Saturn's C ring and Cassini division: Particle sizes from Cassini UVIS, VIMS, and RSS occultations

Abstract Saturn's C ring and Cassini Division share many morphological traits: both contain numerous opaque, sharp–edged ringlets and gaps, broader low optical depth “background” regions, larger-optical depth regions that rise abruptly from the background (known as the C ring's plateaus and the Cassini Division's triple band feature), and linear ramps in optical depth up to the abrupt inner edges of the B ring and A ring, respectively. Throughout the majority of both regions, the surface mass density of the rings is small enough that the Toomre critical wavelength (most unstable wavelength for gravitational collapse) is comparable in size to, or smaller than, the largest individual ring particles. Thus, self-gravity wakes do not form in these regions, unlike the A and B rings where the critical wavelength is tens of meters and the self-gravity wakes introduce strong dependence of the observed optical depth on viewing geometry. In the absence of self-gravity wakes, we model the ring particle size distribution with a simple power-law, where the number of particles per unit area of the rings in the size range [a, a + da] is given by n(a)da = Ca-qda between amin and amax. We fit normal optical depths derived from the power-law size distribution parameters and the thin-layers ring model of Zebker et al. (1985) to the wavelength-dependent optical depth profiles obtained by 3 Cassini Instruments: UVIS at λ = 0.15 μm, VIMS at λ = 2.9 μm, and RSS Ka-band (λ = 9.4 mm), X-band at (λ = 3.4 cm), and S-band (λ = 13.0 cm). We find that the C ring is best characterized by five or more thin layers of particles with a mean power-law index of q ~ 3.16 in the C ring background and q ~ 3.05 in the C ring plateaus, in the rings. We find a minimum particle radius of amin ~ 4.1 mm in the background C ring and plateaus and amin ~ 6 mm in the plateaus. The cross-section-weighted effective particle radius determined using the excess variance of UVIS signal beyond Poisson counting statistics by Colwell et al. (2018) constrains the size of the largest particles in the rings. We find the largest particles contributing to the power-law size distribution, and thus to the optical depth, are amax ~ 10–15 m in the background C ring and amax ~ 5–6 m in the C ring plateaus. This substantial difference in the sizes of the largest ring particles together with the overall shallower power law index in the plateaus explains their optical depth difference relative to the background C ring. Additionally, Baillie et al. (2013) used UVIS stellar occultations to find a distribution of small-scale, low optical depth gaps in the plateaus. These regions, with radial widths of We constrain the particle densities by dividing the surface mass densities determined from the dispersion of spiral density waves by the total particle volume integrated over a square meter of the ring slab. We derive low bulk particle densities of ρ ~ 0.1–0.3 g/cm3 except in the central background C ring where we find ρ ~ 0.9 g/cm3. These low derived densities may be due to inter-particle spaces within 1–20 m particle aggregates that contribute to the measured optical depth and thus to the upper end of the size distribution. Our results are consistent with Zhang et al. (2017) who reported particles with porosities >75% made of water ice with up to 11% silicate contaminate in the central background C ring.