1999-2004 Astronomical Institute of Kharkov University. Department
of Solar, Lunar and Planetary Physics
> Polarization > Model
Model for the Polarimetric and Photometric Characteristics of the
Moon at Moderate Phase Angles Based on Realistic Assumptions on
Yu. I. Velikodsky, V. V. Korokhin,
and L. A. Akimov
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There are known two potential mechanisms for explaining
positive polarization that is observed for atmosphereless celestial
bodies at large phase angles. The first one, Fresnel's reflection,
may take place due to existing of large (in comparison with wavelength)
smooth surfaces in regolith (glasses). The second one, Rayleigh's
scattering, supposes the presence of particles with sizes smaller
than wavelength, i.e. with submicron sizes. It is known that typical
size of regolith particles is about tens of micrometers. The particles
are mainly aggregates of smaller grains of micron- submicron sizes.
Such particles cannot produce a pure Rayleigh polarization. On the
other hand, Fresnel's reflection yields too large phase angles of
the positive polarization maximum and cannot explain this effect
Taking into account that the principal contribution
to scattering (and, hence, to positive polarization) may produce
small particles with subwavelength sizes we propose a combinative
heuristic model using the Rayleigh-Gans approximation, Fresnel's
reflection on large surfaces, shadow-hiding effect, and multiple
scattering on micro- and macro-scales. The model shows a good agreement
with observational data for the Moon for both brightness and polarization
degree phase dependences (Figs. 5 and 6) with the same set of parameters.
Also the model explains Umov's law and decreasing of the phase angle
of polarization maximum with albedo increasing, which is observed
for the Moon and asteroids.
Phase dependence of brightness was approximated at
moderate phase angles (Fig. 6), where a good approximation with
exponential function exists (Akimov, 1988). At large phase angles
the model yields higher values of brightness than the exponent.
It is known that phase dependence at large phase angles differs
from Akimov's exponent, and our model can explain this difference.
To check this we plan to study phase dependence at large phase angles
by absolute observations and investigation of mare-highlands contrast.