1. Cassini Observations and Ring History
Larry W. Esposito
UVIS Team Meeting
11 July 2006

2. Cassini observations show active ring system and short lifetimes
Time variations in ring edges, D & F rings
Inhomogeneities on multiple scales, with steep gradients seen by VIMS and UVIS: ballistic transport has not gone to completion
Density waves have fresher ice, dark haloes
Low density in Cassini Division implies age of less than 105 years
Under-dense moons and propellers indicate continuing accretion
Autocovariance from occultations and varying transparency show ephemeral aggregations

6. Inferred lifetimes are too short for recent creation of entire rings
Are some rings more recent than Australopithecines, not to mention dinosaurs?
Small shepherds have short destruction lifetimes, and it is not surprising to find them near rings
Low density moons in A ring gaps show accretion happens now
B ring not as big a problem: it has longer timescales, more mass

7. VOYAGER, GALILEO AND CASSINI SHOW CLEAR RING - MOON CONNECTIONS
Rings and moons are inter-mixed
Moons sculpt, sweep up, and release ring material
Moons are the parent bodies for new rings
But youth cannot be taken at face value! All objects are likely transient, and may re-assemble.

9. ‘COLLISIONAL CASCADE’ FROM MOONS TO RINGS
Big moons are the source for small moons
Small moons are the source of rings
Largest fragments shepherd the ring particles
Rings and moons spread together, linked by resonances

10. COLLISIONAL CASCADE
USES UP RING MATERIAL TOO FAST!

11. NEW MARKOV MODEL FOR THE COLLISIONAL CASCADE
Improve by considering recycling
Consider collective effects: nearby moons can shepherd and recapture fragments
Accretion in the Roche zone is possible if mass ratio large enough (Canup & Esposito 1995)

12. MARKOV MODEL CONCLUSIONS
Although individual rings and moons are ephemeral, ring/moon systems persist
Ring systems go through a long quasi-static stage where their optical depth and number of parent bodies slowly declines
Lifetimes are greatly extended!

14. Now we see them : F ring clumps and moonlets
F ring objects are abundant
RPX images and movies show numerous objects
UVIS sees 9 events, including opaque object 600m across
Evidence of ‘creeping’ growth of moonlets from ring particles and continuing recycling?

15. Bright arc and object in the F ring (2005 DOY276) N1507015271
Object could be 2004 S3 but is unlikely to be 2004 S6
Best candidate for external impact event (Showalter, 1998), or internal
collision (Barbara & Esposito, 2002)

16. UVIS F ring occultations
7 star occultations cut F ring 9 times
Alp Sco shows 200m feature, also seen by VIMS
This event used as test case to refine search algorithm
Alp Leo shows 600m moonlet
Opaque event! This gives: 105 moonlets, optical depth 10-3 , consistent with predictions

17. Search Method Calculate standard deviation of each data point
Determine baseline for F ring
Assume normal distribution
Flag statistically significant points: Zmin so that 1 event by chance in each occ
Testing unocculted stars gives control, expected number from pure chance
 = √DN
Baseline (Bsln) =
80 point running mean
Z = (DN – Bsln)/
Flagged events
are Zmin from Bsln

18. Persistence test
Ring particle collision rate is proportional to opacity (Shu and Stewart 1985)
Number of collisions needed to escape from an aggregate is proportional to opacity squared
Lifetime against diffusion is the ratio, which increases as opacity increases: the more opaque events are thus more persistent

19. Applying the persistence test
Reexamine points flagged from Z test
Extract events where opacity greater than Pywacket
Particles in such aggregations must collide multiple times each orbit ---> structure persists for some number of orbits
Shu and Stewart for optical depth req.

