Aggregate impacts in Saturn's rings

Ring particle aggregates are formed in the outer parts of Saturn's main rings. We study how collisions between aggregates can lead to destruction or coalescence of these aggregates, with local N-body simulations taking into account the dissipative impacts and gravitational forces between particles. Impacts of aggregates with different mass ratios are studied, as well as aggregates that consist of particles with different physical properties. We find that the outcome of the collision is very sensitive to the shape of the aggregate, in the sense that more elongated aggregates are more prone to be destroyed. We were interested in testing the accretion criterion Barbara and Esposito [Barbara, J.M., Esposito, L.W., 2002. Icarus 160, 161-171] used in their F ring simulations, according to which accretion requires that the masses of the colliding bodies differ at least by a factor of 100. We confirm that such a critical mass ratio exists. In particular, simulations indicate that the exact critical mass ratio depends on the internal density and elasticity of particles, and the distance from the planet. The zone of transition, defined by the distance where individual particles or small aggregates first start to stick on the larger aggregate, and by the distance where two similar sized aggregates on the average eventually coalesce is only about 5000 km wide, if fixed particle properties are used. The rotational state of the aggregates that form via aggregate collision rapidly reaches synchronous rotation, similarly to the aggregates that form via gradual growth.     

A close look at Saturn's rings with Cassini VIMS

Soon after the Cassini-Huygens spacecraft entered orbit about Saturn on 1 July 2004, its Visual and Infrared Mapping Spectrometer obtained two continuous spectral scans across the rings, covering the wavelength range 0.35-5.1 μm, at a spatial resolution of 15-25 km. The first scan covers the outer C and inner B rings, while the second covers the Cassini Division and the entire A ring. Comparisons of the VIMS radial reflectance profile at 1.08 μm with similar profiles at a wavelength of 0.45 μm assembled from Voyager images show very little change in ring structure over the intervening 24 years, with the exception of a few features already known to be noncircular. A model for single-scattering by a classical, many-particle-thick slab of material with normal optical depths derived from the Voyager photopolarimeter stellar occultation is found to provide an excellent fit to the observed VIMS reflectance profiles for the C ring and Cassini Division, and an acceptable fit for the inner B ring. The A ring deviates significantly from such a model, consistent with previous suggestions that this region may be closer to a monolayer. An additional complication here is the azimuthally-variable average optical depth associated with “self-gravity wakes” in this region and the fact that much of the A ring may be a mixture of almost opaque wakes and relatively transparent interwake zones. Consistently with previous studies, we find that the near-infrared spectra of all main ring regions are dominated by water ice, with a typical regolith grain radius of 5-20 μm, while the steep decrease in visual reflectance shortward of 0.6 μm is suggestive of an organic contaminant, perhaps tholin-like. Although no materials other than H₂O ice have been identified with any certainty in the VIMS spectra of the rings, significant radial variations are seen in the strength of the water-ice absorption bands. Across the boundary between the C and B rings, over a radial range of ∼7000 km, the near-IR band depths strengthen considerably. A very similar pattern is seen across the outer half of the Cassini Division and into the inner A ring, accompanied by a steepening of the red slope in the visible spectrum shortward of 0.55 μm. We attribute these trends—as well as smaller-scale variations associated with strong density waves in the A ring—to differing grain sizes in the tholin-contaminated icy regolith that covers the surfaces of the decimeter-to-meter sized ring particles. On the largest scale, the spectral variations seen by VIMS suggest that the rings may be divided into two larger ‘ring complexes,’ with similar internal variations in structure, optical depth, particle size, regolith texture and composition. The inner complex comprises the C and B rings, while the outer comprises the Cassini Division and A ring.     

