Transcript Bradley rings spectroscopy and photometry June 2012 b.ppt
Ring Spectroscopy and Photometry
Todd Bradley June 19, 2012
Outline
• • • Spectral modeling of rings to determine ring particle albedo, A B , and ring particle phase function Analysis of SOI observations Use albedo determined from lit side to model I/F for unlit side A ring.
Explanation for differences in model fits Compositional analysis using A B 2
Assumption regarding the morphology of ring particles A ring particle is a “snowball” like object that is covered by a regolith of grains Each regolith grain covering a ring particle is assumed to have the same phase function and single scattering albedo 3
Ring Particle Spectral Analysis
• • • I have used a single scattering Chandrasekhar Granola bar model to compare with lit side I/F over a wide range of phase angles This resulted in retrieved values of the ring particle albedo (A B ), and the ring particle phase function I used results in the A ring in the transmission form of the Chandrasekhar-Granola bar model to compute I/F and compare with SOI data 4
Model discretely averaged spectra using Chandrasekhar-granola bar model
I F
A B
*
P
* 4
o
o
1 exp
n
/ exp
n
/
o
T
exp
n
S
/
W
/
H
/
W T o
exp
n
S
/
W
/
o
S
/
W H
/
W
sin 1 sin
o
S
/
W
1
wake
wake
cot
B
exp
gap
/ cot
B
' exp
gap
/
o
5
Granola bar model
H W S 6
Assume power law phase function
P
C n
n g
1 2 0
P
cos sin
d
Minimize D
D
1
n n
i
1 (
d i
m i
) 2 Where i = 1 to n is over a range of phase angles and free parameters are A B , d is the measured I/F, and m is the model I/F 7
B 8
Retrieved A B at 180 nm and 155 nm 9
SOI data
10
Chandrasekhar Model for Transmission
I F
A B
*
P
* 4
o
o
exp
n
/ exp
n
/
o
• • • • Use A B and power law index determined from lit side (reflectance) analysis in transmission formulation Use phase angle from SOI observations Do this for 4 regions of the A ring Compare I/F with SOI I/F 11
SOI (unlit side) using A B and power law index, n, determined from lit side analysis Data 220 km pixel resolution 12
Why not a better fit, especially at the outer A ring? • • Salo and Karjalainen (2003) performed Monte Carlo radiative transfer simulations of the rings and showed that multiple scattered light is typically a greater fraction of the total transmitted light than for reflected light Nicholson et al. (2008) notes that all light seen on the unlit side observations must make it through the gaps between wakes.
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Lit side observation: single scattering dominates Unlit side observation: probability for single scattering decreases, making multiple scattering more important 14
Explanation
• • • Our model is a single scattering model For lit side analysis it is probably safe to assume that multiple scattering is negligible For unlit side, even if the correct A B is used, the single scattering transmission model neglects contributions from multiple scattering and results in underestimating I/F 15
Why does the A2 region fit so well
This is from the UVIS wake model of the A ring for wake width, height, separation, and gap optical depth.
Note that the optical depth in the A2 gap is the least of all the gap optical depths and about half the value of the A4 gap.
This argues for multiple scattering being less significant in the A2 region.
Since the gap optical depth is highest in the A4 region then multiple scattering is most important there and explains why the model fits the worst in the A4 region and the best in the A2 region 16
Compositional Analysis
• • • Now that we have a suitable model for dealing with wakes, use retrieved ring particle albedo (A B ) to investigate composition A B is related to regolith grain composition through Hapke-Van de Hulst model (Cuzzi and Estrada, 1998) Need to determine A B at discrete wavelength intervals across the absorption edge 17
Relation of A B to grain single scattering albedo ( ϖ) Cuzzi and Estrada (1998) used a Van de Hulst reflectance approach to relate A B to ϖ
A b
1
S
1 0.139
S
1 1.17
S
where
S
1 1
g
where g is the regolith grain anisotropy parameter 18
Hapke model of
ϖ For species x:
x
Q s
S e
1
S E
1 1
S S I I
and
S E r i
exp
n n
1 1 2 2
k k
2 2 2
d i
0.05 ,
S I
/ 3 1
r i
exp 2
d i
/ 3 where
r i
1 1 1 4 1 / / 2 4
k
/ and is the n and k are the optical constants, d is the grain diameter, α = 4πk/λ and ς is the internal scattering coefficient For multiple species:
x
x f x d x
2
f x d x
2
x
Where f x species x and d x are the fractional abundance and grain diameter of 19
A
B
at discrete wavelength intervals
A B was determined from Chandrasekhar-Granola bar model approach in 3 nm intervals 20
Approach
• • • Use A B determined from lit side analysis Free parameters are compositional grain size, fractional composition of each species, and grain asymmetry parameter Assume grain asymmetry parameter is the same for all species 21
Model for H 2 O only, and intimate mixture of H 2 O and NH 3 , and intimate mixture of H 2 O and a highly absorptive gray contaminant, an intimate mixture of H 2 O, NH 3 , and the absorptive gray contaminant, and an intimate mixture of H 2 O, NH 3 , and a Triton tholin. We fit the model to FUV A B from slide 20 combined with visible A B al. (2005) for the outer A ring. A B from Porco et is represented as asterisks. The H 2 O, NH 3 , and the Triton tholin fit the data best; however the model does not fit the data point at 338 nm.
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Conclusions
• • • None of the mixtures fit the data point near 338 nm The H FUV 2 O:gray (99.5:0.05) fits the long wavelength data about as well as any of the others, however it completely misses in the Optical measurements of icy mixtures from FUV through IR may help constrain the problem 23