Infrared observations of Saturn's rings by Cassini CIRS : Phase angle and local time dependence

Since the Saturn orbit insertion (SOI) of the Cassini spacecraft, in July 2004, the Cassini Composite Infrared Spectrometer (CIRS) has obtained a large number of thermal infrared spectra of Saturn's rings. Over the two and a half years of observations to date, ring temperatures were retrieved for a large range of unique geometries, inaccessible from Earth. Understanding their dependencies with phase angle and local time is a clue to understanding the thermal properties and dynamics of Saturn's ring particles.Azimuthal scans of rings, which have been obtained by CIRS at constant radial distance from the planet, have been planned to measure ring temperature variations with local hour angle. Over 47 azimuthal scans for Saturn's main rings (A, B, C and Cassini Division) have been retrieved to date, on both lit and unlit sides, at different phase angles and spacecraft elevations. The first measurements of the transient thermal episode of eclipse cooling in the planetary shadow have also been obtained for all three rings.In this paper, we present an overview of all azimuthal scans obtained by the Cassini/CIRS instrument so far and the dependencies of the temperature and the filling factor with the phase angle and the local hour angle. The ring temperature varies with longitude as the input heating flux coming from Saturn and the Sun changes. The decrease in temperature with the increasing phase angle on both the lit and the unlit sides and for most of the local time also suggests the presence of slowly rotating particles. The crossing of the planet's shadow generates drastic azimuthal variations in temperature, up to 20 K in the C ring. The strong anisotropy of emission observed outside the shadow between low and high phase angles decreases when ring particles cross the shadow, suggesting that particles are almost isothermal in the shadow. This suggests a thermal inertia associated with a rotating rate of particles low enough to have a thermal contrast on their surface.The temperature in the B ring is less sensitive to the phase angle effect on the lit side, suggesting that particles are close enough to form a flat layer at a scale larger than the particle's radius. On the unlit side, particles in the B ring are less sensitive to the lack of solar input than in the C ring or in the A ring. Azimuthal variations of the filling factor in the A ring are also detected with changing ring local time. This effect might be created by the presence of gravitational instabilities (wakes).     

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.     

Cassini thermal observations of Saturn's main rings: Implications for particle rotation and vertical mixing

In late 2004 and 2005 the Cassini composite infrared spectrometer (CIRS) obtained spatially resolved thermal infrared radial scans of Saturn's main rings (A, B and C, and Cassini Division) that show ring temperatures decreasing with increasing solar phase angle, α, on both the lit and unlit faces of the ring plane. These temperature differences suggest that Saturn's main rings include a population of ring particles that spin slowly, with a spin period greater than 3.6 h, given their low thermal inertia. The A ring shows the smallest temperature variation with α, and this variation decreases with distance from the planet. This suggests an increasing number of smaller, and/or more rapidly rotating ring particles with more uniform temperatures, resulting perhaps from stirring by the density waves in the outer A ring and/or self-gravity wakes.The temperatures of the A and B rings are correlated with their optical depth, τ, when viewed from the lit face, and anti-correlated when viewed from the unlit face. On the unlit face of the B ring, not only do the lowest temperatures correlate with the largest τ, these temperatures are also the same at both low and high α, suggesting that little sunlight is penetrating these regions.The temperature differential from the lit to the unlit side of the rings is a strong, nearly linear, function of optical depth. This is consistent with the expectation that little sunlight penetrates to the dark side of the densest rings, but also suggests that little vertical mixing of ring particles is taking place in the A and B rings.     

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.     