Gravitational accretion of particles in Saturn's rings

Gravitational accretion in the rings of Saturn is studied with local N-body simulations, taking into account the dissipative impacts and gravitational forces between particles. Common estimates of accretion assume that gravitational sticking takes place beyond a certain distance (Roche distance) where the self-gravity between a pair of ring particles exceeds the disrupting tidal force of the central object, the exact value of this distance depending on the ring particles' internal density. However, the actual physical situation in the rings is more complicated, the growth and stability of the particle groups being affected also by the elasticity and friction in particle impacts, both directly via sticking probabilities and indirectly via velocity dispersion, as well as by the shape, rotational state and the internal packing density of the forming particle groups. These factors are most conveniently taken into account via N-body simulations. In our standard simulation case of identical 1 m particles with internal density of solid ice, ρ=900 kg m⁻³, following the Bridges et al., 1984 elasticity law, we find accretion beyond a=137,000-146,000 km, the smaller value referring to a distance where transient aggregates are first obtained, and the larger value to the distance where stable aggregates eventually form in every experiment lasting 50 orbital periods. Practically the same result is obtained for a constant coefficient of restitution εn=0.5. In terms of rp parameter, the sum of particle radii normalized by their mutual Hill radius, the above limit for perfect accretion corresponds to rp<0.84. Increased dissipation (εn=0.1), or inclusion of friction (tangential force 10% of normal force) shifts the accretion region inward by about 5000 km. Accretion is also more efficient in the case of size distribution: with a q=3 power law extending over a mass range of 1000, accretion shifts inward by almost 10,000 km. The aggregates forming in simulations via gradual accumulation of particles are synchronously rotating.     

Organizing some very tenuous things: Resonant structures in Saturn's faint rings

Images of the dusty rings obtained by the Cassini spacecraft in late 2006 and early 2007 reveal unusual structures composed of alternating canted bright and dark streaks in the outer G ring (∼170,000 km from Saturn center), the inner Roche Division (∼138,000 km) and the middle D ring (70,000-73,000 km). The morphology, locations and pattern speeds of these features indicate that they are generated by Lindblad resonances. The structure in the G ring appears to be generated by the 8:7 Inner Lindblad Resonance with Mimas. Based in part on the morphology of the G ring structure, we develop a phenomenological model of Lindblad-resonance-induced structures in faint rings, where the observed variations in the rings' optical depth and brightness are due to alignments and trends in the particles' orbital parameters with semi-major axis. To reproduce the canted character of these structures, this model requires a term in the equations of motion that damps eccentricities. Using this model to interpret the structures in the D ring and Roche Division, we find that the D-ring patterns mimic those predicted at 2:1 Inner Lindblad Resonances and the Roche Division patterns look like those expected at 3:4 Outer Lindblad Resonances. As in the G ring, the effective eccentricity-damping timescale is of order 10-100 days, suggesting that free eccentricities are strongly damped by some mechanism that operates throughout all these regions. However, unlike in the G ring, perturbation forces with multiple periods are required to explain the observed patterns in the D ring and Roche Division. The strongest perturbation periods occur at 10.53, 10.56 and 10.74 hours (only detectable in the D ring) and 10.82 hours (detectable in both the D ring and Roche division). These periods are comparable to the rotation periods of Saturn's atmosphere and magnetosphere. The inferred strength of the perturbation forces required to produce these patterns (and the absence of evidence for other resonances driven by these periods in the main rings) suggests that non-gravitational forces are responsible for generating these features in the D ring and Roche Division. If this interpretation is correct, then some of these structures may have some connection with periodic signals observed in Saturn's magnetic field and radio-wave emissions, and accordingly could help clarify the nature and origin(s) of these magnetospheric asymmetries.     

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.     

Brightness of Saturn's rings with decreasing solar elevation

Early ground-based and spacecraft observations suggested that the temperature of Saturn's main rings (A, B and C) varied with the solar elevation angle, B^′. Data from the composite infrared spectrometer (CIRS) on board Cassini, which has been in orbit around Saturn for more than five years, confirm this variation and have been used to derive the temperature of the main rings from a wide variety of geometries while B^′ varied from near −24^° to 0^° (Saturn's equinox).Still, an unresolved issue in fully explaining this variation relates to how the ring particles are organized and whether even a simple mono-layer or multi-layer approximation describes this best. We present a set of temperature data of the main rings of Saturn that cover the ∼23^°—range of B^′ angles obtained with CIRS at low (α∼30^°) and high (α≥120^°) phase angles. We focus on particular regions of each ring with a radial extent on their lit and unlit sides. In this broad range of B^′, the data show that the A, B and C rings’ temperatures vary as much as 29-38, 22-34 and 18-23 K, respectively. Interestingly the unlit sides of the rings show important temperature variations with the decrease of B^′ as well. We introduce a simple analytical model based on the well known Froidevaux monolayer approximation and use the ring particles’ albedo as the only free parameter in order to fit and analyze this data and estimate the ring particle's albedo. The model considers that every particle of the ring behaves as a black body and warms up due to the direct energy coming from the Sun as well as the solar energy reflected from the atmosphere of Saturn and on its neighboring particles. Two types of shadowing functions are used. One analytical that is used in the latter model in the case of the three rings and another, numerical, that is applied in the case of the C ring alone. The model lit side albedo values at low phase are 0.59, 0.50 and 0.35-0.38 for the A, B and C rings, respectively.     

