Predator-Prey analogs for Saturn's non-linear ring dynamics
Abstract
Cassini observations of straw, gaps, ghosts, kittens, propellers, solitary waves and the edge disruption of the Keeler gap by Daphnis may all indicate non-linear dynamics in Saturn's rings. This dynamical behavior cycles ring material into and out of transient aggregations: We see the rings changing before our eyes! How can we understand the structures seen by Cassini and the rapid times scales? Numerical simulations cannot yet capture all the relevant physics, the multiple spatial scales or the asymptotic behavior at long time scales. An ecological analogy of a predator-prey model provides a non-linear model, including aggregation by sweep-up, disk instability and the stochastic collisions of clumps. In this model, the aggregate mass is the prey, and the dispersion velocity is the predator, since the dispersion 'feeds' off the aggregates stirring the system. This, in turn, limits the growth of the 'prey'. In some cases, the system shows the dynamics of a driven pendulum or of the Duffing oscillator. For specificity, we adopt the 'two-group' model of Goldreich for proto-planetary disks, with the 'groups' being the ring particles and their aggregates. This provides a simplification of the size and velocity distributions. Our analysis gives the phase plane trajectories, the equilibrium points and the size distribution of the largest aggregates.Forcing at mean motion resonances creates non-linear density waves, which increase the surface mass density and decrease the relative velocity in their crests. We use Toomre's criterion to check for disk instability. This triggers aggregation, which is out of phase with the forcing, explaining the 'straw' and associated gaps seen between density wave crests. The largest objects have a steeper size distribution, because of the difficulty of accretion in the tidally influenced regime near the Roche limit. The knee in the size distribution of F ring 'kittens' (at about 700m) may therefore be associated with the transition from adhesive growth to collisional gravity-dominated accretion.The predator-prey model thus provides an intuitive description of the non-linear dynamics that leads to the structures seen in Cassini UVIS and ISS observations.
- Publication:
-
42nd COSPAR Scientific Assembly
- Pub Date:
- July 2018
- Bibcode:
- 2018cosp...42E1010E