Thermal observations of Saturn's main rings by Cassini CIRS: Phase, emission and solar elevation dependence

Two and a half years after Saturn orbit insertion (SOI) the Cassini composite infrared spectrometer (CIRS) has acquired an extensive set of thermal measurements (including physical temperature and filling factor) of Saturn's main rings for a number of different viewing geometries, most of which are not available from Earth. Thermal mapping of both the lit and unlit faces of the rings is being performed within a multidimensional observation space that includes solar phase angle, spacecraft elevation and solar elevation. Comprehensive thermal mapping is a key requirement for detailed modeling of ring thermal properties.To first order, the largest temperature changes on the lit face of the rings are driven by variations in phase angle while differences in temperature with changing spacecraft elevation are a secondary effect. Ring temperatures decrease with increasing phase angle suggesting a population of slowly rotating ring particles [Spilker, L.J., Pilorz, S.H., Wallis, B.D., Pearl, J.C., Cuzzi, J.N., Brooks, S.M., Altobelli, N., Edgington, S.G., Showalter, M., Michael Flasar, F., Ferrari, C., Leyrat, C. 2006. Cassini thermal observations of Saturn's main rings: implications for particle rotation and vertical mixing. Planet. Space Sci. 54, 1167-1176, doi: 10.1016/j.pss.2006.05.033]. Both lit A and B rings show that temperature decreases with decreasing rings solar elevation while temperature changes in the C ring and Cassini Division are more muted. Variations in the geometrical filling factor, β, are primarily driven by changes in spacecraft elevation. For the optically thinnest region of the C ring, β variations are found to be nearly exclusively determined by spacecraft elevation. Both a multilayer and a monolayer model provide an excellent fit to the data in this region. In both cases, a ring infrared emissivity >0.9 is required, together with a random and homogeneous distribution of the particles. The interparticle shadowing function required for the monolayer model is very well constrained by our data and matches experimental measurements performed by Froidevaux [1981a. Saturn's rings: infrared brightness variation with solar elevation. Icarus 46, 4-17].     

Saturn A ring surface mass densities from spiral density wave dispersion behavior

We have undertaken an analysis of the Voyager photopolarimeter (PPS) stellar occultation data of Saturn's A ring. The Voyager PPS observed the bright star δ Scorpii as it was occulted by Saturn's main rings during the spacecraft flyby of the Saturn system in 1981. The occultation measurement produced a ring profile with radial resolution of approximately 100 m, and radial structure is evident in the profile down to the resolution limit. We have applied an autoregressive technique to the data for estimating the power spectrum as a function of radius, which has allowed us to identify 40 spiral density waves in Saturn's A ring, associated with the strongest torques due to forcing from the moons. The majority of the detected waves are observed to disperse linearly in regions beginning a few kilometers from the resonance location. We have used the dispersion behavior for those waves to calculate local surface mass densities in the vicinity of each wave. We find that the inner three-quarters of the A ring (up to the beginning of the Encke gap) has an average surface mass density of , while the outer region has an average surface mass density of . The two regions have different mean surface mass densities with a significance of approximately 0.999993, as estimated with a T-statistic, which corresponds to about 4.5σ. While the mean optical depth of the A ring increases slightly with increasing distance from Saturn, we find that it is not significantly correlated with the surface mass density; the two quantities having a linear Pearson's correlation coefficient of r_corr≈−0.03. The variation of mass density, independent of PPS optical depth, is consistent with previous conjectures that the particle size distribution and composition are not constant across the entire A ring, particularly in the very outer portion. We estimate the mass of Saturn's A ring from our surface mass density estimates as 4.9×10²¹ gm, or 8.61×10⁻⁹ of the mass of Saturn, roughly equivalent to the mass of a 110-km diameter icy satellite. This mass is almost 25% smaller than estimates from previous studies, but is well within the expected errors of the derived mass densities. We also identified three previously unstudied features which exhibit linear dispersion. The strongest of these features is tentatively identified as the Janus 13:11 density wave. The other two features do not fall near any known satellite resonances and may represent density waves created by previously undetected satellites.     

