1. Boom and Bust Cycles in Saturn’s rings? Larry W. Esposito, Bonnie Meinke, Nicole Albers, Miodrag Sremcevic LASP/University of Colorado DPS Pasadena 5 October 2010

2. Cassini UVIS occultations UVIS has observed over 100 star occultations by Saturn’s rings Time resolution of 1-2 msec allows diffraction- limited spatial resolution of tens of meters in the ring plane Multiple occultations provide a 3D ‘CAT scan’ of the ring structure Spectral analysis gives characteristics of ring structures and their dimensions

3. F ring Kittens UVIS occultations initially found 13 statistically significant features Interpreted as temporary clumps and a possible moonlet, ‘Mittens’ Meinke etal (2010) now catalog 25 features from the first 102 stellar occultations For every feature, we have a location, width, maximum optical depth (opacity), nickname

4. New Features

5. I Gatti di Roma

6. We identify our ‘kittens’ as temporary clumps

7. Features Lag Prometheus 12 of 25 features have  =180º ± 20º The maximum optical depth is at  =161º Sinusoidal fit gives Δλ=191º but r 2 only 0.1

8. Sub-km structure seen in wavelet analysis varies with longitude Wavelet analysis from multiple occultations is co-added to give a significance estimate For the B ring edge, the significance of features with sizes 200-2000m shows maxima at 90 and 270 degrees ahead of Mimas For density waves, significance correlated to resonance torque from the perturbing moon

11. Observational Findings F ring kittens more opaque trailing Prom by π Sub-km structure, which is seen by wavelet analysis at strongest density waves and at B ring edge, is correlated with torque (for density waves) and longitude (B ring edge) Structure leads Mimas by π/2, equivalent to π in the m=2 forcing frame The largest structures could be visible to ISS: we thought they might be the equinox objects

14. Do Saturn’s rings resemble a system of foxes and hares? In absence of interaction between size and velocity, prey (mean aggregate mass) grows; predator (velocity) decays When they interact, a stable equilibrium exists with an equilibrium for the size distribution and a thermal equilibrium

16. Model Approach We model accretion/fragmentation balance as a predator-prey model Prey: Mean aggregate mass Predator: Mean random velocity (it ‘feeds’ off the mean mass) Calculate the system dynamics Compare to UVIS HSP data: wavelet analysis (B-ring), kittens (F-ring) Relate to Equinox aggregate images

17. Predator-Prey Model Simplify accretion/fragmentation balance equations, similar to approach used for plasma instabilities Include accretional aggregate growth, collisional disruption, dissipation, viscous stirring Different from Showalter & Burns (1982) moons perturb the system, not just the orbits

18. V2V2 M Phase plane trajectory

19. Amplitude proportional to forcing

20. Wavelet power seen is proportional to resonance torques

21. Predicted Phase Lag Moon flyby or density wave passage excites forced eccentricity; streamlines crowd; relative velocity is damped by successive passes through crests This drives the collective aggregation/ dis-aggregation system at a frequency below its natural limit-cycle frequency Model: Impulse, crowding, damping, aggregation, stirring, disaggregation Aggregate M(t) lags moon by roughly π

23. What Happens at Higher Amplitudes? The moonlet perturbations may be strong enough to force the system into chaotic behavior or into a different basin of attraction around another fixed point (see Wisdom for driven pendulum); or Individual aggregates in the Roche zone may suffer random events that cause them to accrete: then the solid body would orbit at the Kepler rate

24. Conclusions UVIS sees aggregation/disaggregation In a predator-prey model, moon perturbations excite cyclic aggregation at the B ring edge and in the F ring; this explains phase lag Stochastic events in this agitated system can lead to accreted bodies that orbit at Kepler rate: equinox objects (ISS), ring renewal (Charnoz)? Not shown yet…

25. Backup Slides

26. Lotka-Volterra equations describe a predator-prey system This system is neutrally stable around the non-trivial fixed point Near the fixed point, the level curves are ellipses, same as for pendulum The size and shape of the level curves depend on size of the initial impulse The system limit cycles with fixed period Predators lag prey by π/2

27. Lotka-Volterra Equations M= ∫ n(m) m 2 ; V rel 2 = ∫ n(m) V rel 2 dm dM/dt= M/T acc – V rel 2 /v th 2 * M/T coll dV rel 2 /dt= (1-ε 2 )V rel 2 /T coll + M 2 /M 0 2 *V rel 2 /T stir M: mean aggregate mass; V rel 2 : velocity dispersion; V th : fragmentation threshold; ε: restitution coeff; M 0 : reference mass (10m); T acc : accretion; T coll : collision; T stir : viscous stirring timescales

29. Better Model dM/dt= M/T acc – V rel 2 /v th 2 * M/T coll dV rel 2 /dt= (1-ε 2 )V rel 2 /T coll + M 2 /M 0 2 *V esc 2 /T stir In the second equation, we replaced V rel 2 by V esc 2 : This is equivalent to viscous stirring by aggregates of mass M. This is no longer a pure predator-prey model, but it better mimics the ring dynamics.