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.     

Bending waves in Saturn's rings

We investigate certain brightness variations seen in Saturn's A ring and find them to be due to vertical corrugations of the local ring plane caused by a spiral bending wave. This wave is resonantly excited by Mimas and propagates inward via the collective gravity of the ring particles. B. A. Smith et al. [Science212, 163–191 (1981)] had previously associated vertical relief with this feature due to its observed azimuthal variations and its proximity to an inclination resonance with Mimas. We develop the theory of forced bending waves, some aspects of which have been treated in the galactic context by C. Hunter and A. Toomre [Astrophys. J.155, 747–776 (1969)] and by G. Bertin and J.W.-K. Mark [Astron. Astrophys.88, 289–297 (1980)]. Our theory is in good agreement with the observations. In particular, the presence of these bending waves may resolve the conflict between ground-based estimates of 1–2 km for the global ring thickness [e.g., A. Brahic and B. Sicardy, Nature289, 447–450 (1981)] and Voyager stellar occultation measurements of <200 m for the local ring thickness [A. L. Lane et al., Science215, 537–543 (1982); E. A. Marouf and G. L. Tyler, Science217, 243–245 (1982)].     

The tilt effect for Saturn's rings

Multiple-scattering computations are carried out to explain the variation of the observed brightness of the A and B rings of Saturn with declination of the Earth and Sun. These computations are performed by a doubling scheme for a homogeneous plane-parallel scattering medium. We test a range of choices for the phase function, albedo for single scattering, and optical depth of both the rings. Isotropic scattering and several other simple phase functions are ruled out, and we find that the phase function must be moderately peaked in both the forward and backward directions. The tilt effect can be explained by multiple scattering in a homogeneous layer, but, for ring B, this requires a single-scattering albedo in excess of 0.8. The brightest part of ring B must have an optical depth greater than 0.9. We find that the tilt effect for ring A can be reproduced by particles having the same properties as those in ring B with the optical depth for the A ring in the range 0.4 to 0.6.     

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.     

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.     

Ganymede,Europa, Callisto,and Saturn's rings: Compositional analysis from reflectance spectroscopy

The reflectance spectra of Ganymede, Europa, Callisto, and Saturn's rings are analyzed using recent laboratory reflectance studies of water frost, water ice, and water and mineral mixtures. It is found that the spectra of the icy Galilean satellites are characteristic of water ice (e.g., ice blocks or possibly very large ice crystals ? 1 cm) or frost on ice rather than pure water frost, and that the decrease in reflectance at visible wavelengths is caused by other mineral grains in the surface. The spectra of Saturn's rings are more characteristic of water frost with some other mineral grains mixed in the frost but not on the surface. The impurities on all these objects are not in spectrally isolated patches but appear to be intimately mixed with the water. The impurity grains appear to have reflectance spectra typical of minerals containing Fe³⁺. Some carbonaceous chondrite meteorite spectra show the necessary spectral shape. Ganymede is found to have more water ice on the surface than previously thought (～90 wt%), as is Callisto (30–90 wt%). The surface of Europa has a vast frozen water surface with only a few percent impurities. Saturn's rings also have only a few percent impurities. The amount of bound water or bound OH for these objects is 5 ± 5 wt% averaged over the entire surface. Thus with the small amount of nonicy material present on these objects, no hydrated minerals can be ruled out. A new absorption feature is identified in Ganymede, Callisto, and probably Europa at 1.5 μm which is also seen in the spectra of Io but not in Saturn's rings. This feature has not been seen in laboratory studies and its cause is unknown.     

A model for the formation of spokes in Saturn's ring

We suggest that spokes consist of charged micron-sized dust particles elevated from the rings by radially moving dense plasma columns created by meteor impacts on the ring. Dense plasma causes electrostatic wall-sheaths at the ring and charging of the ring with electric fields strong enough to overcome the gravitational force on small dust particles. Under “ordinary” conditions only very few dust particles will be elevated as the probability of a dust particle having at least one excess electronic charge is very low. Dense plasma raises this probability significantly. The radial motion of the plasma column is due to an azimuthal polarization electric field built up by the relative motion between the corotating plasma and the negatively charged dust particles which move with a Keplerian speed.     

Formation of fine dust on Saturn's rings as suggested by the presence of spokes

The common interpretation of spokes on the B ring of Saturn is that they are the result of light scattered by electrostatically levitated micrometer- and submicrometer-size dust particles. The origin of this dust in terms of radiation-induced thermal fatigue and collisions between the particles of the ring as well as meteoritic bombardment is investigated.     

