Ring Spectroscopy and
Photometry
Todd Bradley
June 19, 2012
Outline
• Spectral modeling of rings to determine ring
particle albedo, AB, 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 AB
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 ChandrasekharGranola 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 (AB), 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
o
 AB * P *
1  exp  n / exp  n / o 
F
4  o 


T  expn / 
S /W  H /W sin   


wake
To  expn / o 
 cot B 
S /W  1
S /W  H /W sin 


'


cot
B

o
wake
S /W  1
expgap / 
exp
gap
/ o 
5
Granola bar model
H
W
S
6
Assume power law phase function
P  Cn    
n
1
g
2
 P cos  sin d

0
Minimize D

n
1
2
D  (di  mi )
n i1
Where i = 1 to n is over a range of phase angles and free
parameters are AB, d is the measured I/F, and m is the model I/F
7
B
8
B
A
Retrieved AB at 180 nm and 155 nm
9
SOI data
10
Chandrasekhar Model for Transmission
I
o
 AB * P *
exp  n /   exp  n / o 
F
4  o 


• Use AB 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 AB 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 MonteCarlo 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.
13
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 AB 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
(AB) to investigate composition
• AB is related to regolith grain composition
through Hapke-Van de Hulst model (Cuzzi and
Estrada, 1998)
• Need to determine AB at discrete wavelength
intervals across the absorption edge
17
Relation of AB to grain single scattering
albedo (ϖ)
Cuzzi and Estrada (1998) used a Van de Hulst reflectance approach
to relate AB to ϖ
Ab 
1  S1  0.139S
1 1.17S
1 
where S 
1 g
where g is the regolith grain anisotropy parameter
18
Hapke model of ϖ
For species x:
1  SI
 x  Qs  Se  1  SE 

1  SI 
n 1  k 2
4
SE 
 0.05 , SI  1 
2
2
2
n  1  k
nn  1
ri  exp      2di /3
1   /   

where ri 
1  /   
1 ri exp      2di /3
2


and   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:
 
2
f
d
 x x x
x
2
f
d
xx
x
Where fx and dx are the fractional
abundance and grain diameter of
species x
19
AB at discrete wavelength intervals
AB was determined from Chandrasekhar-Granola bar model
approach in 3 nm intervals
20
Approach
• Use AB 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 H2O only, and intimate mixture of H2O and NH3, and
intimate mixture of H2O and a highly absorptive gray contaminant, an
intimate mixture of H2O, NH3, and the absorptive gray contaminant,
and an intimate mixture of H2O, NH3, and a Triton tholin. We fit the
model to FUV AB from slide 20 combined with visible AB from Porco et
al. (2005) for the outer A ring. AB is represented as asterisks. The H2O,
NH3, and the Triton tholin fit the data best; however the model does
22
not fit the data point at 338 nm.
Conclusions
• None of the mixtures fit the data point near
338 nm
• The H2O:gray (99.5:0.05) fits the long
wavelength data about as well as any of the
others, however it completely misses in the
FUV
• Optical measurements of icy mixtures from
FUV through IR may help constrain the
problem
23