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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 1 Department of Physics, University of Helsinki, Finland 2 Institute of Astronomy, Kharkov National University, Ukraine 3 Army Research Laboratory AMSRL-CI-EM, USA 4 Finnish Geodetic Institute, Finland 5 Institute of Low Temperature Science, Hokkaido University, Japan May 8, 2012

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Polarimetry of Comets Dependence of polarization in comets on phase angle Circumstances of polarimetric observations

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**log(Pmax) linearly depends on log(A)**

Umov Effect The brighter powder, the lower its linear polarization N. Umov, Phys. Zeits. 6, (1905) Origin of the phenomenon – depolarization due to multiple scattering in regolith N. Umov ( ) In , the qualitative law was quantified: log(Pmax) linearly depends on log(A)

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Umov Effect Shkuratov & Opanasenko, Icarus 99, (1992)

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**Umov Effect for Single-Scattering Particles**

As 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. 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.

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**Numerical Simulation of Light Scattering**

Method: Discrete Dipole Approximation (DDA) Basic idea: Gains: (1) arbitrary shape and internal structure (2) simplicity in preparation of sample particles

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**Models for Cometary Dust Particles**

sparse agglomerate agglomerated debris pocked spheres ρ = 0.169 ρ = 0.236 ρ = 0.336

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**Input Parameters for Simulation**

We study 21 (!) various refractive indices m: 1.2+0i i i i 1.4+0i i i i i 1.5+0i i i i i i i i i 1.7+0i i i 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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**Averaging of light-scattering characteristics**

(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)

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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)**

– i 2.2 0.036 i i i 0.063 i 3.4 0.079 i i 3.1 0.067 1.4+0i 2.9 0.066 i 2.6 0.048 i 2.4 0.046 i i 2.3 0.044 i i 1.0 0.021 1.7+0i 3.6 0.081 i i 1.8 0.034 1.5+0i 3.2 0.070 i i 0.054 Whole comets 0.050

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**Application to innermost coma in 26P/Grigg-Skjellerup**

McBride et al., MNRAS 289, (1997)

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**Application to innermost coma in 26P/Grigg-Skjellerup**

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**Application to innermost coma in 26P/Grigg-Skjellerup –**

2.1 0.224 i i 1.2 0.114 1.4+0i i i i i i i 1.7+0i 2.4 0.238 i i 1.5+0i 1.1 0.216 i i Inner coma 0.231

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Summary 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.

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