A Comparison of Orbital Phase-Resolved Mesoscale Structure and Particle Sizes in the Narrow and Eccentric Rings of Saturn and Uranus

We present a comparative occultation analysis of narrow, eccentric ringlets in the Saturnian and Uranian ring systems, focusing on how mesoscale structure and particle size distributions vary with orbital phase (true anomaly). Our study combines the full suite of Cassini stellar and radio occultation profiles of Saturn’s narrow ringlets, obtained by Cassini’s UVIS (λ = 150 nm), VIMS (λ = 2.84 μm), and RSS (Ka-, X-, S-band experiments). We compare our results with a reanalysis of Voyager 2 PPS and RSS occultations of Uranus’s ε, α, β, η, and δ rings.

We group Saturn ringlet profiles into four orbital quadrants—periapsis, apoapsis, and the streamline divergence/convergence sectors—to isolate phase-dependent structure (Figure 1). In each quadrant, we model viewing-geometry dependent normal optical depth using the irregularly spaced, three component, granola bar self-gravity wake model of Esposito et al. (2025) (Figure 2). The model fits the dimensional ratios and cant angles of aligned structures such as self-gravity wakes, particle-depleted lanes, or both. 

Following Green et al. (2024), we compute the normalized central moments of UVIS HSP occultation transparencies to constrain the size of the largest ring particles (amax) and to characterize the clumpiness of the ringlets with orbital phase. We compare these moments to predictions from Esposito et al. (2025) for wake-dominated rings. Simultaneously, we perform multi-wavelength  particle size distribution fits by selecting UVIS, VIMS, and RSS profiles at similar orbital phase and with similar viewing geometries to constrain the power-law index (q) and minimum particle radius (a_min) (Figure 3).

For the Uranian rings, we use the σ-Sagittarii and β-Persei Voyager 2 PPS occultations to extract radial optical depth profiles of the dense narrow rings, supplemented by RSS S/X-band differential attenuation. While the geometry does not allow for true-anomaly-resolved comparisons, we compare Voyager 2 PPS occultation statistics and RSS S and X band optical depths to enable structural comparison.

Our approach incorporates a self-consistent model of wavelength and viewing-geometry dependent optical depths with an analysis of photon counting statistics (Cassini UVIS HSP and Voyager 2 PPS).  We find that Saturn’s ringlets exhibit significant variation in both self-gravity wake dimensions and inferred size distributions between quadrants (Figure 4).

By applying a common framework across two planetary ring systems, we aim to identify techniques to constrain the phase-dependence of the particle size distribution, surface densities, and structure of dense narrow rings from in-situ occultations. This approach is intended not only to advance current understanding but also to inform the design of future occultation experiments at Uranus.

Figure 1. Ringlet edge radii from UVIS, VIMS, and RSS occulations colored by sine of the ring opening angle for the Maxwell Ringlet. Occultations are separated into quadrants (Groups 1 – 4) in true anomaly for orbital phase-dependent analysis.

Figure 2. The irregularly spaced granola bar self-gravity wake model of Esposito et al. (2025). 𝐸[𝜆T] is the expected value of the Toomre critical wavelength or the largest unstable wavelength toward gravitational collapse (Julian and Toomre 1966): λ_Τ = 4π²GΣ/κ² where Σ is the local surface mass density and κ is the local epicyclic frequency.  The black dashed arrow is the line of sight from Cassini to the occulted star (or to Earth in the case of radio occultations.  The red square is the area over which light is collected during a single integration of the UVIS instrument. (see Jerousek et al. (2024) for details on the integration area).

Figure 3. The Maxwell ringlet contains a prominent spiral density wave driven by an outer Lindblad resonance (OLR). We fit optical depths in the first trough of the wave. Structure  nearly disappears at apoapsis when particle streamlines are most widely separated. At other orbital phases, the model best matches a structure with broad radial spacing and variable vertical extent.

Figure 4. Example of particle size distribution fits for the Maxwell ringlet at two orbital phases.. Best-fitting parameters are consistent with Jerousek et al. (2020) for the background C ring near periapsis where q is much larger. Ring particle radii generally range from several millimeters up to 5 – 10 m.

References:

Green, M. R., Colwell, J. E., Esposito, L. W., & Jerousek, R. G. (2024). Particle sizes in Saturn’s rings from UVIS stellar occultations 2. Outlier Populations in the C ring and Cassini Division. Icarus, 416, 116081.

Esposito, L. W., Colwell, J. Ε., Eckert, S., Green, M. R., Jerousek, R. G., & Madhusudhanan, S. (2025). Statistics of Saturn's ring occultations: Implications for structure, dynamics, and origins. Icarus, 429, 116386.

Jerousek, R. G., Colwell, J. E., Esposito, L. W., Tiscareno, M. S., Lewis, M. C., Pohl, L., & Benavides, D. A. (2024). The smallest structures in Saturn’s rings from UVIS stellar occultations. Icarus, 415, 116069.