Ring Spectroscopy and
Photometry
Todd Bradley
January 9, 2014
Overview
• Review of ring particle albedo modeling
• Compositional modeling of the rings using a
Hapke approach
• Compositional modeling of the rings using the
Shkuratov model
Model discretely averaged I/F with Chandrasekhar-granola bar model

I
o
 AB * P *
1  exp  n / exp  n / o 
F
4  o 


I/F at 180 nm
Also did I/F at 155 nm
(not shown)
Need to do this for
more wavelengths and
shorter wavelengths if
possible
3
Compositional Modeling
Cuzzi and Estrada (1998) used a Van de Hulst to relate AB to ϖ
AB
1 S 1 0.139S 


1 1.17S
where S 
1 SI
  Qs  Se  1 SE 

1 SI 



1 r exp 
1 
1  g
g = regolith grain
anisotropy parameter
n 12  k 2
4
SE 

0.05
,
S

1

I
2
n  12  k 2
nn  1
 where r  1 
1
    2d /3
ri  exp  
   2di /3
i
i
i
 /   
 /   
n and k are the optical constants, d is the grain diameter, α = 4πk/λ and ς is the internal
scattering coefficient
4
Two-component mixture
(99.5% calcite; 0.5% nano-phase iron)
1 Calcite crushed with a mortar and pestle
2 nano-phase iron added and lightly crushed and the reflectance (black curve).
3 Mixture was then crushed two more times (blue and red curves).
Compressive Strength of Materials
Material
Compressive Strength (106 N/M2)
Ice at 77K
40-100
Lake Ice
10
Sea ice
0.01-0.04
Basalt
100-350
Coal
20-100
Granite
100-300
Try Two Different Two Component Mixtures
Water Ice and Triton Tholin (irradiation of 0.999:0.001 N2:CH4;
bulk substance: C3H5N4
Linearly
add
optical
constants and get one
single scattering albedo;
a single regolith grain is a
well mixed combination
of components (Cuzzi
and Estrada, 1998)
ni  1 fe nio  fenie
nr  1 fe nro  fenre
Separate grains for each
component. Calculate single
scattering albedo for each.
Add together.
 H O   X

,
1 
2
 x  H o DH o
=
 H o  x Dx
2
2
2
μ = bulk density, ρ = solid density, D = size
Assume ρ is same for both (Hapke, 1993)
7
Linear Mixing Approximation
•Free parameters in the model are the grain size, water ice abundance, and asymmetry
parameters
•The model was compared to either the FUV data points or the FUV-NIR data points in
the minimization routine.
Discrete Grain Mixture
•Free parameters are the water ice grain size, contaminant grain size, water ice
abundance, and asymmetry parameter.
•The model was compared to either the FUV data points or the FUV-NIR data points in
the minimization routine.
Hapke Central A Ring Discrete
Grain Water Ice-Ammonia
Hapke Central A Ring Discrete
Grain Water Ice-Ammonia
Recent Work
• Retrieve ring particle albedo at 3 nm intervals
for more regions of the rings (B2, B3, B4, CD,
A1, A2, A4)
• Consider species other than Triton Tholin (gray
contaminant and ammonia), for FUV
• Use Shkuratov model to compare with data
Ring Particle Bond Albedo
Absorption Values
B3; Hapke model fit
CD; Hapke model fit
Minimum Value of D
Fraction of Water Ice
Grain Size
Shkuratov Model
• Requires geometric (physical, Ap) albedo
• Ratio of brightness of a body at g = 0 to the brightness of a
perfect Lambert disk of the same radius and at the same distance
as the body but illuminated and observed perpendicularly
• Previously I derived ring particle bond (spherical, As) albedos and
ring particle phase functions
As
Ap 
q

q  2  (g)sin gdg
0
Φ(g) is integral phase function, i.e. the relative brightness of a body at
phase angle g normalized to its brightness at 0° phase angle
q = phase integral
Ring Particle Geometric Albedo
Shkuratov Discrete Grain Model
(B3)
Shkuratov Discrete Grain Model
(CD)
Fraction of Water Ice
Ratio of albedos
Comparison of ratio of
albedos to water ice fraction
retrieved from water icetholin model
Porosity
Minimum Value of D
Water Ice Grain Size
Contaminant Grain Size
Summary
• Hapke linear mixture does not fit the data as
well as Hapke discrete mixture
• Hapke water ice-tholin discrete mixture model
fit FUV and long wavelength data very well for
B3
• Hapke water ice-ammonia discrete mixture
model did not fit at long wavelengths
• For Hapke two-component discrete mixture all
three contaminants fit the FUV data about the
same
Summary
• For Shkuratov two-component discrete mixture all three
contaminants fit the FUV data about the same
• Water ice fraction radial distribution appears more believable
from using Shkuratov model but disagrees with albedo ratio at
outer A ring
• Absolute values of water ice fraction from Shkuratov are less
than 0.6
– This could a matter of proper model interpretation
– Could be that model does completely reproduce the
reflectance
– Could be that UVIS is sensitive to small contaminant grains
near surface, which decreases the retrieved water ice
abundance
Conclusions and Future Plans
• May need to consider different mixing models
for broad wavelength range
• May need variable size distribution for broad
wavelength range
• Try Shkuratov model on long wavelength data
provided phase function is available
• Investigate other rings regions at longer wavelengths
where I now have the ring particle albedo
• Try lower spectral resolution sampling to
improve SNR
Different Mixtures for Regolith Grains
Hapke mixture
Cuzzi mixture
Water ice
grains
Contaminant
grains
Water ice grains
Contaminant
grains
Water ice and contaminant are
thoroughly mixed within each grain
Combine fractions of
constants then calculate
single scatter albedo
optical
overall
Water ice and contaminant grains are
separate with their own single
scattering albedo but are thoroughly
mixed within the regolith.
Compute single scattering albedo for
each component and then combine
fractions of single scattering albedos
to get overall single scattering albedo 34
EXTRA
Shkuratov Discrete Grain Model (B3)
Shkuratov Discrete Grain Model (CD)
Shkuratov Linear Mixing Model (B3)
Shkuratov Linear Mixing Model (CD)