Observations and Models of
Accretion in Saturn’s F Ring
PhD Defense
Bonnie Meinke
February 14, 2012
1
Saturn’s Rings
2
Image credit: NASA/JPL
Saturn’s Rings
Broad, dense rings
Gaps
Dusty components
moons
3
Image credit: NASA/JPL
Saturn’s Rings
4
Image credit: NASA/JPL
Saturn’s Rings
5
Saturn’s F Ring
6
Saturn’s F Ring
~10 km wide
7
Saturn’s F Ring
Azimuthally
asymmetric
8
Saturn’s F Ring
Shepherding moons
Pandora and
Prometheus
9
Moons create structure in rings
B ring edge at Equinox
• Mimas resonance builds
structure, both vertical and
density enhancements
ISS image
Keeler Gap Edge
• Daphnis sets up a satellite
wake and wave structure at
edge of gap
10 2007
Murray
Prometheus creates structure in the F ring
Porco, et al. (2005)
11
Prometheus creates structure in the F ring
Movie from Ciclops.org
Murray, et al. (2005)
12
Prometheus creates structure in the F ring
Murray, et al. (2005)
13
The F ring is in the
Roche Zone
• a=140221.3 km from Saturn
• The Roche limit is the
distance from a planet
within which the planet’s
tides can tear apart a body
held together by its own
self‐gravity
• This is better described as
the “Roche Zone” where
accretion and disruption
compete.
14
Image courtesy of Wikimedia Commons
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
What is the lifecycle of moonlets in the F ring?15
101 occultations observed with UVIS
• Cassini UltraViolet Imaging Spectrograph
(UVIS)
• Stellar Occultations observed with the High
Speed Photometer (HSP)
Image Credit: UVIS team site
16
Observing geometry of UVIS
occultations
17
Observing geometry of UVIS
occultations
r
ΔR
λ
18
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
observation
19
We search through occultations to
find statistically significant features
Searched through the
2000 km surrounding
the F ring region in 101
different occultations
139000
141000
Radial distance (km)
F ring core
20
3 parts of the Robust Search Method
1. Sliding bin m-test:
Search for features in occultations that would occur less
than once per occultation by chance
2. Different Radial-size bins
–
–
Repeat the “sliding bin m-test” for bins of different
radial sizes: 25 m, 100 m, 250 m, 500 m, 1 km, 2km
If feature passes “sliding m-test” at two different bin
sizes, then feature is considered statistically significant.
3. Persistence Test
–
–
Statistically significant features are reviewed
Peak normal optical depth for feature must be greater
than that for Pywacket, a feature confirmed by VIMS
(τ=0.4)
21
Normalized stellar signal
25 Significant Features Found
1.0
0.6
0.2
1.0
0.6
0.2
1.0
0.6
0.2
1.0
0.6
0.2
1.0
0.6
0.2
1.0
0.6
0.2
1.0
0.6
0.2
alpleo9
1
126tau8
2
3
alpvir34
4
gamara37
6
alpara63
10 9
12
8
epscen65
14
13
17
betcen81
22
25
0
alpara90
20
alpara98
alpara90
alpara96
21
alpara98
23
alpsco29
epscas104
24
alpvir124
alpvir2134
26
10
betcen89
18
15
Not visible
in this
range
betcen75
11
alpara79
16
205839 57
7
5
alpsco13
0
10
Distance from core (km)
27
0
10
22
We classify significant features
CORE
MOONLET
ICICLE
23
We classify significant features
CORE
MOONLET
ICICLE
24
Typical shape of
occultation profile
Typical Core
“U-shape”
100 km
25
Observed: unusuallyshaped core regions
Normalized stellar signal
1.0
0.6
0.2
1.0
Alp Vir 34 E
W-core
(a)
Eps Cen 65
W-core
(b)
(c)
Alp Ara 90 E
W-core
(d)
0.6
0.2
1.0
Alp Ara 79
W-core
0.6
0.2
1.0
Alp Ara 96 E
V-core
Alp Vir 124
W-core
(e)
Eps Cas 104 E
W-core
(f)
(g)
Alp Vir 134
V-core
(h)
0.6
0.2
-10
0
Distance from core (km)
-10
0
Distance from core (km)
26
Observed: unusuallyshaped core regions
Normalized stellar signal
1.0
0.6
0.2
1.0
Alp Vir 34 E
W-core
(a)
Eps Cen 65
W-core
(b)
(c)
Alp Ara 90 E
W-core
(d)
0.6
0.2
1.0
Alp Ara 79
W-core
0.6
0.2
1.0
Alp Ara 96 E
V-core
Alp Vir 124
W-core
(e)
Eps Cas 104 E
W-core
(f)
(g)
Alp Vir 134
V-core
(h)
0.6
0.2
-10
0
Distance from core (km)
-10
0
Distance from core (km)
27
Charnoz (2009)
28
Two Observed Moonlets
1.
