© 1999-2004 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, e-mail: 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. Mean-square deviation (in P %) of observed data from approximation curve (1) for l_eff = 461 nm

Fig.6. Mean-square 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 FITS-files. 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, 3-10 (1988) [in Russian].

A. Dollfus, and E. Bowell, Polarimetric properties of the lunar surface and its interpretation. I. Telescope observations, Astron. Astrophys. 10, 29-52 (1971).

V. V. Korokhin, S.A. Beletsky, Yu. I. Velikodsky, V.V. Konichek and I.E. Sinelnikov, The experience of CCD-photometry using on KHAO, Kinematika i Fizika Nebesnykh Tel 16, 80-86 (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, 468-484 (1992).

2003/09/19