How much oxygen is too much? Constraining Saturn's ring atmosphere

The discovery of a molecular oxygen atmosphere around Saturn's rings has important implications for the electrodynamics of the ring system. Its existence was inferred from the Cassini in situ detection of molecular oxygen ions above the rings during Saturn Orbit Insertion in 2004. Molecular oxygen is difficult to observe remotely, and theoretical estimates have yielded only a lower limit (Nn?¹⁰¹³ cm⁻²) to the O₂ column density. Comparison with observations has previously concerned matching ion densities at spacecraft altitudes far larger than the scale height of the neutral atmosphere. This is further complicated by charged particle propagation effects in Saturn's offset magnetic field. In this study we adopt a complementary approach, by focusing on bulk atmospheric properties and using additional aspects of the Cassini observations to place an upper limit on the column density. We develop a simple analytic model of the molecular atmosphere and its photo-ionization and dissociation products, with Nn a free parameter. Heating of the neutrals by viscous stirring, cooling by collisions with the rings, and torquing by collisions with pickup ions are all included in the model. We limit the neutral scale height to h?3000 km using the INMS neutral density nondetection over the A ring. A first upper limit to the neutral column is derived by using our model to reassess O₂ production and loss rates. Two further limits are then obtained from Cassini observations: corotation of the observed ions with the planet implies that the height-integrated conductivity of the ring atmosphere is less than that of Saturn's ionosphere; and the nondetection of fluorescent atomic oxygen over the rings constrains the molecular column from which it is produced via photo-dissociation. These latter limits are independent of production and loss rates and are only weakly dependent on temperature. From the three independent methods described, we obtain similar limits: Nn?2×¹⁰¹⁵ cm⁻². The mean free path for collisions between neutrals thus cannot be very much smaller than the scale height.     

A multilayer model for thermal infrared emission of Saturn’s rings II: Albedo, spins, and vertical mixing of ring particles inferred from Cassini CIRS

Since the Saturn orbit insertion of the Cassini spacecraft in mid-2004, the Cassini composite infrared spectrometer (CIRS) measured temperatures of Saturn’s main rings at various observational geometries. In the present study, we apply our new thermal model (Morishima, R., Salo, H., Ohtsuki, K. [2009]. Icarus 201, 634-654) for fitting to the early phase Cassini data (Spilker, L.J., and 11 colleagues [2006]. Planet. Space Sci. 54, 1167-1176). Our model is based on classical radiative transfer and takes into account the heat transport due to particle motion in the azimuthal and vertical directions. The model assumes a bimodal size distribution consisting of small fast rotators and large slow rotators. We estimated the bolometric Bond albedo, A_V, the fraction of fast rotators in cross section, f_fast, and the thermal inertia, Γ, by the data fitting at every radius from the inner C ring to the outer A ring. The albedo A_V is 0.1-0.4, 0.5-0.7, 0.4, 0.5 for the C ring, the B ring, the Cassini division, and the A ring, respectively. The fraction f_fast depends on the ratio of scale height of fast rotators to that of slow rotators, h_r. When h_r = 1, f_fast is roughly half for the entire rings, except for the A ring, where f_fast increases from 0.5 to 0.9 with increasing saturnocentric radius. When h_r increases from 1 to 3, f_fast decreases by 0.2-0.4 for the B and A rings while no change in f_fast is seen for the optically thin C ring and Cassini division. The large f_fast seen in the outer A ring probably indicates that a large number of small particles detach from large particles in high velocity collisions due to satellite perturbations or self-gravity wakes. The thermal inertia, Γ, is constrained from the efficiency of the vertical heat transport due to particle motion between the lit and unlit faces, and is coupled with the type of vertical motion. We found that in most regions, except for the mid B ring, sinusoidal vertical motion without bouncing is more reasonable than cycloidal motion assuming bouncing at the midplane, because the latter motion gives too large Γ as compared with previous estimations. For the mid B ring, where the optical depth is highest in Saturn’s rings, cycloidal vertical motion is more reasonable than sinusoidal vertical motion which gives too small Γ.     

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.     

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.     

