1. Cassini Observations and Ring History Larry W. Esposito COSPAR Beijing 18 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 10 5 years Under-dense moons and propellers indicate continuing accretion Autocovariance from occultations and varying transparency show ephemeral aggregations

6. 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.

8. COLWELL AND ESPOSITO PROPOSED A ‘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

9. COLLISIONAL CASCADE USES UP RING MATERIAL TOO FAST!

10. 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)

11. 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!

13. 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 These short-live objects argue for ‘creeping’ growth of moonlets from ring particles and continuing recycling…

14. N1507015271 N1507099722 Bright arc and object in the F ring (2005 DOY276) 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)

15. 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: 10 5 moonlets, optical depth 10 -3, consistent with predictions

16. Search Method Calculate standard deviation of each data point Determine baseline for F ring Assume normal distribution Flag statistically significant points: Z min 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 Z min  from Bsln

17. 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

18. 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

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

20. “Mitttens”

21. Alp Leo Starts at 139962 km 21 integ- rations Width: 0.6 km, and opaque

22. Observed Events 9 events 30m to 600m wide

23. Observed Events Barbara and Esposito ‘02 q~2.5

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

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

26. 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 or halving size in dt

27. Random Walk Results Solve for irreducible distribution For power-law size distribution with index -3 –p/q = 2 –Mass loss rate: 4 x 10 12 g/year –dt > 10 5 years to maintain distribution against shattering of largest objects by external impacts For a clump or temporary aggregation with 10 3 collisions/year: 10 8 interactions to double in mass! This ‘creeping’ growth is below the resolution of N-body and statistical calculations

28. 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

32. RING AGE TRACEBILITY MATRIX

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

34. 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 10 5 years Ongoing recycling resets clocks and reconciles youthful features (size, color, embedded moons) with ancient rings: rings will be around a long time!

35. What’s Next? Determine persistence of F ring objects: track them in images. Measure A ring structures, events, and color variations Characterize aggregations from wakes to moonlets: is this a continuum? Compare to Itokawa and other ‘rubble piles’ Run pollution models for color evolution Develop ‘creeping growth’ models

36. Summary Numerous features seen in RPX images UVIS sees an opaque moonlet and other events in 7 occultations: implies 10 5 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 implies rings will be around a long time!

37. Backup Slides

38. 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

39. 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.

40. 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

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

42. 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

43. Observed Events Pywacket –In Alp Sco Egress –200m wide –At 140552km from Saturn Mittens –In Alp Leo –600m wide –139917km from Saturn

44. Observed Events 9 events 30m to 600m wide

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