Thermal response of Iapetus to an eclipse by Saturn's rings

Measurements of Iapetus as seen at 20 and 2.2 μm in the shadow of Saturn's ring are given, providing the thermal response to a rapidly varying heat input. The 20 μm thermal emission follows the 2.2 μm flux input closely. The observations, plus a simple diffusion calculation, imply that the surface of Iapetus is made of material having a very small thermal inertia, probably .     

Cassini imaging of Saturn's rings: II. A wavelet technique for analysis of density waves and other radial structure in the rings

We describe a powerful signal processing method, the continuous wavelet transform, and use it to analyze radial structure in Cassini ISS images of Saturn's rings. Wavelet analysis locally separates signal components in frequency space, causing many structures to become evident that are difficult to observe with the naked eye. Density waves, generated at resonances with saturnian satellites orbiting outside (or within) the rings, are particularly amenable to such analysis. We identify a number of previously unobserved weak waves, and demonstrate the wavelet transform's ability to isolate multiple waves superimposed on top of one another. We also present two wave-like structures that we are unable to conclusively identify. In a multi-step semi-automated process, we recover four parameters from clearly observed weak spiral density waves: the local ring surface density, the local ring viscosity, the precise resonance location (useful for pointing images, and potentially for refining saturnian astrometry), and the wave amplitude (potentially providing new constraints upon the masses of the perturbing moons). Our derived surface densities have less scatter than previous measurements that were derived from stronger non-linear waves, and suggest a gentle linear increase in surface density from the inner to the mid-A Ring. We show that ring viscosity consistently increases from the Cassini Division outward to the Encke Gap. Meaningful upper limits on ring thickness can be placed on the Cassini Division (3.0 m at r∼118,800 km, 4.5 m at r∼120,700 km) and the inner A Ring (10-15 m for r<127,000 km).     

The influence of particle adhesion on the stability of agglomerates in Saturn's rings

In planetary rings, binary collisions and mutual gravity are the predominant particle interactions. Based on a viscoelastic contact model we implement the concept of static adhesion. We discuss the collision dynamics and obtain a threshold velocity for restitution or agglomeration to occur. The latter takes place within a range of a few cm s⁻¹ for icy grains at low temperatures. The stability of such two-body agglomerates bound by adhesion and gravity in a tidal environment is discussed and applied to the saturnian system. A maximal agglomerate size for a given orbit location is obtained. In this way we are able to resolve the borderline of the zone where agglomerates can exist as a function of the agglomerate size and thus gain an alternative to the classical Roche limit. An increasing ring grain size with distance to Saturn as observed by the VIMS-experiment on board the Cassini spacecraft can be found by our estimates and implications for the saturnian system will be addressed.     

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.     

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.     

Hydrodynamical and radiative transfer modeling of meteoroid impacts into Saturn's rings