“Mittens”
•
•
•
•
•
600 m radial width
~3 km outside core
Comparatively sharp
edges
Stellar signal goes to
background level
Opaque  A possible
consolidated object
139915
139916
139917
Radial distance (km)
139918
29
Two Observed Moonlets
2.
“Sylvester”
•
107 m radial width
• ~5 km inside the
secondary core
• Near-Sharp edges
• Stellar signal goes to
background level
• Opaque  A possiblyconsolidated object
29.0
139900
139920
Radial distance (km)
139940
29.2
29.4
29.6
Radial distance (km)
29.8
30
30.0
Observed: Icicles
Currently 2 subclasses:
Simple
•Intermediate opacity
•Simple, symmetric dip in
signal
•Radial width:
22 m – 763 m
-15km
0
15km
Multiple
•Intermediate opacity
•Usually composed of
several adjacent dips in
signal
•Resembles uneven
overlap of simple icicles
•Radial width:
93 m - 2.2 km
-15km
0
15km
31
Evolution of classes?
Icicles  Moonlets
• Natural to imagine moonlets as later
evolutionary stage of icicle
• Optical depth is indicator of clumping
because more-densely aggregated
material blocks more light
• Looser clumps of material compact to form
a feature that appears opaque in
occultation: moonlet
32
Where do features lie with respect to
Prometheus?
Compare these F ring
features with images
that show ring material
stirred up after a
Prometheus passage
(Murray, et al. 2008)
Esposito et al. (2012)
predator-prey model
predicts a competition
between aggregation
and disaggregation in
the ring system
33
We examine the 17 features that fall into
the Icicle and Moonlet classes for trends
with respect to Prometheus
Meinke et al (2012) interpret certain features as
temporary aggregations
– Moonlets
– Icicles
17 features in these classes have parameters that trend
with Prometheus
– Separation from Prometheus
– Optical Depth
34
Trailing:
Prometheus recently
encountered feature and
surrounding material
Leading:
Prometheus has not
encountered feature in a long
time
(synodic period = 68 days)
35
Features cluster at Prometheus’s antipode
9 of 17 features
in the range
 =180° ± 20°
36
Feature optical depth weakly correlates to
Prometheus proximity
Pearson Correlation Coefficient
r2=0.1
Simple icicle
Multi-icicle
Observed
Maximum
at 161º
Fit Maximum
at -190º
37
Clumps lag Prometheus by 180°
Optical depth and frequency correlate to the
relative position of Prometheus
Influence of Prometheus causes identifiable
features with lifetimes comparable to a synodic
period
We infer that competition between aggregation
and disaggregation give temporary clumps that
lag Prometheus by 180°
38
UVIS observations indicate clumping
occurs in the F ring
• 17 Significant, clump-related features found --- clumps are common
• ~10% of the significant features are opaque
moonlets ---- consolidated moonlets are rare
• Prometheus may stimulate accretion and build
moonlets
39
Observed distribution is not consistent
with previous models of the F ring
Observed
cumulative
distribution
Barbara and
Esposito (2002)
Q=1.5
40
Observed distribution is not consistent
with previous models of the F ring
Observed
cumulative
distribution
Barbara and
Esposito (2002)
Q=1.5
N obs 2p R
NF =
N occ Raxes wr
41
The coagulation equation has been used to
model accretion in collisional systems
Fragmentation
Accretion
Pre-collision bodies
m1
Post-collision bodies
M-m1
M
m
m1
m m
m m
m
m
m
M
m2
m
m m
m m
m m m
m
m
m m
Collision of
bodies 1 and
2 result in
redistribution
of fragments
sized
M<0.5m2
45
Model does not match Barbara and
Esposito (2002) or observations
Note: incremental distributions plotted
47
Allowing bodies to compact does not make
model consistent with observations
48
Artificially increasing accretion makes the
model consistent with observations
Note: incremental distributions plotted
49
Artificially increasing accretion makes the
model consistent with observations
