Saturn's F ring is confined by Prometheus and negative diffusion

Abstract

Saturn's narrow, clumpy F ring is a region disturbed by chaotic orbital dynamics, that we model as a stochastic process (specifically, a finite Markov chain). The ring appears dominated by dust in camera images, but the main mass of this ring resides in a core of elongated clumps we call kittens, observed by ring occultations. Cassini UVIS sees such features about 1/3 of the time, the same frequency as the radio occultation detections of the F ring core; both have similar size distribution. We model the F ring core as composed of these transient aggregates, with size.

100 m < dr < 3 km. The Markov chain follows transitions between states in discrete semi-major axis bins, including both perturbations due to Prometheus encounters and mutual collisions. We solve for the stationary state and convert the semi-major axis distribution to distribution in longitude by modeling the libration as a simple harmonic oscillator. We find that without confinement, the probability of detecting the kittens is uniformly distributed. With corotation resonance confinement, the stationary state is sharply peaked, inconsistent with a purely random distribution. Considering shepherding alone, the Cassini radio observations are nonetheless better fit by the non-confinement stationary distribution, and even better by just 20 % confined. We find acceptable fits for fractions up to 70 % of the clumps shepherded in the 109:110 Prometheus corotation eccentricity resonance (CER), as proposed by Cuzzi et al. (2024). This finding expands their explanation to allow us to conclude that either some fraction of the population, or some fraction of the time, the F ring is shepherded by Prometheus. Additionally, we argue that the persistence of the F ring is due to negative diffusion, where the ring is confined by Prometheus aligning particle phases. Including the negative diffusion in the Markov chain using an Ehrenfest diffusion model, a small asymmetry explains the distribution in resonant angle of the radio occultation detections. In both these explanations, Prometheus is the agent for confinement. We conclude the F ring is shepherded by a combination of a Prometheus corotation and a Lindblad resonance that yields non-isotropic collisions. When the centroid of mass of the material in the F ring (the mass-weighted semi-major axis) is ever located at the Lindblad resonance with Prometheus, perturbations will drive negative diffusion to maintain that location. For our combined model: Shepherded fraction has the range f_shep < 0.2; Diffusion asymmetry factor P_neg has the range 0.48–0.50. The negative diffusion thus can maintain the longitudinal distribution either alone, or in combination with shepherding, if the mean motion resonance coincides with the true core of the F ring.