Origin and Evolution of Saturn’s F Ring with Negative Diffusion

Saturn’s narrow, clumpy F ring is in a region disturbed by chaotic orbital dynamics. 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 Cassini UVIS and RSS ring occultations. Approximating this chaos as a random process, I model the F ring core as a finite Markov chain of transient aggregates [20m < dr < 3 km]. The model includes perturbations due to Prometheus encounters, resonance confinement, and mutual collisions. The best description for the current ring is the stationary state of this stochastic process. In this model, the persistence of the F ring is due to negative diffusion [described by Sickafoose and Lewis 2024, to explain the persistence of Chariklo’s rings], where the ring is confined by Prometheus aligning particles when they are driven to collide when their streamlines cross. The F ring is thus shepherded by a combination of a Prometheus corotation and a Lindblad resonance.  Whenever the center of mass of the material in the F ring is located at the Lindblad resonance with Prometheus, perturbations will drive negative diffusion to maintain that location. Likewise, negative diffusion can maintain apse alignment and thus ring eccentricity. If the F ring originated from the destruction of a small moon on an elliptical orbit, negative diffusion preserves the original orbital elements of the moon against differential precession and collisional spreading.

The stages in F ring history are as follows. A progenitor moon, say ‘Festus’, accretes from viscous spreading of Saturn’s rings material that crosses the Roche limit. Later, Prometheus accretes. Prometheus, being larger, moves out faster, with a tidal evolution time scale of 10-100 million years… and captures Festus in a mean motion resonance. After that, the two evolve together with the exact resonance evolving chaotically with Prometheus own history of jumps and glitches. If Festus is thus ever out of resonance it is soon re-captured. The mean motion resonance excites Festus eccentricity. Festus (in an eccentric orbit, caught in or near resonance) is shattered by an impact (the estimated lifetime is of the order of 100 million years); the debris mass would be dominated the largest objects (kittens); they would experience anisotropic collisions at streamline crossing that would maintain the moon’s original [a, e, φ] via the negative diffusion. Fragments trapped in nearby resonances have lower optical depth, negative diffusion is weaker and the fragments gradually diffuse away; or they leak into capture within the resonance site with the most original mass. The evaporation of ring material where regular diffusion dominates leaves behind the confined eccentric F ring. Caught in resonance with Prometheus, it will evolve further from Saturn and may eventually re-accrete into a small moon like Anthe.