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

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

A Ring Brightness from Cassini UVIS Saturn Insertion

UVIS SOI (150 km resolution elements)

Close-up of UVIS SOI reflectance at Janus 5:4 density wave 300 km, Peak I/F = 0.0090 300 km, Peak I/F = 0.0082 150 km, I/F = 0.0077

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

‘Straw’ in images

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]

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

Phase plane trajectory V2 M

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)

Log plot of updated system trajectories

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’

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