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
Key Cassini Observations
• High resolution SOI images of straw,
propellers, embedded moons, F ring
objects. Occ’s confirm structure, selfgravity wakes, overstability
• Multiple UVIS, RSS and VIMS occ’s
• Equinox images of embedded objects
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
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 200-2000m shows
maxima at 90 and 270 degrees ahead of
Mimas
• For density waves, significance correlated to
resonance torque from the perturbing moon
Edges also show structure
• Some explained by multiple modes
• Other sharp features appear stochastic,
likely caused by local aggregates
From
Albers etal
2012
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
New Features
I Gatti di Roma: temporary features in an ancient structure
We identify our ‘kittens’ as transient clumps
Prometheus excites F ring structures
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
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
100
m
1km
5km
21
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
Predator-Prey model of Moon-triggered Accretion?
Phase plane trajectory
V2
M
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
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
Analogy: Coast Redwoods
1 in 104 seeds
grows to a tree!
Like Beijing, rings contain
both new and
ancient structures!
Backup Slides
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
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)
37
Clump observed in UVIS line of
sight
r
ΔR
a
λ
We detect clump if center of
clump is within a semi-major
axis length of the occultation
track.
This defines the region of
41
observation
Coagulation equation describes competing
accretion and disruption
Fragmentation
Accretion
Pre-collision bodies Post-collision bodies
m
1
Mm1
M
m
m
1
m2
m m
m m
m
m
m
M
m m
m m m
m
m
m
m
m
m m
Collision
of bodies
1 and 2
result in
redistribut
ion of
44
fragments
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 λ0 Vorb
enhanced ΩF
growth
Body within
area of
enhanced
Δ
Vorb
growth
λ
ΩF
Ωparticles~
ΩF HD
R
Body after
encounter with
λ0+Δλ area of
enhanced
Ω = growth
Δ
R
HDR
ΩProm
ΔΩ = ΩFΩHDR
Angular
speed46 at
which the
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
47
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
48 F rin
What is the lifecycle of moonlets in the
The F ring may be the easiest place to observe
aggregation/disaggregation
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 51
Alternate explanation: clumps grow where streamlines crowd
F ring model profiles show streamline crowding (Lewis & Stewart)
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]
- A0 cos(ωt)
[gravitational stirring]
[forcing by streamline crowding]
Amplitude proportional to forcing
B ring phase plane trajectories
Wavelet power seen is proportional to resonance torques
F ring phase lag
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
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.