1. A Season in Saturn’s Rings: Cycling, Recycling and Ring History
Larry W. Esposito, Bonnie K. Meinke, Nicole Albers and Miodrag Sremcevic
LASP
19 March 2012

2. Key Cassini Observations
High resolution SOI images of straw, propellers, embedded moons, F ring objects. Occ’s confirm structure, self-gravity wakes, overstability
Multiple UVIS, RSS and VIMS occ’s
Equinox images of embedded objects

3. Saturn Equinox 2009
Oblique lighting exposed vertical ring structure and embedded objects
Rings were the coldest ever
Images inspired new occultation and spectral analysis
Steady progress and new discoveries continue: More complex, time variable

6. 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
For density waves, significance correlated to resonance torque from the perturbing moon

8. We identify this structure as temporary clumps

9. Edges also show structure
Some explained by multiple modes
Other sharp features appear stochastic, likely caused by local aggregates

10. From
Albers etal
2012

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

13. New Features

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

16. We identify our ‘kittens’ as transient clumps

17. Prometheus excites F ring structures

19. Buerle etal 2010:
Bright spots cast shadows.

20. Meinke Dissertation Results: Size Evolution Models
Wavy, quasi-periodic behavior in the size distribution is due to sharp thresholds and their echoes. Multiple modes are not just artifacts!
Porosity evolution makes larger objects more compact and persistent
Matching the observed kitten shallow size distribution requires enhanced accretion for larger objects
This may result from passage through high density regions, triggered by Prometheus streamline crowding

21. Parameters for this model are:
qswarm=qej
rkitten= 640 m
ΣHDR= 40 g cm-2
μcrit = 100
BEST FIT MODEL
Upper limit on object like S/2004 S 6
10m
100m
1km
5km

23. Visibility of Propellers
Moonlet perturbation larger than random motions: Rmoonlet > H; Lewis Mmoonlet > 30 Mmax
Moonlet perturbation larger than caused by SGW accelerations: Rmoonlet > λcrit (Michikoshi)
Propeller width ~ 2-4 * Rmoonlet
Propeller length ~ 50 * Rmoonlet; longer in occultations?
Evidence for moonlets in Rings A, B, C, CD

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

25. Phase plane trajectoryV2 M

26. Observations Small bodies in the F ring and outer B ring cast shadows
Vertical excursions evident at ring edges and in other perturbed locations
Multimodal ringlet and edge structure: free and forced modes, or just stochastic?
Temporary F ring aggregates
Propellers and gaps in A, B, C rings

27. 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
shield their interiors from meteoritic dust pollution
release pristine material when disrupted by an external impact

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

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

30. Backup Slides

31. F ring Kittens
UVIS occultations initially found 13 statistically significant features
Interpreted as temporary clumps and a possible moonlet, ‘Mittens’
Meinke etal (2012) now catalog 25 features from the first 102 stellar occultations
For every feature, we have a location, width, maximum optical depth (opacity), nickname

37. Model consistent with observations must include enhanced growth of larger bodies
The largest bodies in the system are the only ones that have increased accretion in the HDRs because gravitational instabilities form around them
The numbers of the smallest bodies decrease as the larger bodies sweep them up
This “flattens” the distribution by preferentially removing small bodies
Thus, the “kittens” that UVIS sees may be themselves swept up by even larger moonlets (S/2004 S 6)

41. Clump observed in UVIS line of sighta λ
We detect clump if center of clump is within a semi-major axis length of the occultation track.
This defines the region of observation
We would observe a clump if it were within distance a of the observation path, so the width of the observed area is L=2a
The length of that area is the width of the ring, deltaR.
Extrapolate to the total number in the F ring by accounting for the total area observed in N_occs.

42. Coagulation equation describes competing accretion and disruption
Pre-collision bodies Post-collision bodies
M-m1 M m1
Fragmentation Accretion m m m m m m
Collision of bodies 1 and 2 result in redistribution of fragments M m m2 m1 m m m m m m m m m m m m m

44. Body experiences enhanced accretion when it enters a High Density Region (HDR) Body approximated at a line mass (line along the azimuth where clumps are likely elongated, triaxial ellipsoids)
Body approaching area of enhanced growth
Body within area of enhanced growth
Body after encounter with area of enhanced growth λ0
Vorb ΩF ΔR Δλ
Vorb ΩF
λ0+Δλ
Ωparticles~ΩF
HDR
ΩHDR=ΩProm
ΔΩ = ΩF-ΩHDR
Angular speed at which the body moves through the HDR
HDR
HDR fixed to Prometheus

45. Observations and Model tell a story of how moonlets are made
Observations show us:
Compaction occurs, but is rare
Clumps are correlated to Prometheus
Model shows us:
Binary accretion is not sufficient to match observations
Bodies must have enhanced growth, and Prometheus provides that opportunity
Together:
Complicated moonlet-construction occurs in the F ring
Moonlets are rare but possible
Accretion is winning in the F ring long-term

46. The F ring is a natural lab for studies of accretion
30+ years of observations
Models to date:
Beurle, et al. (2010) show that Prometheus makes it possible for “distended, yet long‐lived, gravitationally coherent clumps” to form
Barbara and Esposito (2002) show bimodal distribution of F ring material, which predicts a belt of ~1 km-sized moonlets
What is the lifecycle of moonlets in the F ring?

47. The F ring may be the easiest place to observe
aggregation/disaggregation

49. Increasing accretion 1000x gives consistent slope, but predicts larger clumps that would have seen by UVIS
~few km:
UVIS should have seen more than 3

50. Alternate explanation: clumps grow where streamlines crowd
F ring model profiles show streamline crowding (Lewis & Stewart)

53. 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/erosion]
dVrel2/dt= -(1-ε2)Vrel2/Tcoll + (M/M0)2 Vesc2/Tstir
[dissipation] [gravitational stirring]
- A0 cos(ωt) [forcing by streamline crowding]

54. Amplitude proportional to forcing
B ring phase plane trajectories

55. Wavelet power seen is proportional to resonance torques

57. F ring phase lag

58. Post-Equinox View
Cassini Equinox observations show Saturn’s rings as a complex geophysical system, incompletely modeled as a single-phase fluid: clumps evident; particles segregate by size; viscosity depends on shear; shear reverses in perturbed regions; rings are far from equilibrium in perturbed regions
Self-gravity causes wakes, viscosity, overstabilty and local aggregate growth
Larger fragments: seeds for growth

59. Implications
Self-gravity is key: Rings may suffer viscous and 2-stream instability
Resonances and Kepler shear provide the forcing for a multitude of dynamics
Structure forms at scales from meters to kilometers
Accretion may continue today to renew the ring material.