Rings Spectroscopy Todd Bradley January 05, 2011 Outline • Dependence of photon mean path length (L) on phase angle • InvesEgaEon of inter-­‐parEcle scaGering • InvesEgaEon of spectral raEos • DeterminaEon of single scaGer albedo for regolith grains covering ring parEcles 2 Data ReducEon • Lit side data chosen based on high signal and spaEal coverage • Azimuthally binned spectral radiance over 4 regions of the rings: Central A Ring: 125400-­‐130500 km Cassini Division: 117930-­‐122000 km B3 region: 104500-­‐110000 km C ring: 79000-­‐84000 km • Computed I/F for each data point 3 4 Modeling • Used approach by Poulet et al (2002) to specify asymmetry parameter for the Shkuratov et al (1999) model • Compute model over a range of photon path lengths (L) and asymmetry parameter (g) • Scale model to I/F and fit to both spectral locaEon and slope of absorpEon feature 5 6 7 8 9 10 11 12 InterpretaEon • Icy bodies in the outer solar system have been shown to be backscaGering (Bura[, 1985; Verbiscer et al, 1990) • Single scaGering should dominate at low phase angles • ContribuEon to signal from mulEple scaGering increases as the phase angle increases • Photons that have been mulEple scaGered have traveled more within the ice • This results in greater absorpEon and thus shi^s the absorpEon edge towards longer wavelengths 13 InvesEgaEon of inter-­‐parEcle scaGering • Compare a single scaGering model to the data • Choose a power law phase funcEon a^er the example of Dones et al., 1993 • Let ring parEcle albedo and asymmetry value be free parameters 14 An expression for single scaGering from the rings that uses the classical Chandrasekhar expression for single scaGering from an opEcally thin atmosphere is given by: I
µo
= A* P*
1 − exp( −τ n / µ) exp( −τ n / µo ) ]
[
F
4(µ + µo )
€
A = ring parEcle bond albedo P = ring parEcle phase funcEon τn = normal opEcal depth µ = cos(emission angle), µo = cos(incidence angle)!
Power law phase funcEon with g related to n as follows: P = C n (π − α )
1
g=−
2
n
π
∫ P (α ) cos α sin αdα
0
15 Average I/F from 175-­‐185 nm 16 Average I/F from 152-­‐158 nm 17 Average I/F from 175-­‐185 nm 18 €
For the A and B rings try replacing the exponenEal expressions from Chandrasekhar with the wake model from Colwell T = exp( −τ n / µ)
S /W − H /W sin(φ − φ
[
=
wake
) cot B]
S /W +1
(
exp −τ gap / µ
)
To = exp( −τ n / µo )
[
=
S /W − H /W sin(φ o − φ wake ) cot B'
S /W +1
] exp(−τ
gap
/ µo
)
T = transmission funcEon for emiGed light, To = transmission funcEon for incident light, B = observer elevaEon angle, B’ = solar elevaEon angle, ϕ = observer azimuth angle,
ϕo = incidence azimuth angle, S = separaEon of wakes, H = height of wakes, W = width of wakes, gap = opEcal depth of gap 19 Average I/F from 175-­‐185 nm 20 Average I/F from 152-­‐158 nm 21 Average I/F from 175-­‐185 nm 22 Average I/F from 152-­‐158 nm 23 Average I/F from 175-­‐185 nm 24 Average I/F from 152-­‐158 nm 25 OpEcal depth profile 26 Brightness raEos and dependence on geometry • The albedo on the long wavelength side of the absorpEon feature is greater than the albedo on the short wavelength side • Look at raEos of spectra to see if there are geometrical dependences 27 Example of spectra from central A ring and C ring Long wavelength Short wavelength 28 Solar elevaEon angle dependence Solar elevation angle
dependence
Difference in behavior of low
albedo ratios compared to
high albedo ratios implies
this is not due to shadowing,
etc.
This seems to be due to
increased contributions from
multiple scattering for higher
solar elevation angles
29 30 RelaEve brightness raEos normalized to central A ring 31 InterpretaEon • Hypothesis for shi^ in L with phase angle relies on mulEple scaGering • The fact that this effect it is observed from icy moons implies mulEple scaGering within regolith grains • The spectral raEos also imply mulEple scaGering • Model for ring parEcle single scaGering compared well with A and C rings • Interpret this as negligible amount of inter-­‐parEcle scaGering but non-­‐negligible mulEple scaGering among the regolith grains that cover a ring parEcle 32 Following the example of Cuzzi and Estrada (1998), solve for the regolith single scaGer albedo using the Van de Hulst relaEon between ring parEcle albedo and asymmetry parameter (1 − S)(1 − 0.139S)
A=
1+1.70S
1−ϖ
S=
1 − ϖg
33 Derived parameters assuming single scaGering between ring parEcles 175-­‐185 nm C ring B ring CD A ring A 0.060 0.090 0.080 0.085 g -­‐ 0.77 -­‐0.69 -­‐0.66 -­‐0.68 ϖ 0.163 0.245 0.225 0.19 152-­‐158 nm C ring B ring CD A ring A 0.015 0.020 0.030 0.015 g -­‐0.81 -­‐0.68 -­‐0.51 -­‐0.72 ϖ 0.041 0.06 0.096 0.043 34 Discussion and Future Work • Regolith grain mulEple scaGering affects retrieved values of L as well as brightness raEos • An understanding of the scaGering behavior of the rings is essenEal for constraining physical parameters such as the regolith single scaGer albedo, abundance of water ice, and idenEficaEon of contaminants • Future work involves modeling amount of contaminaEon required for calculated single scaGer albedo • More sophisEcated scaGering model, especially for the B ring 35 36 Shkuratov model rb = Rb + 1/2TeTiRi exp(-2)/(1 – Ri exp(-))
rf = Rf + Te Ti exp(-) + 1/2 Te Ti Ri exp(-2)/(1 – Ri exp(-))
Re ~ (n-1)2 / (n + 1)2 + 0.05
Ri ~ 1.04 – 1/n2
Rb ~ (0.28 n – 0.20)Re
R f = Re – R b
 = 4kL/ !
 b = q * rb
f = q*rf + 1 – q
From Poulet et al., 2002:
rf − rb
ω = rf + rb , g =
rf + rb
37 €