In a small hypervelocity impact, superheated gas and particles glow brightly with thermal emission for a brief time interval at short wavelengths; this phenomenon is referred to as an impact flash. Over the past decade, impact flashes have been observed on the Moon and in the laboratory in both the IR and visible portions of the spectrum. These phenomena have been used to constrain impactor parameters, such as impact size, velocity and composition. With the arrival of the Cassini spacecraft at Saturn, we embarked on a study of impact flashes in Saturn's rings. We present results on the feasibility of observing impact flashes and therefore estimating the flux of meteoroids impacting Saturn's rings using Cassini's Ultraviolet Imaging Spectrograph (UVIS). Our modeling effort is two-fold. We start by simulating impacts using the CTH hydrodynamical code. Impacts involve an icy ring particle and a serpentine meteoroid, modeled with the ANEOS equation of state. The objects are centimeters to meters in diameter and collide at 30 to 50 km s⁻¹. We then use the resulting temperatures and densities of the impact plumes in a radiative transfer calculation. We calculate bound-free, free-free, electron scattering and negative ion opacities along a line-of-sight through the center of each impact plume. Our model has shown that impact flashes will not be seen with the UVIS because (1) the plumes are optically thick when their central temperatures are high, with photosphere temperatures too cool to emit observable UV flux and (2) when the plumes become optically thin, even the hottest region of the plume is too cool to observe in the UV. This corroborates the lack of UVIS impact flash detections to date. Impact flashes are not likely to be seen by other Cassini instruments because of the short lifetimes of the plumes.     

An analysis of bending waves in Saturn's rings using voyager radio occultation data

The oblique geometry of the Voyager 1 radio occulation of Saturn's rings resulted in a strong coupling between the local slope of the ring midplane and the associated radio opacity (optical depth). We apply a model of this relationship to those regions of the rings where bending waves have been observed in the radio data. Using the Shu et al. linear model for a bending wave (F.H. Shu, J.N. Cuzzi, and J.J. Lissauer, 1983,Icarus53, 185–206), we obtain height profiles for the Mimas 5:3 and 7:4 bending waves. The first oscillation of the Mimas 5:3 bending wave has an amplitude of about 800 m, in agreement with the prediction of the Shu et al. model. However, the rest of the wave may be explained only by either a greatly decreased amplitude in the region beyond the second cycle, or by a significant enhancement in radio optical depth in the region of the bending wave. The shape of the enhancement necessary is similar to that of the enhancement at photopolarimetry wavelengths (L.W. Esposito, M. O'Callaghan, and R.A. West, 1983,Icarus56, 439–452), but differs in the region of the first cycle. Our solution gives 131,901±6 km as the resonance location, and a surface mass density of 35±6g cm⁻². The error bars on the resonance location do not include the uncertainty in the radial scale of the radio occultation data, which is approximately 10 km (R.A. Simpson, G.L. Tyler, and J.B. Holberg, 1983,Astron. J.88, 1531–1536). The Mimas 7:4 bending wave conforms more closely to the linear model, and requires no reduction in amplitude or enhancement in optical depth. We find a surface mass density of 30.5±9 g cm⁻², and resonance location at 127,765±7km.     

Features around embedded moonlets in Saturn's rings: The role of self-gravity and particle size distributions

This paper presents the results of N-body simulations of moonlets embedded in broad rings, focusing specifically on the saturnian A ring. This work adds to previous efforts by including particle self-gravity and particle size distributions. The discussion here focuses primarily on the features that form in the background particles as a result of the moonlet. Particle self-gravity tends to damp out features produced by embedded moonlets and this damping is enhanced if the moonlet is simply the largest member of a continuous size distribution. Observable features around an embedded moonlet appear to require that the largest ring particles be no more massive than 1/30 the mass of the moonlet. These results, compared with current and future Cassini observations, will provide insight into the nature of the particle population in the saturnian rings. Some time is also spent analyzing the way in which the background particles cluster around the moonlet. The accretion of small particles onto the moonlet can be limited by disruptive collisions with the largest ring particles in the particle size distribution.     

Keck near-infrared observations of Saturn's E and G rings during Earth's ring plane crossing in August 1995

We present near-infrared (1.24-2.26 μm) images of Saturn's E and G rings which were taken with the W.M. Keck telescope in 1995 August 9-11, during the period that Earth crossed Saturn's ring plane. Our data confirm that the E ring is very blue. Its radial and vertical structure are found to be remarkably similar to that apparent in the HST ringplane crossing data at visible wavelengths, reinforcing models of the ring's peculiar narrow or very steep particle size distribution. Our data show unambiguously that the satellite Tethys is a secondary source of material for the E ring. The G ring is found to be distinctly red, similar in color to Jupiter's main ring, indicative of a (more typical) broad particle size distribution.     

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.     

