Cassini Observations and Ring
History
Larry Esposito
4 January 2006
Cassini observations show active
ring system and short lifetimes
• Time variations in ring edges, D & F rings
• Inhomogeneous on multiple scales, with sharp
gradients seen by VIMS and UVIS: ballistic
transport has not gone to completion
• Density waves have fresher ice
• Low density in Cassini Division implies age of
less than 10^5 years
• Under-dense moons and propellers indicate
continuing accretion
• Autocovariance from occultations shows
ephemeral aggregations
YOUTHFUL RINGS: DESTRUCTIVE
PROCESSES ACT QUICKLY
• Grinding and sputtering
• Spreading and momentum transfer to small
moons
• Darkening from meteoroid bombardment
• Ring ages: 107 to 109 years
Inferred lifetimes are too short
for recent creation of entire rings
• Are rings more recent than
Australopithecines, not to mention
dinosaurs?
• B ring has longer timescales, more mass
• Small shepherds have short destruction
lifetimes, and should be found near rings
• Low density moons show accretion happens
now
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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!
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
• Small moons caught in resonances with
larger moons: this slows linked evolution
COLLISIONAL CASCADE
MARKOV MODEL FOR THE
COLLISIONAL CASCADE
• Improve by considering recycling
• Collective effects: nearby moons can
shepherd and recapture fragments
• Accretion in the Roche zone is possible if
mass ratio large enough (Canup & Esposito
1995)
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):
E1=(1-pn)/(pnq)
~n, for nq << 1
(linear)
~n2, for nq ~ 1
(like diffusion)
~2n+1-2, for p=q=1/2
~p-n, as q goes to 1 (indefinitely long)
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
• Below some threshold, recycling declines
and the rings are rapidly lost
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.
• 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
Accretion as a random walk
• Emphasize random events like fortunate
orientation, local melting and annealing,
collapse to spherical shape
• Differs from solving accretion equation,
which involves “accretion coefficient” with
two indices
• Probabilities p,q for doubling, halving size
in dt
Random Walk
• Solve for irreducible distribution
• Power-law size distribution with index -3
– p/q = 2
– Mass loss rate: 4 x 1012 g/year
– dt > 105 years
• 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
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 create
‘hopeful monsters’ like in evolution of life,
that is, melting, annealing, reorientation