Saturn’s F Ring is Confined by Prometheus and Negative Diffusion

Saturn’s narrow, clumpy F ring is a region disturbed by chaotic orbital dynamics. We therefore model it 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 called 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 kittens (transient aggregates with size 100 m < dr < 3 km), including perturbations due to Prometheus encounters, resonance confinement, and mutual collisions. We solve for the stationary state. Without confinement, the probability of detecting the kittens is uniformly distributed. With corotation resonance confinement [1], the stationary state is sharply peaked, consistent with the longitudinal distribution of detections of the F ring by radio occultation. 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 CER. This alternative combines with the explanation of [1] to conclude that some fraction of the population, or some fraction of the time, the F ring is shepherded by Prometheus. We explain the persistence of the F ring due to negative diffusion [2][3], where the ring is confined by Prometheus aligning particle phases. We include the negative diffusion in the Markov chain using an Ehrenfest diffusion model [4]. A small asymmetry explains the distribution in resonant argument of the radio occultation detections. In all cases, Prometheus is the agent for confinement. The F ring is shepherded by a combination of a Prometheus corotation and a Lindblad resonance that yields non-isotropic collisions: For combined model: Shepherded fraction <  0.2 ; Diffusion asymmetry factor  F =  0.48 - 0.50.In all cases, ‘negative diffusion’ 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.

 

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