Saturn's electrostatic discharges: Properties and theoretical considerations

The properties of Saturn's electrostatic discharges (SED) as observed by the Voyager Planetary Radio Astronomy experiment during the two Voyager encounters with Saturn are summarized. Several models for the formation of SED are discussed in light of these observations. The most likely source regions appear to be either the equatorial zone of the planet or the dense part of the B ring near 1.80 R_s. The strenghts and weaknesses of each of these possibilities are examined. Neither possibility accounts fully for the observed SED properties in a simple way. A search for an anomaly near 1.80 R_s in the data of other experiments aboard Voyager has been carried out, and at least one and possibly more such experiments do indeed obtain anomalous data at this point in the ring system. There thus appears to be unexplained phenomena at this point, independent of the PRA data, and it is a short step to postulate that a single object may be the cause of all such phenomena.     

The evolution of spokes in Saturn's B ring

The optical appearance of spokes was studied in high resolution (?200 km/lp) images obtained by Voyager 2. Spokes are classified into three categories. (1) Extended spokes are seen in the distance interval of 100,000 to 112,000 km from Saturn's center. They have diffuse edges and are slightly wedge shaped. Their width at the base (towards Saturn) is about 20,000 km. Their active times (during which they increase in width) range from 4000 to 12,000 sec. (2) Narrow spokes are found in the distance range 104,000 to 116,000 km, have sharply defined edges, and are narrowest at the corotation distance (112, 300 km). Their typical radial extension and width is 6000 and 2,000 km, respectively. (3) Filamentary spokes are found outside 110,000 km mostly joined with a wider spoke further in. They are typically 3000 km in length and 500 km in width. Their active time is less than 1000 sec. Several narrow spokes were observed during formation along radial lines in the sunlit portion of the ring. The formation time is typically ?5 min for a 6000-km-long spoke. The rate of spoke formation is highest at the morning ansa outside Saturn's shadow. Several spokes have been found where one edge revolves with Keplerian speed whereas the other edge stays radial. Recurrent spoke patterns have been observed at the period of Saturn's rotation. From edge-on views of the ring system, an upper limit for the height of spokes of 80 km is derived.     

Orbits of Saturn's F ring and its shepherding satellites

The shape and orientation of Saturn's F ring and the orbits of its two shepherding satellites have been determined from Voyager images. The data and processing are described, and orbital parameter estimates and associated uncertainties are presented. In addition, evidence that suggests that the F-ring braids are formed very near the conjunctions of the shepherding satellites is presented.     

A multilayer model for thermal infrared emission of Saturn’s rings. III: Thermal inertia inferred from Cassini CIRS

The thermal inertia values of Saturn’s main rings (the A, B, and C rings and the Cassini division) are derived by applying our thermal model to azimuthally scanned spectra taken by the Cassini Composite Infrared Spectrometer (CIRS). Model fits show the thermal inertia of ring particles to be 16, 13, 20, and 11 J m⁻² K⁻¹ s^−1/2 for the A, B, and C rings, and the Cassini division, respectively. However, there are systematic deviations between modeled and observed temperatures in Saturn’s shadow depending on solar phase angle, and these deviations indicate that the apparent thermal inertia increases with solar phase angle. This dependence is likely to be explained if large slowly spinning particles have lower thermal inertia values than those for small fast spinning particles because the thermal emission of slow rotators is relatively stronger than that of fast rotators at low phase and vise versa. Additional parameter fits, which assume that slow and fast rotators have different thermal inertia values, show the derived thermal inertia values of slow (fast) rotators to be 8 (77), 8 (27), 9 (34), 5 (55) J m⁻² K⁻¹ s^−1/2 for the A, B, and C rings, and the Cassini division, respectively. The values for fast rotators are still much smaller than those for solid ice with no porosity. Thus, fast rotators are likely to have surface regolith layers, but these may not be as fluffy as those for slow rotators, probably because the capability of holding regolith particles is limited for fast rotators due to the strong centrifugal force on surfaces of fast rotators. Other additional parameter fits, in which radii of fast rotators are varied, indicate that particles less than ∼1 cm should not occupy more than roughly a half of the cross section for the A, B, and C rings.     

On the evolution of Saturn's “spokes”: Theory

Starting with the assumption that negatively charged micron-sized dust grains may be elevated above Saturn's ring plane by plasma interactions, the subsequent evolution of the system is discussed. The discharge of the fine dust by solar uv radiation produces a cloud of electrons which moves adiabatically in Saturn's dipolar magnetic field. The electron cloud is absorbed by the ring after one bounce, alters the local ring potential significantly, and reduces the local Debye length. As a result, more micron-sized dust particles may be elevated above the ring plane and the spoke grows. This process continues until the electron cloud has dissipated.     