Saturn's rings, the Yarkovsky effects, and the Ring of Fire

Saturn's icy ring particles, with their low thermal conductivity, are almost ideal for the operation of the Yarkovsky effects (photon thrust due to temperature gradients across the ring particles). An extremely simple case of the Yarkovsky effects is examined here, in which orbital evolution is computed as though each particle travels around Saturn alone in a circular orbit, so that there are no collisions, shadowing, or irradiance from other particles; nor are resonances, tumbling, or micrometeoroid erosion considered. The orbital evolution for random spin orientations appears to be a competition between two effects: the seasonal Yarkovsky effect, which makes orbits contract, and the Yarkovsky-Schach effect, which makes orbits expand. There are values of the far infrared and visible particle albedos for which (working radially out from the planet) the along-track particle acceleration S is negative, then positive, and then negative again; the region for which S>0 is interpreted as a region where stable rings are possible. Typical timescales for centimeter-sized particles to travel half a Saturn radius are ¹⁰⁷-¹⁰⁸ yr. Collisions, shadowing, and resonances may lengthen the timescales, perhaps considerably. It is speculated here that the C ring may be depleted of particles because of the seasonal Yarkovsky effect, and small particles that are present in the C ring ultimately fall on Saturn, possibly creating a “Ring of Fire” as they enter the planet's atmosphere.     

Keck infrared observations of Saturn's main rings bracketing Earth's August 1995 ring plane crossing

We present results of near-infrared (2.26 μm) observations of Saturn's main rings taken with the W.M. Keck telescope during August 8-11, 1995, surrounding the time that Earth crossed Saturn's ring plane. These observations provide a unique opportunity to study the evolution of the ring brightness in detail, and by combining our data with Hubble Space Telescope (HST) results (Nicholson et al., 1996, Science 272, 453-616), we extend the 12-hour HST time span to several days around the time of ring plane crossing (RPX). In this paper, we focus on the temporal evolution of the brightness in Saturn's main rings. We examine both edge-on ring profiles and radial profiles obtained by “onion-peeling” the edge-on data. Before RPX, when the dark (unlit) face of the rings was observed, the inner C ring (including the Colombo gap), the Maxwell gap, Cassini Division and F ring region were very bright in transmitted light. After RPX, the main rings brighten rapidly, as expected. The profiles show east-west asymmetries both before and after RPX. Prior to RPX, the evolution in ring brightness of the Keck and HST data match one another quite well. The west side of the rings showed a nonlinear variation in brightness during the last hours before ring plane crossing, suggestive of clumping and longitudinal asymmetries in the F ring. Immediately after RPX, the east side of the rings brightened more rapidly than the west. A quantitative comparison of the Keck and HST data reveals that the rings were redder before RPX than after; we ascribe this difference to the enhanced multiple scattering of photons passing through to the unlit side of the rings.     

Phosphine on Jupiter and Saturn from Cassini/CIRS

The global distribution of phosphine (PH₃) on Jupiter and Saturn is derived using 2.5 cm⁻¹ spectral resolution Cassini/CIRS observations. We extend the preliminary PH₃ analyses on the gas giants [Irwin, P.G.J., and 6 colleagues, 2004. Icarus 172, 37-49; Fletcher, L.N., and 9 colleagues, 2007a. Icarus 188, 72-88] by (a) incorporating a wider range of Cassini/CIRS datasets and by considering a broader spectral range; (b) direct incorporation of thermal infrared opacities due to tropospheric aerosols and (c) using a common retrieval algorithm and spectroscopic line database to allow direct comparison between these two gas giants.The results suggest striking similarities between the tropospheric dynamics in the 100-1000 mbar regions of the giant planets: both demonstrate enhanced PH₃ at the equator, depletion over neighbouring equatorial belts and mid-latitude belt/zone structures. Saturn's polar PH₃ shows depletion within the hot cyclonic polar vortices. Jovian aerosol distributions are consistent with previous independent studies, and on Saturn we demonstrate that CIRS spectra are most consistent with a haze in the 100-400 mbar range with a mean optical depth of 0.1 at 10 μm. Unlike Jupiter, Saturn's tropospheric haze shows a hemispherical asymmetry, being more opaque in the southern summer hemisphere than in the north. Thermal-IR haze opacity is not enhanced at Saturn's equator as it is on Jupiter.Small-scale perturbations to the mean PH₃ abundance are discussed both in terms of a model of meridional overturning and parameterisation as eddy mixing. The large-scale structure of the PH₃ distributions is likely to be related to changes in the photochemical lifetimes and the shielding due to aerosol opacities. On Saturn, the enhanced summer opacity results in shielding and extended photochemical lifetimes for PH₃, permitting elevated PH₃ levels over Saturn's summer hemisphere.     

