Micro-structural size properties of
Saturn’s rings determined from ultraviolet
measurements made by the Cassini
Ultraviolet Imaging Spectrograph
Todd Bradley
UVIS Team Meeting
Boulder, Colorado
June, 2008
Investigation summary
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Analyzed multiple observations in FUV
Observations were all of lit side
Phase angles ranged from 0.8° to 27°
Computed I/F
Fit I/F with Hapke model for single scattering
albedo
• Found variations in microstructure with radius
2
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Water ice absorption feature
• Imaginary index of
refraction for water ice
decreases with
increasing wavelength
• Solar flux is mostly
featureless from 150 to
175 nm
• I/F = Measured
radiance/solar
irradiance
• Absorption feature at ~
165 nm characteristic
of water ice
4
UCF
Chandrasekar Classical Radiative
Transfer Approach
  1  1  

o
I
1  e   o   f water  (1  f water ) Rc
  o P  
F
4(    o ) 

I
 oK  C
F
I/F is the bidirectional reflectance
wo is the single scattering albedo
P() is the phase function
 and o are the cosine of the incidence and emission angles, respectively
 is the optical depth
fwater is the fraction of water ice
Rc is the reflectance of a “grey” contaminant
UCF
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Hapke formulation of the scattering
efficiency
For short wavelengths (2pa/l >> 1), Hapke (1992) models the single scattering
albedo in this way
 o  Qs  Se  1  Se 
1  S 
i
1  Si 
Se = Fresnel reflection coefficient for externally incident light
Si = Fresnel reflection coefficient for internally incident light
Both Se and Si are computed from the complex index of refraction
 is the internal transmission
factor and is modeled as:
  exp

4 pk
l
L
where <L> is the mean path length
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Mean path length
• <L>is a measure of the distance light
travels after an encounter with a ring
particle
• <L> is affected by:
– the microscopic size of water ice grains on
the much larger ring particles
– distance between cracks or other scattering
surfaces
– mean spacing between contaminants in a
water-ice matrix
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Data processing and analysis
Outer A ring
• Bin pixels
azimuthally in 4000
km radial bins
• Using Hapke model
along with
bidirectional
reflectance data,
scale the magnitude
of the model to the
data
• Fit model to extract
<L>
Rayleighs
Cassini division
Inner B ring
Inner C ring
Saturn
Observation: UVIS_036RI_SUBML17LP001_CIRS
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Least squares extraction of <L>
• Compute
D =1/Nl*∑(model – I/F)2
over a range of path
lengths
• Minimum D = <L>
• Width of curve denotes
uncertainty
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Retrieval technique is independent
of I/F magnitude (7.125 microns)
2X
+ .03
2X + .03
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Use extracted <L> in model
Center = 7.125 microns
• Plot of model using <
L > from minimum
squared difference
(blue)
• Red curves are model
results for additional
path lengths in 1
micron increments
• For a single spectra,
can only distinguish to
within 2 – 3 microns
from center
• Compare multiple
observations
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Multiple observations
Inner C
ring
Inner B
ring
Cassini
Division
Outer A
ring
Mean  ~ 7
to 27
• Decrease
uncertainty by
considering
multiple
observations
• Clearly
observations are
repeatable with
some exceptions
Mean  ~
0.85 to 0.84
UCF
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Phase angle () dependence
• Observations within
the B ring
• As  increases, the
photon has to scatter
more times within an
ice grain in order to
escape
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 dependence for different radial
distances
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Heuristic model interpretation of
interaction of photon with ice grain
Ice grains
Could be contaminants, cracks, etc.
UCF
• For low 
observations, the
photon has probably
had few scatterings
• For high , the
photon probably had
to scatter multiple
times
• For high , photon
travels more within
ice leading to more
absorption (shifts
absorption edge to
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longer wavelengths)
I/F displacement
• Observations
from the same
location in the
A ring
• Larger 
shifts
absorption
edge to longer
wavelengths
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Average of larger  observations
Inner C
ring
Inner B
ring
Cassini
Division
Outer A
ring
• <L> as a function of
radius for all 6 high
 observations
averaged
• Average I/F for
same 6 observations
does not seem
correlated with < L >
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Summary
<L>
microns
planet
79,400 km
135,400 km
For  > 7
UCF
• UVIS offers unique
ability to see
microphysical
variations
• Comparing multiple
observations gives
more confidence in the
results
• Present model does
not relate  to < L >
• If simple heuristic
model is correct, then
low  deals more with
single scattering
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Future/ongoing work
• Need to incorporate more low  and high  >
50°) observations
• If the explanation for phase angle effects is
multiple scattering from contaminants, then need
to start thinking about fraction of contaminant
• Need to use a model that accounts for phase
angle effects/multiple scattering in the path
length in order to constrain ice grain size
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