Saturn's ring and nearby faint satellites

Observations of Saturn's rings during passage of the Earth through the ring plane, coupled with those of others, suggest a ring thickness of 1.3 ± 0.3 km. The wide disparity in the optical depth of Cassini's division found by other investigators is resolved, and for conservative isotropic single scattering, a normal optical depth for Cassini's division of 0.060 ± 0.006 is obtained. We find the mean normal optical depth of ring C to be 0.074 ± 0.007. Analysis of all available observations of faint objects near Saturn indicates the presence of at least one previously undiscovered satellite of Saturn. The orbit for Janus determined by Dollfus is supported. These satellites may be major members of an extended ring.     

Tidal dissipation,orbital evolution,and the nature of Saturn's inner satellites

Estimates of tidal damping times of the orbital eccentricities of Saturn's inner satellites place constraints on some satellite rigidities and dissipation functions Q. These constraints favor rock-like rather than ice-like properties for Mimas and probably Dione. Photometric and other observational data are consistent with relatively higher densities for these two satellites, but require lower densities for Tethys, Enceladus, and Rhea. This leads to a nonmonotonic density distribution for Saturn's inner satellites, apparently determined by different mass fractions of rocky materials. In spite of the consequences of tidal dissipation for the orbital eccentricity decay and implications for satellite compositions, tidal heating is not an important contributor to the thermal history of any Saturnian satellite.     

Saturn's icy satellites: Thermal and structural models

Thermal histories of the small icy Saturnian satellites Mimas, Tethys, Dione, Rhea, and Iapetus are constructed by assuming that they formed as homogeneous ice-silicate mixtures. The models include effects of radiogenic and accretional heating, conductive and subsolidus convective heat transfer, and lithospheric growth. Accretional heating is unlikely to have melted the water ice in the interiors of these bodies and solid state creep of the predominately ice material precludes melting by radiogenic heating. Mimas is so small that its thermal evolution is essentially purely conductive; at present it is a cold, nearly isothermal body. Any subsolidus convection or thermal activity in Mimas would have been confined to a brief period in its early history and would have been due to a warm formation. The four largest satellites are big enough and contain sufficient heat-producing silicates that solid state convection beneath a rigid lithosphere is inevitable independent of initial conditions. Dione and Rhea have convective interiors for most of their thermal histories, while Tethys and Iapetus have mainly conductive thermal histories with early periods of convective 0activity. The thermal histories of the five satellites for the last 4 by are independent of initial conditions; at present they have cold, conductive interiors. The model thermal histories are qualitatively consistent with the appearances of these satellites: Mimas has an ancient heavily cratered surface, Tethys and probably Iapetus have both heavily cratered and more lightly cratered areas, and Dione and Rhea have extensively modified surfaces. Because of their similar sizes and densities, Mimas and Enceladus are expected to have similar surfaces and thermal histories, but instead Enceladus has the most modified surface of all the small icy Saturnian satellites. Our results suggest a heat source for Enceladus, in addition to radiogenic and accretional heating; tidal dissipation is a possibility. Because the water ice in these bodies does not melt, resurfacing must be accomplished by the melting of a low-melting-temperature minor component such as ammonia hydrate.     

Resurfacing Saturn's satellites: Models of partial differentiation and expansion

The faulting seen on the surfaces of Saturn's icy moons may have been caused either by external events, such as large impacts, or internal stresses caused by the expansion of the moons as long-lived radionuclides produced internal heating and phase changes. We estimate the stress as a function of radius expansion is σ = 44 (Δr/r) kbar. The extensional stress needed for fracture is probably something less than 40 bar so extensional fracture is likely to occur when Δr/r is greater than one part in a thousand. The radius change for these moons can be calculated analytically, given suitable assumptions; in addition, detailed time-dependent computer models of the thermal and physical evolution of Tethys, Dione, Rhea, and Iapetus were carried out. From these calculations we conclude that the most reasonable cause for rifting on Dione and Rhea is the refreezing of an ammonia-water eutectic melt inside these moons roughly two billion years after their formation, while the rift on Tethys was caused by a large impact, and little rifting should be expected on Iapetus.     