Empirical models of pressure and density in Saturn's interior: Implications for the helium concentration, its depth dependence, and Saturn's precession rate

We present ‘empirical’ models (pressure vs. density) of Saturn's interior constrained by the gravitational coefficients J₂, J₄, and J₆ for different assumed rotation rates of the planet. The empirical pressure-density profile is interpreted in terms of a hydrogen and helium physical equation of state to deduce the hydrogen to helium ratio in Saturn and to constrain the depth dependence of helium and heavy element abundances. The planet's internal structure (pressure vs. density) and composition are found to be insensitive to the assumed rotation rate for periods between 10h:32m:35s and 10h:41m:35s. We find that helium is depleted in the upper envelope, while in the high pressure region (P?1 Mbar) either the helium abundance or the concentration of heavier elements is significantly enhanced. Taking the ratio of hydrogen to helium in Saturn to be solar, we find that the maximum mass of heavy elements in Saturn's interior ranges from ∼6 to 20 M_⊕. The empirical models of Saturn's interior yield a moment of inertia factor varying from 0.22271 to 0.22599 for rotation periods between 10h:32m:35s and 10h:41m:35s, respectively. A long-term precession rate of about ^0.754″ yr⁻¹ is found to be consistent with the derived moment of inertia values and assumed rotation rates over the entire range of investigated rotation rates. This suggests that the long-term precession period of Saturn is somewhat shorter than the generally assumed value of 1.77×¹⁰⁶ years inferred from modeling and observations.     

Saturn's Rings: Azimuthal variations,phase curves,and radial profiles in four colors

Four-color photographic photometry of Saturn for the 1977–1979 apparitions has been analyzed to determine the dependence of ring brightness on wavelength, solar phase angle, ring particle orbital phase angle (azimuthal effect), declination of the Earth relative to the ring plane (tilt angle), and radial distance from Saturn. Azimuthal brightness variations up to ±20% relative to the ansae are clearly apparent for the maximum of ring A, but are not detectable for ring B or the outer portion of ring A. The shape of the intensity (I) versus orbital phase angle (θ) curve varies with ring tilt (B) and probably with wavelength, and shows 180° symmetry. As characterized by its slope near the ansae, this curve suggests that the azimuthal effect increases as B decreases from 26 to ≈11°. The phase curves l(α) for the ansae show very little dependence on ring tilt (26° > B > 6°), on wavelength, or on radial distance from Saturn; possibly the curves are somewhat steeper at the smallest tilt angles and for ring A relative to ring B. The radial profile of both rings becomes flatter with decreasing tilt angle and with decreasing wavelength. The latter effect is a natural result of the classical, many-particle-thick ring model.     

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

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

Infrared radiometry of the rings of Saturn

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

Cassini observations of Saturn's inner plasmasphere: Saturn orbit insertion results

