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
150 km, I/F = 0.0077
300 km,
Peak I/F
= 0.0090
300 km,
Peak I/F
= 0.0082
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]
- A0 cos(ωt)
[gravitational stirring]
[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