Larry W. Esposito
COSPAR Beijing
18 July 2006

• 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

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 reassemble.

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

COLLISIONAL CASCADE
USES UP RING MATERIAL TOO FAST!

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)

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!

• 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…

N1507015271 N1507099722
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)

• 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

• 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

• 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

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

• Spans 3 integrations
• Also seen in
VIMS data
• At 140610.5 km
• ~0.2 km wide
“Pywacket”

“Mitttens”

• Starts at
139962 km
• 21 integrations
• Width:
0.6 km, and opaque

• 9 events
• 30m to
600m wide

q~2.5
Barbara and
Esposito
‘02

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

Figure from Tiscareno etal 2006
*
Mittens: 600m

• 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

• 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

• 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

RING AGE TRACEBILITY MATRIX
Ring Feature
Narrow ringlets in gaps
Embedded moonlets
"Propeller" objects
F ring clumps
F ring moonlets
Inferred/observed age months months tens to millions of years
Implications
Variable during Cassini mission millions of years Density shows accretion less than a million years Need better pix
Sizes not a collisional distrib
Quickly ground to dust Cassini Div density waves 100,000 years
Ring pollution (from color)
A
B
C
1E7 - 1E8 years
1E8 - 1E9 years
Expected more polluted than B
Meteoroid flux not so high?
Color/spectrum varies in A 1E6 - 1E7 years
Shepherd moons Breakup: 1E7 years
Self-gravity wakes
Ring composition not homogenized
Momentum: 1E7 years No contradiction in ages!
days Particles continually collide; self gravity enhances aggregation
OLDYOUNG RENEWED
OK OK
OK OK
?
? ?
OK
OK OK
OK OK
?
OK OK
OK
OK OK
OK OK OK

• 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.

• 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!

• 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

• 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!

• 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

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.

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

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)

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

• Pywacket
– In Alp Sco Egress
– 200m wide
– At 140552km from Saturn
• Mittens
– In Alp Leo
– 600m wide
– 139917km from Saturn

• 9 events
• 30m to
600m wide

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

Events compared to Barbara and Esposito 2002