Mutual phenomena of Jupiter's five inner satellites in 1979

In this paper, we first predict eclipses and occultations of the Galilean satellites in 1979 and find that, although circumstances are generally poor, about 75 events are observable. We have then made a special point of including 40 eclipses of J5 (Amalthea) by the Galilean satellites in the hope that both visual and far-infrared light curves can be obtained—the former giving accurate astrometric information for J5, and the latter possibly bearing on its surface stucture or composition.     

Long-term changes in Saturn's troposphere

We report the results of monitoring Saturn's H₂ quadrupole and CH₄ band absorptions outside of the equatorial zone over one-half of Saturn's year. This interval covers most of the perihelion half of Saturn's elliptical orbit, which happens to be approximately bounded by the equinoxes. Marked long-term changes occur in the CH₄ absorption accompanied by weakly opposite changes in the H₂ absorption. Around the 1980 equinox, the H₂ and CH₄ absorptions in the northern hemisphere appear to be discontinuous with those in the southern hemisphere. This discontinuity and the temporal variation of the absorptions are evidence for seasonal changes. The absorption variations can be attributed to a variable haze in Saturn's troposphere, responding to changes in temperature and insolation through the processes of sublimation and freezing. Condensed or frozen CH₄ is very unlikely to contribute any haze. The temporal variation of the absorption in the strong CH₄ bands at south temperate latitudes is consistent with a theoretically expected phase lag of 60° between the tropopause temperature and the seasonally variable insolation. We model the vertical haze distribution of Saturn's south temperature latitudes during 1971–1977 in terms of a distribution having a particle scale height equal to a fraction of the atmospheric scale height. The results are a CH₄/H₂ mixing ratio of (4.2 ± 0.4) × 10^?3, a haze particle albedo of $\text{ω}\text{= 0.995 ± 0.003}$, and a range of variation in the particle to gas scale-height ratio of 0.6 ± 0.2. The haze was lowest near the time of maximum temperature. We also report spatial measurements of the absorption in the 6450 Å NH₃ band made annually since the 1980 equinox. A 20 ± 4% increase in the NH₃ absorption at south temperate latitudes has occurred since 1973–1976 and the NH₃ absorption at high northern latitudes has increased during spring. Increasing insolation, and the resulting net sublimation of NH₃ crystals, is probably the cause. Significant long-term changes apparently extend to the deepest visible parts of Saturn's atmosphere. An apparently anomalous ortho-para H₂ ratio in 1978 suggests that the southern temperate latitudes experienced an unusual upwelling during that time. This may have signaled a rise in the radiative-convective boundary from deep levels following maximum tropospheric temperature and the associated maximum radiative stability. This would be further evidence that the deep, visible atmosphere is governed by processes such as dynamics and the thermodynamics of phase changes, which have response times much shorter than the radiative time constant.     

Plasma clouds in Saturn's rings

The expansion and ionization of vapor produced by impacts of meteorites on Saturn's rings is described. There is an “impact plasma” produced in the initial collision, and a “secondary plasma” produced by subsequent ionization of the neutral gas ejecta. The dynamics of these plasma clouds, their size, density, and life time are calculated. It is suggested that large clouds, produced by meter-sized meteorites (or a collection of such clouds produced, e.g., by the impact of a swarm of meteorites) may lead to the formation of spokes by the mechanism discussed in Goertz, C. K., and Morfill, G. E. (Icarus53, 219–229, 1983).     

