©
19992004 Astronomical Institute of Kharkov University. Department
of Solar, Lunar and Planetary Physics
DSLPP
> Moon
> Polarization > Mapping
Mapping
the Parameters of Maximum of Positive Polarization of the Moon
V.
V. Korokhin, and Yu. I. Velikodsky
Astronomical
Institute of Kharkov University, 35, Sumskaya Str.,
Kharkov 61022, Ukraine, email: dslpp@astron.kharkov.ua
The
surface of the Moon is a good sample of athmosphereless
cosmic bodies’ surface. Due to the facts that albedo of the Moon
varies in wide range and the lunar surface is available for observations
from the Earth in practically full range of phase angles it is possible
to study different dependences of optical parameters. For example,
degree of positive polarization (and maximum of positive polarization
P_{max} in particular) – albedo dependence is studied well.
But the distribution of phase angle a_{max} of P_{max} over the lunar disk and correlation
with other optical parameters are not practically investigated.
Observations
and data processing
Therefore
the maps of maximum of positive linear polarization degree
P_{max} and of
its phase angle a_{max} have been constructed for the eastern
hemisphere of the Moon, based on a set of polarimetric observations
of lunar. The observations were carried out at Kharkov Observatory
in 2 wavelengths l_{eff}=461
nm (Dl=106.4 nm) and l_{eff}=669
nm (Dl=125.0 nm) with an imaging CCD–polarimeter (Korokhin
et al, 2000) and a camera lens of 3 cm diameter, and 30 cm focal
length.
For
curve of phase dependence of polarization approximation the modified
Rayleigh’s function has been used:
_{},
(1)
where _{} is a maximum shift parameter,
W is a maximum width parameter, dePol
is a depolarization parameter.
Behavior
of this function and approximation examples for some lunar regions
are shown on fig.1 and 2.
Fig.1. Behavior of approximation function
Fig.2.
Approximation examples
for some lunar regions
The
results of the approximation are represented on fig.3 and 4. The
solutions for them are obtained using observations at 10 different
phase angles from 45° to 123° with fixed values of W parameter (W=0.75
for l_{eff}_{
}= 461 nm and W=0.88 l_{eff}_{
}= 669 nm). Those values of W have been calculated as means
from previous solution with W variation.
Errors
of approximation are shown on fig.4 and 5
Fig.3. Solution for
l_{eff}_{ }= 461 nm
(W=0.75)
Fig.4. Solution for
l_{eff}_{ }= 669 nm
(W=0.88)
Fig.5.
Meansquare deviation (in P %) of observed data from approximation
curve (1) for l_{eff}_{ }= 461 nm
Fig.6.
Meansquare deviation (in P %) of observed data from approximation
curve (1) for l_{eff}_{ }= 669 nm
The
P_{max }and a_{max}
maps are represented in the external perspective projection (distance=221.1739
of R_{Moon}, image radius=225
pix) and are accessible at as FITSfiles. A pixel size is equal
to about 8 km on lunar surface.
Data processing was
fully carried out using our "IRIS" software complex (http://www.cyteg.com).
Histograms
of P_{max} and a_{max} distribution
A
histogram of P_{max} distribution (fig.7) over the lunar
disk has distinct maximum, – P_{max}=7.3% for l_{eff}=461
nm and P_{max}=5.25% for l_{eff}=669
nm, – corresponding to highlands. Distribution of P_{max}
for mares is more diffuse. The range of P_{max} variations
is 4.0..21.0% for l_{eff}=461
nm and 3.0..15.0% for l_{eff}=669
nm.
Fig.7. Histogram
of P_{max} distribution (l_{eff}_{ }= 461 nm
 up, l_{eff}_{ }= 669 nm
 down)
A
histogram of a_{max}_{
} distribution (fig.8) is distinctly bimodal, with the
first peak at a=99.7° (highlands), and the second one at a=104.1° (mares) for l_{eff}=461
nm. For l_{eff}=669
nm we have a=96.8° and a=101.2°, respectively. The histogram is in
a whole more narrow in blue light, – 94.0°..106.0°,  as compared to red (90.0°..105.0°). As a rule, the maximum of polarization occurs
at larger phase angles in the blue band.
Fig.8. Histogram
of a_{max}
distribution (l_{eff}_{ }= 461 nm
 up, l_{eff}_{ }= 669 nm
 down)
Correlation
diagrams a_{max}  albedo
and a_{max}  P_{max}
Correlation diagrams a_{max} (in degrees) versus equigonal albedo
(Akimov, 1998) r(a=8.4°) were plotted (fig.9), having given
a_{max}= (141.91±0.03) r + 110.45±0.42 for l_{eff} =461 nm, and a_{max}=(110.14±0.03) r +108.58±0.31 for l_{eff} =669 nm. Correlation coefficient is
equal 0.893 for l_{eff}
=461 nm and 0.877 for l_{eff} =669 nm, i.e., a significant linear anticorrelation is observed.
Fig.9.
Correlation
diagrams a_{max} (in degrees) versus equigonal
albedo r(a=8.4°)
Also
correlation diagrams a_{max} (in degrees)
versus P_{max} were plotted (fig.10). Dolfus
and Bowell (1971) and Kvaratzkhelia
(1988) have constructed a_{max}  P_{max}
diagram before us. But they supposed linear relationship between
these parameters. Our data shows sharply nonlinear dependence.
Fig.12. Correlation diagrams a_{max} (in degrees) versus P_{max}
(%)
And
finally we have construct correlation diagrams max versus log(P_{max})
(fig.13). This relationship shows light nonlinearity also, but we
can make note of practically identity of linear regression for both
spectral diapasons: a_{max}=
(13.6±0.04) log(P_{max})
+ 114.83±0.04
for eff =461 l_{eff},
and a_{max}
= (14.25±0.04) log(P_{max})
+ 115.21±0.04
for l_{eff}
=669 nm.
Fig.13. Correlation diagrams a_{max} (in degrees) versus log(P_{max})
The
analysis of these data, especially combined with other optical parameters,
is helpful in obtaining more information about the fine structure
of the regolith of athmosphereless cosmic bodies (Shkuratov,
Opanasenko, 1992).
References
L. A. Akimov, Light reflection by the
Moon, Kinematika i
Fizika Nebesnykh Tel 4, 310
(1988) [in Russian].
A.
Dollfus, and E. Bowell, Polarimetric properties of the lunar surface and its interpretation. I.
Telescope observations, Astron. Astrophys.
10, 2952 (1971).
V.
V. Korokhin, S.A. Beletsky, Yu. I. Velikodsky, V.V. Konichek and I.E. Sinelnikov, The experience of CCDphotometry using on KHAO, Kinematika
i Fizika Nebesnykh Tel 16, 8086 (2000) [in Russian].
O.
I. Kvaratzkhelia,
Spectropolarimetry The
experience of lunar surface and its ground samples, Bull. Abastumani
Astrophys. Obs. B4,
312 (1988) [in Russian].
Yu. G. Shkuratov,
and N. V. Opanasenko,
Polarimetric and Photometric Properties of the Moon: Telescope Observation
and Laboratory Simulation. 2. The Positive Polarization, Icarus
99, 468484 (1992).
2003/09/19
