Extracting Information from
Statistical Moments in UVIS
Stellar Occultation Data
Wednesday, January 9, 13
Variance in Occultation Data
Related to Particle Sizes
• For Poisson-distributed data, the
2
variance equals the mean: σ = I
• Finite size of ring particles compared to
the UVIS HSP field of view results in
higher variance.
• Get particle autocorrelation length from
excess variance. Technique pioneered
by Showalter and Nicholson (1990) with
Voyager PPS data. Cassini UVIS data
offer higher signal and spatial resolution.
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
2
If the rings were a translucent screen like this
Then the variance = mean (Poisson statistics)
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
3
...if they look like this, the variance is small.
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
4
This simulated data from the previous particle model
shows variance equal to the mean, as expected for
Poisson counting statistics.
(The discretization of the simulated data reflects the
simulation of the Cassini UVIS compression
algorithm.)
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
5
If the rings look like this, the variance is large.
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
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This simulated data from the previous particle model
shows variance in excess of Poisson counting
statistics.
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
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Particle Autocorrelation Length
AµΔσ
Reff =
2 −τ /µ
−τ /µ
π I 0 e (1− e )
2
A=area of region in rings sampled by a single
measurement
I0=unocculted stellar signal
τ=measured optical depth
Δσ2=excess variance
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
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Excess variance is larger for larger
characteristic particle sizes.
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
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B1 Region
C Ring
Cassini Division
Rings Geography
Ramp
Ramp
A Ring
B Ring
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
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BetCen77_1
The data show multiple distinct populations:
points do not follow a single-valued curve.
C ring
A ring
B ring
Wednesday, January 9, 13
Cassini Division Ramp
Model curves (solid)
and data show at
least three distinct
particle populations in
the C ring and Cassini
Division.
C Ring Ramp
C Ring Plateaus
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
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Dependence on Area
• Direct signal from the smeared Fresnelscale spot of the star in the ring plane.
• Scattered signal from a larger area
dependent on the particle size.
2
π
AS ≈
λ L + ds + 2 λ L + ds f (ϕ ) dsm
µ
(
)
λL
ds =
2r
(
)
• Substitute AS into expression for Reff
and solve for root of 4th order
polynomial.
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
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Correlation coefficient = 0.75
DPS October 19, 2012, Reno NV
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Correlation Coefficient = 0.5
DPS October 19, 2012, Reno NV
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Correlation Coefficient = 0.1
DPS October 19, 2012, Reno NV
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Less Scatter with Brighter Stars
DPS October 19, 2012, Reno NV
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Green: Alp Vir
Blue: Bet Cen
DPS October 19, 2012, Reno NV
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DPS October 19, 2012, Reno NV
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DPS October 19, 2012, Reno NV
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Summary
• Effective particle size in C ring plateaus smaller
than surrounding areas by factor of 1.6.
• C ring ramp similar to the rest of the C ring
while CD ramp similar to the A ring.
• CD ramp Reff 1.7 times Reff of rest of CD.
• Changes in Reff seen in some regions without
obvious corresponding changes in structure:
•
Inner ~700 km of B ring shows distinct, smaller
autocorrelation length than remainder of B1 region.
•
Decrease in Reff at 89,400 km in C ring.
• A ring autocorrelation length behavior
dominated by self-gravity wake structures.
DPS October 19, 2012, Reno NV
Wednesday, January 9, 13
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VIMS/UVIS Self Gravity Wake Results
Josh Colwell and Richard Jerousek
Wednesday, January 9, 13
Self-Gravity Wakes
crκ
Q≈
1
Gσ
UVIS Team Meeting July 7-9, 2013, UCF
Wednesday, January 9, 13
λcrit = 4π Gσ / κ ≈ 1− 100 m
2
2
23
Azimuthal View Angle
Dependence on Opacity
UVIS Team Meeting July 7-9, 2013, UCF
Wednesday, January 9, 13
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Self-Gravity Wake Properties
UVIS Team Meeting July 7-9, 2013, UCF
Wednesday, January 9, 13
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Granola Bar Model (Colwell et al.)
Pasta Model
(Hedman et al.)
UVIS Team Meeting July 7-9, 2013, UCF
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B Ring
UVIS Team Meeting July 7-9, 2013, UCF
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B Ring
UVIS Team Meeting July 7-9, 2013, UCF
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B Ring
UVIS Team Meeting July 7-9, 2013, UCF
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B Ring
UVIS Team Meeting July 7-9, 2013, UCF
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A Ring
UVIS Team Meeting July 7-9, 2013, UCF
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A Ring
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A Ring
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A Ring
UVIS Team Meeting July 7-9, 2013, UCF
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A Ring
UVIS Team Meeting July 7-9, 2013, UCF
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S-­‐G Wake Summary
• Something strange is going on.
• Differences between VIMS and UVIS do not seem to be (enGrely) due to:
–UVIS ramp-­‐up behavior
–observaGonal geometry differences between VIMS and UVIS
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Wednesday, January 9, 13
Faint and Narrow Rings
• Systematic search for ringlets in gaps
throughout the ring system.
• Several ringlets detected, but
generally only in a handful of
occultations.
• Working on assembling everything
into a coherent presentation.
UVIS Team Meeting July 7-9, 2013, UCF
Wednesday, January 9, 13
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Ghosts Update
• Paper in 2nd revision with
Astronomical Journal.
UVIS Team Meeting July 7-9, 2013, UCF
Wednesday, January 9, 13
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