Microwave observations of Saturn's rings: anisotropy in directly transmitted and scattered saturnian thermal emission

We present a new Very Large Array (VLA) image of Saturn, made from data taken in October 1998 at a wavelength of λ3.6 cm. The moderate ring opening angle (B≈15°) allows us to explore direct transmission of microwave photons through the A and C rings. We find a strong asymmetry of photons transmitted through the A ring, but not in the C ring, a new diagnostic of wake structure in the ring particles. We also find a weak asymmetry between east and west for the far side of the ansae. To facilitate quantitative comparison between dynamic models of the A ring and radio observations, we extend our Monte Carlo radiative transfer code (described in Dunn et al., 2002, Icarus 160, 132-160) to include idealized wakes. We show the idealized model can reproduce the properties of dynamic simulations in directly transmitted light. We examine the model behavior in directly transmitted and scattered light over a range of physical and geometric wake parameters. Finally, we present a wake model with a plausible set of physical parameters that quantitatively reproduces the observed intensity and asymmetry of the A ring both across the planet and in the ansae.     

The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings

This paper addresses the fine-scale axisymmetric structure exhibited in Saturn's A and B-rings. We aim to explain both the periodic microstructure on 150-220 m, revealed by the Cassini UVIS and RSS instruments, and the irregular variations in brightness on 1-10 km, reported by the Cassini ISS. We propose that the former structures correspond to the peaks and troughs of the nonlinear wavetrains that form naturally in a viscously overstable disk. The latter variations on longer scales may correspond to modulations and defects in the wavetrains' amplitudes and wavelength. We explore these ideas using a simple hydrodynamical model which captures the correct qualitative behaviour of a disk of inelastically colliding particles, while also permitting us to make progress with analytic and semi-analytic techniques. Specifically, we calculate a family of travelling nonlinear density waves and determine their stability properties. Detailed numerical simulations that confirm our basic results will appear in a following paper.     

Modeling of global variations and ring shadowing in Saturn's ionosphere

A time-dependent one-dimensional model of Saturn's ionosphere has been developed as an intermediate step towards a fully coupled Saturn Thermosphere-Ionosphere Model (STIM). A global circulation model (GCM) of the thermosphere provides the latitude and local time dependent neutral atmosphere, from which a globally varying ionosphere is calculated. Four ion species are used (H⁺, H⁺₂, H⁺₃, and He⁺) with current cross-sections and reaction rates, and the SOLAR2000 model for the Sun's irradiance. Occultation data from the Voyager photopolarimeter system (PPS) are adapted to model the radial profile of the ultraviolet (UV) optical depth of the rings. Diurnal electron density peak values and heights are generated for all latitudes and two seasons under solar minimum and solar maximum conditions, both with and without shadowing from the rings. Saturn's lower ionosphere is shown to be in photochemical equilibrium, whereas diffusive processes are important in the topside. In agreement with previous 1-D models, the ionosphere is dominated by H⁺ and H⁺₃, with a peak electron density of ∼¹⁰⁴ electrons cm⁻³. At low- and mid-latitudes, H⁺ is the dominant ion, and the electron density exhibits a diurnal maximum during the mid-afternoon. At higher latitudes and shadowed latitudes (smaller ionizing fluxes), the diurnal maximum retreats towards noon, and the ratio of [H⁺]/[H⁺₃] decreases, with H⁺₃ becoming the dominant ion at altitudes near the peak (∼1200-1600 km) for noon-time hours. Shadowing from the rings leads to attenuation of solar flux, the magnitude and latitudinal structure of which is seasonal. During solstice, the season for the Cassini spacecraft's encounter with Saturn, attenuation has a maximum of two orders of magnitude, causing a reduction in modeled peak electron densities and total electron column contents by as much as a factor of three. Calculations are performed that explore the parameter space for charge-exchange reactions of H⁺ with vibrationally excited H₂, and for different influxes of H₂O, resulting in a maximum diurnal variation in electron density much weaker than the diurnal variations inferred from Voyager's Saturn Electrostatic Discharge (SED) measurements. Peak values of height-integrated Pedersen conductivities at high latitudes during solar maximum are modeled to be ∼42 mho in the summer hemisphere during solstice and ∼18 mho during equinox, indicating that even without ionization produced by auroral processes, magnetosphere-ionosphere coupling can be highly variable.