1. Predator-Prey Model for Saturn’s A Ring Haloes
LW Esposito, ET Bradley, JE Colwell,
M Sremcevic
2012 AGU Meeting

2. Cassini Observed ‘Haloes’ in Saturn’s A Ring
Annuli of increased brightness were seen by VIMS and UVIS at Saturn Orbit Insertion
Found at strongest density waves, but not at Mimas 5:3 bending wave

3. A Ring Brightness from Cassini UVIS Saturn Insertion

4. UVIS SOI (150 km resolution elements)

5. Close-up of UVIS SOI reflectance at Janus 5:4 density wave
300 km, Peak I/F =
300 km, Peak I/F =
150 km, I/F =

6. VIMS effective grain size at Janus 5:4 resonance
From Hedman etal Icarus 2012

7. ‘Straw’ in
images

9. Modified Predator-Prey Equations for Ring Clumping
M= ∫ n(m) m2 dm / <M>;
Vrel2= ∫ n(m) Vrel2 dm / N
dM/dt= M/Tacc – Vrel2/vth2 M/Tcoll
[accretion] [fragmentation/erosion]
dVrel2/dt= -(1-ε2)Vrel2/Tcoll + (M/M0)2 Vesc2/Tstir
[dissipation] [gravitational stirring]
- A0 cos(ωt) [forcing by streamline crowding]

10. In the Predator-Prey Model
Periodic forcing from the moon causes streamline crowding
This damps the relative velocity, and allows aggregates to grow
About a quarter phase later, the aggregates stir the system to higher relative velocity
The limit cycle repeats each orbit, with relative velocity ranging from nearly zero to a multiple of the orbit average: 2-10x is possible

11. Phase plane trajectoryV2 M

12. Upgrades to Predator-Prey Model – Collisions among Ring Particles
Add stochastic forcing to simulate aggregate collisions: Random outcome doubles or halves aggregate mass. Previously, no collisions.
Add threshold for gravity-bound aggregates: above this it is harder to disrupt aggregates. Previously, threshold for erosion of aggregates from Blum (2007)

13. Log plot of updated system trajectories

14. Effects on Ring Particle Regolith
In the perturbed region, collisions erode the regolith, removing smaller particles
The released regolith material settles in the less perturbed neighboring regions
Diffusion spreads these ring particles with smaller regolith into a ‘halo’

16. Conclusions
Cyclic velocity changes cause perturbed regions to reach higher collision speeds, which preferentially removes small regolith particles
This forms a bright halo around the ILR, like the ‘Brazil Nut’ effect
Surrounding particles diffuse back too slowly to erase the effect; diffuse away to form the halo
Predicts no UVIS spectroscopic change longward of H2O absorption edge, only photometric brightening of 10-50%, consistent with UVIS SOI
Predicts larger effective size at ring edges, too