₃ models is ?0.009 and only marginally different from the observed value.     

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.     

Far-infrared spectral observations of Saturn and its rings

The spectrum of Saturn and its rings between 45 and 115 μm has been measured at an average resolving power of 14 from the NASA Lear Jet. The combined brightness temperature of the rings and planetary disk decreases beyond 65 μm, in disagreement with previous results. A brightness temperature of 65 ± 10°K is obtained for the planetary disk in the 80–110-μm wavelength range if a large-particle, constant-emissivity model is assumed for the rings. The possible effects of small particles in the rings are briefly considered.     

Estimates of the size of the particles in the rings of saturn and their cosmogonic implications

Very low values of the radio brightness temperature of the rings of Saturn indicate that their high refar reflectivity is not simply due to a gain effect in the backscattering direction. These two sets of observations are consistent with the ring particles having a very high single scattering albedo at radio wavelenghts, with multiple scattering effects being important. Comparison of scattering calculations for ice and silicate particles with the radio and radar observations imply a mean particle radius of ～1 cm. The ice bands observed in the rings' near-infrared reflectivity spectra are formed by scattering within a microstructure on the surface of the ring particles, with the scattering centers being 25–125 μm in size. The Poynting-Robertson effect has caused a significant spiraling-in of the ring particles, probably resulting in a broadening of the rings. The inferred mean size is consistent with a model in which meteoroid impacts have caused a substantial reduction in the mean particle size from its initial value.     

Far-infrared brightness temperature of Saturn's disk and rings

We present far-infrared observations of Saturn in the wavelength band 76–116 μm, using a balloon-borne 75-cm telescope launched on 10 December 1980 from Hyderabad, India, when B′, the Saturnicentric latitude of the Sun, was 4°.3. Normalizing with respect to Jupiter, we find the average brightness temperature of the disk-ring system to be 90 ± 3° K. Correcting for the contribution from rings using experimental information on the brightness temperature of rings at 20 μm, we find T_D, the brightness temperature of the disk, to be 96.9 ± 3.5° K. The systematic errors and the correction for the ring contribution are small for our observations. We, therefore, make use of our estimate of T_D and earlier observations of Saturn when contribution from the rings was large and find that for wavelengths greater than 50 μm, there is a small reduction in the ring brightness temperature as compared to that at 20 μm.     

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.     

Photometric properties of Saturn's rings

The spectral reflectivity of Saturn's rings between 0.36 and 1.06 μm is derived from observations of the combined light of the Saturn system and the previously determined spectrum of the disk of Saturn. The rings are red relative to the Sun for wavelengths λ? 0.7 μm; at longer wavelengths, the spectral reflectivity declines. The amplitude of the opposition effect (anomalous brightening at very small phase angles) shows a maximum at both ends of our spectral range.     

Microwave brightness of Saturn's rings

It is shown that a lower limit exists on the microwave brightness of the rings of Saturn, if they are assumed to be composed of Mie scatterers of geological composition. The lower limit (about 15°K) is due to scattering of planetary microwave emission. Significant variation of brightness with azimuth along the rings is expected if the particles are typically of 2–3cm radius. Implications for the multiple-scattering hypothesis of the radar cross section of the rings are noted.     

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.     

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: 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.     

Far-infrared spectrophotometry of Saturn and its rings

The spectrum of Saturn was measured from 80 to 350 cm^?1 (29 to 125 μm) with ≈6-cm^?1 resolution using a Michelson interferometer aboard NASA's Kuiper Airborne Observatory. These observations are of the full disk, with little contribution from the rings. For frequencies below 300 cm^?1, Saturn's brightness temperature rises slowly, reaching ≈111°K at 100 cm^?1. The effective temperature is 96.8 ± 2.5°K, implying that Saturn emits 3.0 ± 0.5 times as much energy as it receives from the Sun. The rotation-inversion manifolds of NH₃ that are prominent in the far-infrared spectrum of Jupiter are not observed on Saturn. Our models predict the strengths to be only ≈2 to 5°K in brightness temperature because most of the NH₃ is frozen out; this is comparable to the noise in our data. By combining our data with those of an earlier investigation when the Saturnicentric latitude of the Sun was B′ = 21.2°, we obtain the spectrum of the rings. The high-frequency end of the ring spectrum (ν > 230 cm^?1) has nearly constant brightness temperature of 85°K. At lower frequencies, the brightness temperature decreases roughly as predicted by a simple absorption model with an optical depth proportional to ν^1.5. This behavior could be due to mu-structure on the surface of the ring particles with a scale size of 10 to 100 μm and/or to impurities in their composition.     

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.     

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.