~few kms
UVIS should have seen >3
Note: incremental distributions plotted
50
The binary coagulation equation does not produce a
distribution consistent with F ring observations
• The incremental distribution of observed clump-like
features in the F ring has a much smaller (shallower)
power-law index than my simple binary collision model
(as described in previous slides)
An improvement to the model is data driven
• Multiple comparisons show that accretion must be
easier than fragmentation by a large factor to seriously
affect the modeled distribution
Discussions with Glen Stewart and Esposito et al (2012)’s
predator-prey model motivate this view of enhanced
aggregate construction
51
New method to boost accretion
Allow for enhanced accretion of bodies larger than a threshold size
in special regions. During enhanced growth, a body efficiently
sweeps up smaller bodies/aggregates. An additional “production
term” in the coagulation equation incorporates this mechanism and
results in a modeled distribution consistent with observations.
These enhanced growth regions are related to Prometheus.
52
Satellite
Wakes
HDR
HDR
53
Satellite Wakes create High Density
Regions (HDRs)
HDR
HDR
54
HDR
Prometheus
clump
55
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 enhanced
growth
λ0
Vorb
ΩF
Body within area of
enhanced growth
Δλ
Vorb
ΩF
Body after encounter
with area of enhanced
growth
λ0+Δλ
ΔR
Ωparticles~ΩF
HDR
ΩHDR=ΩProm
ΔΩ = ΩF-ΩHDR
Angular speed
at which the
body moves
through the
56
HDR
Aggregates experience more collisions in
High Density Regions
Tcoll
Torb
»
4t
avgFring
coll
T
HDR
coll
T
5x10 4
5
»
» 1.25x10 s
4(0.1)
4
5x10
»
» 4200s
4(3)
Esposito et al (2012) approximate the collision time for a power law
distribution of particle sizes with the above equation from Shu and
Stewart (1985, after their Eq. (9)).
Esposito et al (2012)’s
predator-prey model
predicts shorter collision
timescales in HDR, which
means more collisions and
lower dispersion velocity
If the entire ring were
this optical depth, there
we could expect ~12
collisions per orbit. HDRs
are only about ¼ of
orbital distance, so we
could expect 3 collisions
per particle’s orbit. 57
Increase in collision rate damps the dispersion
velocity, which leads to Toomre instability if optical
depth is near unity. Thus, increased collisional
“sweep up” leads to “gravitational collection”
growth. Both are at work in these HDRs.
Q Toomre =
csk
p GS
Glen Stewart, private communication
<1
Condition for instability in
the disk
58
The enhanced growth is radial
gravitational infall of ring material
x
vorbital
aggregate
y
Infall of
material
The production term describes the one dimensional
gravitational collapse of material onto a body in a
high density region that leads to enhanced growth
of that body. The collapse is along the radial
coordinate in a circular shear flow with self-gravity.
59
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
100m
1km
5km
67
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
100m
1km
5km
68
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
100m
1km
5km
69
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)
70
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
71
This model can be applied
beyond the F ring
Other collisional systems:
Uranus’ ν Ring
• Kuiper Belt: Not enough
accretion for my model to apply
• Can predict probability of observing
moons of certain sizes. Check
consistency with lack of an observed
moonlet belt.
• Asteroid Belt: Again, not enough
accretion for my model to apply
• Protoplanetary Disks: Also
require enhanced accretion to
create planet cores. Addition of
a production term is needed for
both systems. Few systems can
be realistically described using a
simple binary collision
Accretion/Fragmentation model.
72
Questions?
73