Particle Sizes and
Clumps from Stellar
Occultations
Josh Colwell, Richard Jerousek,
and James Cooney (UCF)
Larry Esposito and Miodrag Sremcevic (CU)
UVIS Team Meeting June 4-6, 2013, St. George Utah
Variance in Occultation Data
Related to Particle Sizes
• For Poisson-distributed data, the
2
σ
=
I
variance equals the mean:
• 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.
UVIS Team Meeting June 4-6, 2013, St. George Utah
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If the rings were a translucent screen like this
Then the variance = mean (Poisson statistics)
UVIS Team Meeting June 4-6, 2013, St. George Utah
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...if they look like this, the variance is small.
UVIS Team Meeting June 4-6, 2013, St. George Utah
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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
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If the rings look like this, the variance is large.
UVIS Team Meeting June 4-6, 2013, St. George Utah
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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
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Particle Autocorrelation Length
AµΔσ
Reff =
2 −τ /µ
−τ /µ
π I 0 e (1− e )
2
(Esposito and
Sremcevic)
A=area of region in rings sampled by a single
measurement
I0=unocculted stellar signal
τ=measured optical depth
Δσ2=excess variance
Δσ =
2
2 −τ /µ
0
πI e
(1− e
Aµ
−τ /µ
UVIS Team Meeting June 4-6, 2013, St. George Utah
)
Reff
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Particle Autocorrelation Length
(Showalter and
Nicholson (1990),
assuming large
particles)
AµΔσ µ
Reff =
2 −2 τ / µ
π I0 e
τ
2
Gives the following relation for excess variance as a
function of optical depth for a given Reff:
2 −2 τ / µ
0
πI e
Δσ =
Aµ
2
τ
Reff
µ
UVIS Team Meeting June 4-6, 2013, St. George Utah
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Excess Variance Dependence on Optical Depth
UVIS Team Meeting June 4-6, 2013, St. George Utah
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Excess variance is larger for larger
characteristic particle sizes.
DPS October 19, 2012, Reno NV
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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
DPS October 19, 2012, Reno NV
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DPS October 19, 2012, Reno NV
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Halo Signature in Particle Autocorrelation Length
DPS October 19, 2012, Reno NV
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!
DPS October 19, 2012, Reno NV
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!
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Summary
• Significant changes in particle
autocorrelation length seen at some
major ring boundaries as well as at
locations with no obvious structural
change.
• Evidence for anti-correlation of
autocorrelation length with optical depth
in strong density waves.
• Decreased autocorrelation length in
density wave halo regions.
DPS October 19, 2012, Reno NV
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VIMS/UVIS Self Gravity Wake Results
Self-Gravity Wakes
crκ
Q≈
1
Gσ
λcrit = 4π Gσ / κ ≈ 1− 100 m
UVIS Team Meeting June 4-6, 2013, St. George Utah
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2
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Self-Gravity Wake Properties
UVIS Team Meeting June 4-6, 2013, St. George Utah
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Granola Bar Model (Colwell et al.)
Pasta Model
(Hedman et al.)
UVIS Team Meeting June 4-6, 2013, St. George Utah
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S-­‐G Wake Status
• Previously found discrepant results fi?ng VIMS-­‐
only or UVIS-­‐only data to S-­‐G wake model, regardless of model.
• Differences between VIMS and UVIS likely due to absolute differences in opHcal depths due to diffracHon in VIMS observaHons.
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VIMS Occultations
• Star is placed in one pixel 0.25 by 0.5
mrad
• Light curves based on 2.9 micron channel
(low background)
• At that wavelength, some light is diffracted
out of the pixel by particles smaller than
1.2 cm in diameter.
• If small particles are present, VIMS will
lose more light than UVIS does and will
report a higher optical depth, skewing S-G
wake parameters.
UVIS Team Meeting June 4-6, 2013, St. George Utah
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New S-G Wake Model
• Unless occultations are at identical
geometries between the two instruments,
cannot extract particle size information from
direct comparison because S-G wakes affect
observed optical depth.
• Use differences in VIMS and UVIS
wavelengths to extract information on
population of small particles via S-G wake
model.
• Fractional optical depth due to small
particles in gaps between S-G wakes is new
parameter for S-G wake model.
UVIS Team Meeting June 4-6, 2013, St. George Utah
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!
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!
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Derived "small particle" optical depth
from UVIS/VIMS joint fit to S-G wakes
UVIS Team Meeting June 4-6, 2013, St. George Utah
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Summary
• Get direct measure of sub-cm population
with handful of Vega occultations.
• Get additional information on small
particles in S-G wakes from new S-G
wake model: preliminary results show
increase abundance of sub-cm particles in
outer half of A ring. See also next talk by
Becker.
• Occultation statistics show decrease in
particle autocorrelation length in perturbed
regions, including haloes.
UVIS Team Meeting June 4-6, 2013, St. George Utah
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