Rings Spectroscopy Todd Bradley June 28, 2011 Outline • Retrieve ring par=cle albedo and ring par=cle phase func=on using Chandrasekhar-­‐granola bar model • Retrieve mean photon path length, L, using Shkuratov model • Must deal with mul=ple scaHering issues Recall water ice absorp=on feature Model discretely averaged spectra using Chandrasekhar-­‐granola bar model I
µo
= A* P*
1 − exp( −τ n / µ) exp( −τ n / µo ) ]
[
F
4(µ + µo )
€
T = exp( −τn / µ)
S /W − H /W sin( φ − φ
[
=
wake
) cot B ]
S /W + 1
exp( −τgap / µ)
To = exp( −τn / µo )
[
=
S /W − H /W sin( φo − φwake ) cot B '
S /W + 1
] exp( −τ
gap
/ µo )
Assume power law phase func=on P = C n (π − α )
1
g=−
2
€
n
π
∫ P (α ) cos α sin αdα
0
Minimize D
n
1
2
D = ∑ (Di − M i )
n i=1
From January, 2011 mee=ng 175-­‐185 nm Divide data according to solar eleva=on angle Fit to lower solar eleva=on angles Fit to higher solar eleva=on angles Do the same for the shorter wavelength side of the absorp=on edge Inves=gate solar incidence angle effect • Single scaHering equa=on: assump=on is that op=cal depth and/or albedo are small • Even with the Colwell granola bar model this is s=ll a single scaHering assump=on • Single scaHering in terms of ring par=cle to par=cle scaHering, not regolith grain scaHering • Solar eleva=on angle effect is due to mul=ple scaHering • Compare retrieved albedo and g value from lower and higher solar eleva=on angles for the longer wavelength average I/F Compare ra=o of long wave to short wave albedo to FUV color ra=o • Take ra=o of long wave albedo at both low and high solar eleva=on angles to short wave albedo • For FUV color ra=o use high quality observa=on at low phase angle, low solar eleva=on angle, and complete radial coverage • Rev 036RI_SUBML17LP001 • Phase goes from 12° to 8.5° from the C ring to the outer A ring, respec=vely • Solar eleva=on angle = 14° Example of spectra from central A ring and C ring Long wavelength Short wavelength 17 Compare to albedos at longer wavelengths Long wavelength albedos from Porco et al. 2005. Determina=on of L • 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 loca=on and slope of absorp=on feature 21 Phase angle effect • Icy bodies in the outer solar system have been shown to be backscaHering (Burac, 1985; Verbiscer et al, 1990) • Single scaHering should dominate at low phase angles • Contribu=on to signal from mul=ple scaHering increases as the phase angle increases • Photons that have been mul=ple scaHered have traveled more within the ice • This results in greater absorp=on and thus shies the absorp=on edge towards longer wavelengths Incidence angle effect • For low solar eleva=on angles more mul=ple scaHering events occur • For high solar eleva=on angles fewer mul=ple scaHering events occur for the photon to exit Summary of retrieved parameters region Ab (long Ab (long wave, low El) wave, hi El) Ab (short g (long wave) wave, low El) G (long g (short L (y intercept) wave, hi wave) (microns) El) C3 0.045 0.050 0.010 -­‐0.74 -­‐0.74 -­‐0.81 2.4 B1 0.055 0.060 0.015 -­‐0.69 -­‐0.72 -­‐0.68 2.9 B2 0.080 0.090 0.020 -­‐0.68 -­‐0.68 -­‐0.65 2.8 B3 0.080 0.100 0.020 -­‐0.71 -­‐0.68 -­‐0.66 2.5 B4 0.080 0.105 0.018 -­‐0.72 -­‐0.69 -­‐0.72 2.7 CD2 0.050 0.055 0.010 -­‐0.71 -­‐0.73 -­‐0.74 2.4 A1 0.065 0.065 0.015 -­‐0.73 -­‐0.75 -­‐0.66 3.1 A2 0.060 0.075 0.015 -­‐0.74 -­‐0.71 -­‐0.68 2.6 A3 0.055 0.060 0.015 -­‐0.74 -­‐0.71 -­‐0.66 2.4 A4 0.055 0.065 0.015 -­‐0.69 -­‐0.66 -­‐0.63 2.3 Conclusions • I/F and albedo ra=os suggest that the outer B ring is the most pure water ice and the C ring and CD the most polluted • g values imply the rings are highly backscaHering in the FUV • L is posi=vely correlated with phase angle which is aHributed to mul=ple scaHering • Y intercept of L provides measure of twice the distance to first scaHering center, i.e., single scaHering L value • Single scaHering L is close to constant across the rings, sugges=ng outermost 1.5 microns of rings have same structural proper=es Future work • Try to find observa=ons for C1, C2, and CD1 regions, but can’t promise this • Knowing the albedo puts us in a beHer posi=on to inves=gate the composi=onal proper=es of the rings • Working on numerical ray tracing model that may help validate these analy=cal results Modified model I
= A*P*
F
x
B
*
µ
+
1
−
B
µ
[
]
( o
o)
4 ( µ + µo )
[1 − exp(−τ / µ) exp(−τ
n
n
/ µo )
]
B = 0.2 and x = 1.2
B = 0.2 and x = 1.2