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

Polarimetry of Comets

Circumstances of polarimetric observations

Dependence of polarization in comets on

phase angle

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

Shkuratov & Opanasenko, Icarus 99, 468-484 (1992)

Umov Effect

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.

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

sparse agglomerate

agglomerated debris

pocked spheres

Models for Cometary Dust Particlesρ = 0.169

ρ = 0.236

ρ = 0.336

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).

(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

Application to whole Comet C/1996 B2 (Hyakutake)

Application to whole Comet C/1996 B2 (Hyakutake)

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

Application to innermost coma in 26P/Grigg-Skjellerup

McBride et al., MNRAS 289, 535-553 (1997)

Application to innermost coma in 26P/Grigg-Skjellerup

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

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