Saturn's rings and Pioneer 11

Quantitative predictions of the diffuse reflection and transmission properties of Saturn's rings, relevant to the September 1979 Pioneer 11 flyby, are presented. Predictions are based on an elementary anisotropic scattering model. Interparticle separations are considered to be sufficiently large that mutual shadowing is negligible. Likely ranges in both the single scattering albedo and perpendicular optical thickness of the ring are considered. Situations of pronounced back-scattering and of isotropic scattering are treated individually. Spacecraft measurement of the radiation suffering diffuse scattering by the ring can provide a useful test of the basic ring model.     

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 velocity dispersion in Saturn's rings

The surface of Mercury exhibits a global tectonic system consisting of an ancient set of NE and NW trending lineaments and a younger set of planimetrically arcuate escarpments interpreted as thrust or high-angle reverse faults. The trends, distribution, and age relations of these tectonic features can be explained by a combination of tidal despinning and global contraction of the planet. In our model, early tidal despinning resulted in conjugate shear fractures trending roughly N60°E and N60°W which were subsequently modified by a variety of surface processes to produce the presently visible set of lineaments. Continued despinning plus global contraction produced thrust faults with roughly north-south trends. Final contraction may have postdated despinning and produced randomly oriented thrust faults. All of these events predated the formation of Caloris basin, because basin-associated deposits blanket both lineaments and arcuate thrust faults.     

Bending waves and the structure of Saturn's rings

The surface mass density profiles at four locations within Saturn's rings are calculated using Voyager spacecraft images of spiral bending waves. Bending waves are vertical corrugations in Saturn's rings which are excited at vertical resonances of a moon, e.g., Mimas, whose orbit is inclined with respect to the mean plane of the rings. Bending waves propagate toward Saturn by virtue of the rings' self-gravity; their wavelength depends on the local surface mass density of the rings. Observations of bending waves can thus be used to determine the surface density in regions of Saturn's rings near vertical resonances. The average surface density of the outer B ring near Mimas' 4:2 inner vertical resonance is 54 ± 10 g cm^?2. Surface density in this region probably varies by ～ 30% over radial length scales of tens of kilometers; and irregular radial structure is present on similar length scales in this region. Surface densities ranging from 24 g cm^?2 to 45 g cm^?2 are found in the A ring. Small scale variations in surface density are not seen in the A ring, consistent with its more uniform optical appearance.     

Delay-Doppler radar observations of Saturn's rings

The relative radar reflectiveness of Saturn's classical ring sections were estimated from delay-Doppler observations made at 12.6-cm wavelength. The A and B rings are responsible for most, if not all, of the radar echo. The average radar reflectivity per unit projected area of the A ring is nearly (～90%) as large as that of the B ring. The outer half of the B ring contains the most reflective part of the ring system. There is no firm evidence for detection of radar backscattering from particles interior to the B ring, exterior to the A ring, or from the planet itself. The radar reflectivity of the C ring is certainly no more than one-half that of the B ring, and probably is much less. Unexpectedly large amounts of power at Doppler shifts near the center of the echo spectrum, previously reported at both λ3.5 and λ12.6 cm for ring-plane tilt angles δ ≥ 24.4°, are not apparent in λ3.5- or 12.6-cm spectra obtained at δ ≤ 21.4°.     

A numerical study of Saturn's F-ring

We study the short-term effects of “shepherding” satellites on narrow rings, in the general case where all bodies move along eccentric orbits. We do this by following numerically a ring of test particles as their orbits evolve under the gravitational perturbations of the shepherds. Planar motion is assumed. Our numerical scheme vastly improves (by a factor of ～10⁴) the computation speed over conventional orbital integration methods by constructing a table of the perturbation integrals and then utilizing it over and over. The approach is applicable to any narrow ring with a nearby satellite, such as a ring confined by the shepherding mechanism of P. Goldreich and S. Tremaine [Nature277, 97–99 (1979)]. We arrive at results for a variety of orbital configurations, and then apply these to the F-ring of Saturn. Several features of the numerical integration are reminiscent of the kinks and clumps observed by Voyager. If the ring-to-satellite distance changes significantly due to eccentricities, then the ring can break up into periodic clumps in an azimuthal domain which trails the satellite. This region may lag somewhat in longitude. The perturbations may also cause the ring to vary significantly in width, being narrowest near the point of closest approach of the shepherd and widest at the opposite side. It is as yet unclear whether this effect is, or could be, observed in the Voyager images. And finally, the perturbations of the shepherds can impact a significant, but probably time variable, eccentricity to the ring. The short-term tendency is not toward alignment of ring and satellite apsides; longer time effects have not been explored.     

