umov effect for single-scattering agglomerate particles e. zubko, 1,2 g. videen, 3 yu. shkuratov, 2...
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Umov effect for single-scattering agglomerate particles
E. Zubko,1,2 G. Videen,3 Yu. Shkuratov,2
K. Muinonen,1,4 and T. Yamamoto5
May 8, 2012
1 Department of Physics, University of Helsinki, Finland2 Institute of Astronomy, Kharkov National University, Ukraine3 Army Research Laboratory AMSRL-CI-EM, USA4 Finnish Geodetic Institute, Finland5 Institute of Low Temperature Science, Hokkaido University, Japan
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Polarimetry of Comets
Circumstances of polarimetric observations
Dependence of polarization in comets on
phase angle
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The brighter powder, the lower its linear polarization
N. Umov (1846-1915)
N. Umov, Phys. Zeits. 6, 674-676 (1905)
In 1960-1970, the qualitative law was quantified:
log(Pmax) linearly depends on log(A)
Origin of the phenomenon – depolarization due to multiple scattering in regolith
Umov Effect
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Shkuratov & Opanasenko, Icarus 99, 468-484 (1992)
Umov Effect
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Geometric albedo A for single particles:
A=(S11(0))/(k2G)
Here, S11(0) is the Mueller matrix element at back-scattering, k – wavenumber, and G – the geometric cross-section of the particle.
Umov Effect for Single-Scattering ParticlesAs was found in Zubko et al. (2011, Icarus, 212,
403– 415), the Umov effect holds also for single-scattering particles with size comparable to wavelength. Therefore, it can be applied to comets.
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Basic idea:
Gains: (1) arbitrary shape and internal structure (2) simplicity in preparation of sample
particles
Method: Discrete Dipole Approximation (DDA)
Numerical Simulation of Light Scattering
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sparse agglomerate
agglomerated debris
pocked spheres
Models for Cometary Dust Particlesρ = 0.169
ρ = 0.236
ρ = 0.336
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We study 21 (!) various refractive indices m:
Input Parameters for Simulation
1.2+0i 1.2+0.015i 1.313+0i 1.313+0.1i
1.4+0i 1.4+0.0175i 1.4+0.02i 1.4+0.05i 1.4+0.1i
1.5+0i 1.5+0.02i 1.5+0.05i 1.5+0.1i
1.6+0.0005i 1.6+0.02i 1.6+0.05i 1.6+0.1i 1.6+0.15i
1.7+0i 1.7+0.1i 1.855+0.45i
Size parameter x=2r/ (r – radius of circumscribing sphere and – wavelength) is varied from 1 throughout 26 – 40 (depending on m).
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(1) Over particle shapes:
For each pair of x and m, we consider minimum 500 particle shapes.
(2) Over particle size:
Size distribution is considered to be a power law r–a
. The power index a is varied from 1 to 4.
Note: this range is well consistent with in situ study of Comet 1P/Halley: 1.5a3.4 (Mazets et al., 1986)
Averaging of light-scattering characteristics
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Application to whole Comet C/1996 B2 (Hyakutake)
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Application to whole Comet C/1996 B2 (Hyakutake)
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Application to whole Comet C/1996 B2 (Hyakutake)
mm aa AA mm aa AA
1.2+01.2+0ii – – 1.5+0.051.5+0.05ii 2.22.2 0.0360.036
1.2+0.0151.2+0.015ii – – 1.5+0.11.5+0.1ii – –1.313+01.313+0ii 2.22.2 0.060.06
331.6+0.00051.6+0.0005ii 3.43.4 0.0790.079
1.313+0.11.313+0.1ii – – 1.6+0.021.6+0.02ii 3.13.1 0.0670.067
1.4+01.4+0ii 2.92.9 0.060.0666
1.6+0.051.6+0.05ii 2.62.6 0.0480.048
1.4+0.01751.4+0.0175ii 2.42.4 0.040.0466
1.6+0.11.6+0.1ii – –
1.4+0.021.4+0.02ii 2.32.3 0.040.0444
1.6+0.151.6+0.15ii – –
1.4+0.051.4+0.05ii 1.01.0 0.020.0211
1.7+01.7+0ii 3.63.6 0.0810.081
1.4+0.11.4+0.1ii – – 1.7+0.11.7+0.1ii 1.81.8 0.0340.034
1.5+01.5+0ii 3.23.2 0.070.0700
1.855+0.451.855+0.45ii – –
1.5+0.021.5+0.02ii 2.92.9 0.050.0544
Whole Whole comets comets
0.0500.050
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Application to innermost coma in 26P/Grigg-Skjellerup
McBride et al., MNRAS 289, 535-553 (1997)
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Application to innermost coma in 26P/Grigg-Skjellerup
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mm aa AA mm aa AA
1.2+01.2+0ii – – 1.5+0.051.5+0.05ii – –1.2+0.0151.2+0.015ii – – 1.5+0.11.5+0.1ii – –1.313+01.313+0ii – – 1.6+0.00051.6+0.0005ii 2.12.1 0.2240.224
1.313+0.11.313+0.1ii – – 1.6+0.021.6+0.02ii 1.21.2 0.1140.114
1.4+01.4+0ii – – 1.6+0.051.6+0.05ii – –1.4+0.01751.4+0.0175ii – – 1.6+0.11.6+0.1ii – –1.4+0.021.4+0.02ii – – 1.6+0.151.6+0.15ii – –1.4+0.051.4+0.05ii – – 1.7+01.7+0ii 2.42.4 0.2380.238
1.4+0.11.4+0.1ii – – 1.7+0.11.7+0.1ii – –1.5+01.5+0ii 1.11.1 0.210.21
661.855+0.451.855+0.45ii – –
1.5+0.021.5+0.02ii – – Inner coma Inner coma 0.2310.231
Application to innermost coma in 26P/Grigg-Skjellerup
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Using the Umov effect, one can estimate albedo of single-scattering dust particles.
When this technique is applied to whole Comet C/1996 B2 (Hyakutake), it yields the geometric albedo in the range A=0.034–0.079, that is well consistent with the expected value of A=0.05.
For the innermost coma studied by Giotto in 26P/Grigg-Skjellerup, the Umov effect reveals dramatically higher geometric albedo A=0.23.
Summary