1. 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

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

3. 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)

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

5. 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.

6. 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

7. Models for Cometary Dust Particles
sparse agglomerate
agglomerated debris
pocked spheres
ρ = 0.169
ρ = 0.236
ρ = 0.336

8. 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=2r/ (r – radius of circumscribing sphere and  – wavelength) is varied from 1 throughout 26 – 40 (depending on m).

9. 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: 1.5a3.4 (Mazets et al., 1986)

10. Application to whole Comet C/1996 B2 (Hyakutake)

11. Application to whole Comet C/1996 B2 (Hyakutake)

12. 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

13. Application to innermost coma in 26P/Grigg-Skjellerup
McBride et al., MNRAS 289, (1997)

14. Application to innermost coma in 26P/Grigg-Skjellerup

15. 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

16. 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.