Anisotropic optical scattering within Saturn's rings

Visual photometric function data for Saturn's rings are analyzed in terms of elementary anisotropic scattering radiative transfer models which involve the Henyey-Greenstein function. Limits are placed on the combinations of single scattering albedo and backscattering directivity which are permitted by observation. Particles with both microscopic and macrscopic lunar-like scattering properties are excluded by the analysis. Results are consistent with the ring particles being nearly pure spherical conglomerates of H₂O frost.     

Observations of Saturn's outer ring and new satellites during the 1980 edge-on presentation

Observations of Saturn's satellites and external rings during the 1980 edge-on presentation were obtained with a focal coronograph. A faint satellite traveling in the orbit of Dione and leading it by 72° has been detected, together with the two inner satellites already suspected (cf. J. W. Fountain and S. M. Larson, 1978,Icarus36, 92–106). The external ring has been observed on both east and west sides; it may extend up to $\text{?8.3}$ Saturn radii, and appears structured.     

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.     

A theoretical photometric function of Saturn's rings

A photometric theory of Saturn's rings is developed on the assumption that partially elastic collisions have brought all the ring particles into the same plane. The resulting photometric function explains the tilt effect of the rings, but the opposition peak must originate in the particles themselves.     

Photometry of Saturn's satellites: The opposition effect of Iapetus at maximum light and the variability of Titan

We present photometry, V and (B - V), of Iapetus at six western elongations (the phase of maximum brightness) that span a range in solar phase, α, from ≈6° to <0°.4, and we find that a substantial opposition effect, >0.12 mag (V), is present. We make a few cautious remarks about the possible relevance of the use of this result to interpret the phase curve of Saturn's ring. We also give a few measures of Rhea and Hyperion, at $\text{α ? 0.3°}$, and more of Titan, which indicate that the latter has been anomalously bright during much of 1973 and 1974, sometimes by nearly 0.1 mag (V).     

On the azimuthal brightness variations of Saturn's rings

We present a simple, semiquantitative explanation that accounts both for the presence of the azimuthal brightness variations in Saturn's ring A and for their absence in ring B. Our explanation avoids any ad hoc reliance on albedo variations and/or synchronous rotation of ring particles. Instead, it requires only some degree of self-gravitation between nearby orbiting bodies. A bias in the particle distribution and corresponding photometric effects are thereby produced—the latter corresponding very closely to the variations observed in ring A. Their absence in ring B is primarily a consequence of the higher optical thickness and decreasing importance of self-gravitation in that ring.     

Some constraints on particles in Saturn's spokes

The consequences of taking into account some physical processes previously ignored in the context of Saturn's spokes were studies. Secondary emission, which can ensure large changes of potential following small environment variations, may provide a plausible mechanism for triggering spoke formation. Taking into account the grains' centrifugal disruption due to their spin, should modify the constraints on size previously derived on the basis of electrostatic disruption alone. Taking into account the dielectric polarization when calculating the electrostatic forces on grains resting on parent bodies gives ejection conditions more stringent than previously expected. Finally, a simplified evaluations shows that if secondary emission properties of ring particle are of the order of those of many other oxides, and if the plasma temperature is near one of their threshold temperatures, then a very small environmental variation can trigger the ejection of about 0.1- to 1-μm grains from about 1-mm to 10-cm parent bodies in a very short time scale.