1. A Predator-Prey Model for Clumping in Saturn’s Rings
Larry W. Esposito
LASP
14 November 2012

4. Key Cassini Observations
High resolution images of propellers, straw, embedded moons, F ring objects. These show aggregation in the rings!
Occ’s confirm structure, self-gravity wakes, B ring propellers, ghosts. More evidence for aggregates.
Equinox images: embedded objects
Key question: Are Saturn’s rings young or old?

5. Motivation
Processes observed in in the planetary ring systems parallel those that occurred at the time of origin of the planets.
Many processes occuring in the rings resemble those in the solar nebula, like the interaction between the disk and the protoplanets.
Rings are our best local laboratory for studying phenomena in flattened disks:
Detailed ring observations help develop good models for the processes in the rings, which may be useful in understanding these processes

8. Sub-km structure seen in wavelet analysis varies with longitude
Wavelet analysis from multiple UVIS occultations is co-added to give a significance estimate
For the B ring edge, the significance of features with sizes m shows maxima at 90 and 270 degrees ahead of Mimas. Same distance where objects are seen in the images!

10. We identify this structure as temporary clumps

11. Edges also show structure
Some of this can be explained by multiple modes
Other sharp features appear stochastic, likely caused by local aggregates

13. From
Albers etal
2012

14. F ring Observations
27 significant features in F ring: ‘Kittens’ from 22m to 3.7km, likely they are elongated and transient
They have weak correlation to Prometheus, may evolve into moonlets

15. New Features

17. I Gatti di Roma: temporary features in an ancient structure

18. We identify our ‘kittens’ as transient clumps

19. Prometheus excites F ring structures

21. Buerle etal 2010:
Bright spots cast shadows.

22. ‘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]

23. In the Modified 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

24. Predator-Prey model of Moon-triggered Accretion?

25. Phase plane trajectoryV2 M

26. Amplitude proportional to forcing
B ring phase plane trajectories

27. Wavelet power seen is proportional to resonance torques

28. 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

29. F ring profiles show streamline crowding (Lewis & Stewart)

30. F ring phase lag

31. Rare accretion can renew rings
Solid aggregates are persistent, like the absorbing states in a Markov chain
Even low transition probabilities can populate the states: e.g., 10-9 per collision to an absorbing state
These aggregates can renew the rings:
shield their interiors from meteoritic dust pollution
release pristine material when disrupted by an external impact

32. Predator-prey model explains bright haloes of density waves in Saturn’s Rings
VIMS sees brighter and fresher water ice spread in a halo on both sides of strong density waves.
The Cassini image at left shows that km-size clumps form by compaction in the crests of the strong density waves. The clumps stir the collision speeds of nearby particles far more than on average, eroding the particles. The clumps can then grow again. This cycling is described by the “predator-prey” model.
Lynx and hare populations fluctuate in time
“Haloes” of relatively pure water ice are seen by UVIS and VIMS on both sides of strong density waves. It is believed these are created by unusually violent collisions excited by huge, but transient, clumps that form in densely compacted crests of density waves. The grains then spread radially, forming a halo around the density wave. The stirring creates a cycle of high speed collisions and erosion that resembles the economic ‘boom-bust’ cycle of predator and prey in an ecological system.
Esposito etal Predator-Prey Model for Saturn’s A Ring Haloes 2012 DPS; Hedman etal Connection between spectra & structure in Saturn's main rings based on Cassini VIMSata2012 Icarus,in press

33. 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)

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

35. Updated Model Results

36. Log plot of updated system trajectories

37. Analogy: Coast Redwoods
1 in 104 seeds
grows to a tree!

38. Like Beijing, rings contain
both new and
ancient structures!

39. Conclusions
Although rings show youthful features, this may imply renewal instead
Changes since Voyager and abundant embedded objects indicate accretion
A predator-prey model shows how moons can trigger accretion today
Are rings young or old? Yes, maybe both!
Key measurement: Ring mass in 2017.

40. Conclusions: Haloes
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
Surrounding particles diffuse back too slowly to erase the effect