We present new and definitive results of Cassini plasma spectrometer (CAPS) data acquired during passage through Saturn's inner plasmasphere by the Cassini spacecraft during the approach phase of the Saturn orbit insertion period. This analysis extends the original analysis of Sittler et al. [2005. Preliminary results on Saturn's inner plasmasphere as observed by Cassini: comparison with Voyager. Geophys. Res. Lett. 32, L14S07, doi:10.1029/2005GL022653] to L∼10 along with also providing a more comprehensive study of the interrelationship of the various fluid parameters. Coincidence data are sub-divided into protons and water group ions. Our revised analysis uses an improved convergence algorithm which provides a more definitive and independent estimate of the spacecraft potential Φ_SC for which we enforce the protons and water group ions to co-move with each other. This has allowed us to include spacecraft charging corrections to our fluid parameter estimations and allow accurate estimations of fluctuations in the fluid parameters for future correlative studies. In the appendix we describe the ion moments algorithm, and minor corrections introduced by not weighting the moments with sinθ term in Sittler et al. [2005] (Correction offset by revisions to instruments geometric factor). Estimates of the spacecraft potential and revised proton densities are presented. Our total ion densities are in close agreement with the electron densities reported by Moncuquet et al. [2005. Quasi-thermal noise spectroscopy in the inner magnetosphere of Saturn with Cassini/RPWS: electron temperatures and density. Geophys. Res. Lett. 32, L20S02, doi:10.1029/2005GL022508] who used upper hybrid resonance (UHR) emission lines observed by the radio and plasma wave science (RPWS) instrument. We show a positive correlation between proton temperature and water group ion temperature. The proton and thermal electron temperatures track each with both having a positive radial gradient. These results are consistent with pickup ion energization via Saturn's rotational electric field. We see evidence for an anti-correlation between radial flow velocity V_R and azimuthal velocity V_φ, which is consistent with the magnetosphere tending to conserve angular momentum. Evidence for MHD waves is also present. We show clear evidence for outward transport of the plasma via flux tube interchange motions with the radial velocity of the flow showing positive radial gradient with functional dependence for 4<L<10 (i.e., if we assume to be diffusive transport then D_LL∼D₀L¹¹ for fixed stochastic time step δt). Previous models with centrifugal transport have used D_LL∼D₀L³ dependence. The radial transport seems to begin at Enceladus’ L shell, L∼4, where we also see a minimum in the W⁺ ion temperature . For the first time, we are measuring the actual flux tube interchange motions in the magnetosphere and how it varies with radial distance. These observations can be used as a constraint with regard to future transport models for Saturn's magnetosphere. Finally, we evaluate the thermodynamic properties of the plasma, which are all consistent with the pickup process being the dominant energy source for the plasma.     

Estimating the masses of Saturn’s A and B rings from high-optical depth N-body simulations and stellar occultations

We have completed a series of local N-body simulations of Saturn’s B and A rings in order to identify systematic differences in the degree of particle clumping into self-gravity wakes as a function of orbital distance from Saturn and dynamical optical depth (a function of surface density). These simulations revealed that the normal optical depth of the final configuration can be substantially lower than one would infer from a uniform distribution of particles. Adding more particles to the simulation simply piles more particles onto the self-gravity wakes while leaving relatively clear gaps between the wakes. Estimating the mass from the observed optical depth is therefore a non-linear problem. These simulations may explain why the Cassini UVIS instrument has detected starlight at low incidence angles through regions of the B ring that have average normal optical depths substantially greater than unity at some observation geometries [Colwell, J.E., Esposito, L.W., Srem?evi?, M., Stewart, G.R., McClintock, W.E., 2007. Icarus 190, 127-144]. We provide a plausible internal density of the particles in the A and B rings based upon fitting the results of our simulations with Cassini UVIS stellar occultation data. We simulated Cassini-like occultations through our simulation cells, calculated optical depths, and attempted to extrapolate to the values that Cassini observes. We needed to extrapolate because even initial optical depths of >4 (σ > 240 g cm⁻²) only yielded final optical depths no greater than 2.8, smaller than the largest measured B ring optical depths. This extrapolation introduces a significant amount of uncertainty, and we chose to be conservative in our overall mass estimates. From our simulations, we infer the surface density of the A ring to be , which corresponds to a mass of . We infer a minimum surface density of for Saturn’s B ring, which corresponds to a minimum mass estimate of . The A ring mass estimate agrees well with previous analyses, while the B ring is at least 40% larger. In sum, our lower limit estimate is that the total mass of Saturn’s ring system is 120-200% the mass of the moon Mimas, but significantly larger values would be plausible given the limitations of our simulations. A significantly larger mass for Saturn’s rings favors a primordial origin for the rings because the disruption of a former satellite of the required mass would be unlikely after the decay of the late heavy bombardment of planetary surfaces.