20. Alp Sco Spans 3 integrations Also seen in VIMS data At 140610.5 km
~0.2 km wide
“Pywacket”

21. “Mitttens”

22. Alp Leo
Starts at km
21 integ-rations
Width:
0.6 km,
and opaque

23. Observed Events Pywacket Mittens In Alp Sco Egress 200m wide
At km from Saturn
Mittens
In Alp Leo
600m wide
139917km from Saturn

24. Observed Events 9 events 30m to 600m wide
Maybe a linearvertical scale is better for this figure?

25. Are these caused by structures like those we see in F ring?

26. Figure from Tiscareno etal 2006
* Mittens: 600m

27. Ring History: Model accretion as a random walk
This model emphasizes random events like fortunate orientation, local melting and annealing, collapse to spherical shape
Differs from solving accretion equation, which involves “accretion coefficient” with indices for accreting mass bins
Instead, parameterize probabilities p,q for doubling, halving size in dt

28. Random Walk Results Solve for irreducible distribution
For power-law size distribution with index -3
p/q = 2
Mass loss rate: 4 x 1012 g/year
dt > 105 years to maintain distribution against shattering of largest objects by external impacts
For a clump or temporary aggregation with 103 collisions/year: 108 interactions to double in mass!
This ‘creeping’ growth is below the resolution of N-body and statistical calculations

29. Random Walk Conclusions
Multiple collisions and random factors may invalidate standard accretion approach
Slowly growing bodies could re-supply and re-cycle rings
Key considerations: fortunate events (that is, melting, sintering, reorientation) create ‘hopeful monsters’ like in evolution of life

33. RING AGE TRACEBILITY MATRIX

34. What do the processes imply?
Unidirectional size evolution (collisional cascade): Then the age of rings is nearly over!
Binary accretion is thwarted by collisions, tides: Larger objects must be recent shards
Creeping growth (lucky aggregations are established by compression/adhesion; melting/sintering; shaking/re-assembly): Rings will persist in an equilibrium distribution

35. A plausible ring history
Interactions between ring particles create temporary aggregations: wakes, clumps, moonlets
Some grow through fortunate random events that compress, melt or rearrange their elements
At equilibrium, disruption balances growth, producing a power law size distribution, consistent with observations by UVIS, VIMS, radio and ISS
Growth rates require only doubling in 105 years
Ongoing recycling reconciles youthful features (size, color, embedded moons) with ancient rings: rings will be around a long time!

36. What’s Next? Persistence of F ring objects: track in images?
A ring structures, events, color variations
Characterize aggregations from wakes to moonlets
Compare to Itokawa and other ‘rubble piles’
Pollution models
‘Creeping growth’ models

37. Backup Slides

40. Summary Numerous features seen in RPX images
UVIS sees an opaque moonlet and many other events in 7 occultations: implies 105 F ring moonlets, roughly consistent with models
Previous models did not distinguish between more or less transient objects: this was too simple, since all objects are transient
Particle distribution can be maintained by balance between continuing accretion and disruption
Ongoing recycling reconciles youthful features (size, color, embedded moons) with ancient rings: rings will be around a long time!

41. MODEL PARAMETERS
n steps in cascade, from moons to dust to gone…
With probability p, move to next step (disruption)
With probability q, return to start (sweep up by another moon)
p + q = 1.

42. LIFETIMES
This is an absorbing chain, with transient states, j= 1, …, n-1
We have one absorbing state, j=n
We calculate the ring/moon lifetime as the mean time to absorption, starting from state j=1

43. EXPECTATION VALUES E1=(1-pn)/(pnq) Lifetimes (steps):
~n, for nq << (linear)
~n2, for nq ~ (like diffusion)
~2n+1-2, for p=q=1/2
~p-n, as q goes to 1 (indefinitely long)

44. EXAMPLE: F RING
After parent body disruption, F ring reaches steady state where accretion and knockoff balance (Barbara and Esposito 2002)
The ring material not re-collected is equivalent to ~6km moon; about 50 parent bodies coexist…
Exponential decay would say half would be gone in 300 my.
But, considering re-accretion, loss of parents is linear: as smaller particles ground down, they are replaced from parent bodies. The ring lifetime is indefinitely extended

45. .
Number of events observed, corrected by subtracting number detected in control regions. Searches with bins of 1, 5, 10.

46. Events compared to Barbara and Esposito 2002