Optical reflectance polarimetry of Saturn's globe and rings: IV. Aerosols in the upper atmosphere of Saturn

From 1958 to 1976 the degree and direction of polarization of the light at Saturn's disk center were measured in orange light over 74 nights and at five wavelenghts over 19 nights. Measurements were also recorded at limb, terminator, and pole. In addition, extensive regional polarization measurements were collected over Saturn's disk and several polarization maps were produced. These data were analyzed on the basis Mie scattering theory and of transfer theory in planetary atmospheres. A model of the Saturn upper atmosphere aerosol structure is derived in which the top part of the the main cloud layer is composed of spherical transparent particles of radius 1.4 μm and refractive index 1.44. Above this layer, a fine haze of submicron-sized grains was detected by its production of a component of polarization which is always directed poleward; this upper haze is interpreted as having nonspherical particles which are systematically oriented. This upper haze layer covers approximately the whole planet uniformly but varies in thickness from year to year. The clear gas above the cloud layer has an optical thickness of around 0.1.     

Comment on radar scattering from Saturn's rings

Transparent particle scattering is proposed to explain the unexpectedly large radar cross section recently observed for Saturn's rings. According to this theory, only 10% of the optically observed material in the A, B, and C rings need consist of smooth ice fragments larger than 8 cm in radius to yield the radar results.     

Theoretical interpretation of the ground-based photometry of Saturn's B ring

New photographic photometry at small tilt angles during the 1979 and 1981 apparitions is combined with earlier data to yield several physical parameters for Saturn's B ring in red and blue colors. Phase curves are obtained for a mean tilt angle B ? 6°. The value of the volume density D is 0.020±0.004 with no indication of dependence on either the color or the tilt angle for 6°<B<26°. This conclusion is not altered significantly if the individual ring particles have a phase function similar to the phase curves of bright solar system objects. For the geometric albedo of a single particle we derive 0.61±0.04 (red) and 0.41±0.03 (blue), which are superior to earlier estimates because of the additional data now available. These values and the derived amount of multiple scattering as a function of tilt angle constrain the particle phase function in the red to be moderately backscattering. Inferred values of the particle single-scattering albedo are $\text{0.7≤}\text{ω}{}_0\text{(}\text{red}\text{) ≤0.92}$ and $\text{0.5≤}\text{ω}{}_0\text{(}\text{blue}\text{) ≤0.7}$, depending on the choice of phase function. No indication was found that the particle photometric properties might depend on the vertical distance from the central plane. Our results show that the ground-based photometry is entirely consistent with the classical, many-particle-thick ring model.     

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 electrostatic discharges: Could lightning be the cause?

It is proposed that Saturn's electrostatic discharges (SED) might be generated in the planet's equatorial atmosphere, perhaps as lightning from a storm system. The 10^h10^m periodicity of the signal envelope duplicates that of Saturn's equatorial jet. The rings shield the atmosphere from solar EUV photons, and thereby substantially reduce the local ionospheric cutoff frequency to allow low-frequency SED to leak out. Many of the unusual properties of SED could be explained in terms of changes in the storm system, the relative spacecraft position in the beaming pattern of the source, local refraction of the signal by the highly disturbed ionosphere, and the influence of the ring particles on the highest frequency component of SED. A comparison of SED with planetary lightning on other planets shows that the two are similar in general character and some time behavior; the power output of SED may be higher than most planetary lightnings but that is unclear because of uncertainties in the measurements and variations in the signal's spectrum. Our simple discussion suggests that lightning could be a viable source for SED and that exotic ring mechanisms are not necessarily required.     

Saturn's nonaxisymmetric ring edges at 1.95 Rs and 2.27 Rs

The outer edges of Saturn's A and B rings, at 2.27 R_s and 1.95 R_s, have been examined using data acquired by four Voyager experiments. The shapes and kinematics of these features are influenced by their proximity to strong low-order Lindblad resonances. The data for the A-ring edge are consistent with a seven-loded radial distortion of amplitude 6.7 ± 1.5 km which rotates with the mass-weighted mean angular velocity of the coorbital satellite system. The B-ring edge has essentially a double-lobed figure of radial amplitude 74 ± 9 km which rotates with the mean motion of Mimas, though there is an indication that it is not completely described withe a simple Saturn-centered ellipse. An upper limit of 10 m has been placed on the vertical thickness in the unperturbed region of the B ring.     

Saturn's E ring: I. CCD observations of March 1980

The tenuous E ring of Saturn is found to commence abruptly at 3 Saturn radii, to peak sharply in the vicinity of the orbit of the satellite Enceladus (about 4 radii), and to spread out thinly to more than 8 radii. This distribution strongly suggests it to be associated with Enceladus and perhaps to be material ejected from Enceladus. The spread of E-ring material above and below the ring plane is greater in its tenuous outskirts than in its denser inner region, suggesting that the E ring may be at an early stage in its evolution. Thus far, our analysis reveals only a marginal variation of the ring with time or Enceladus azimuth. In this paper we describe the special instrumentation used for photometric observations of the E ring, and we present some of the data obtained in March 1980. In Paper II we shall derive the three-dimensional distribution of material in the E ring and discuss its cosmogonic implications.