Polarized Light Scattered from Asteroid Surfaces. Vi

47th Lunar and Planetary Science Conference (2016) 1068.pdf

POLARIZED LIGHT SCATTERED FROM ASTEROID SURFACES. VI. POLARIMETRIC AND PHOTOMETRIC INTERRELATIONS FROM MULTISPECTRAL DATA. D. I. Shestopalov, L. F. Golubeva, Shemakha Astrophysical Observatory, Shemakha AZ-3243 Azerbaijan, ([email protected], la- [email protected]).

Analysis of the polarimetric and photometric the lensing effect of relatively large semitransparent properties of asteroids in a visible spectral range is surface particles. usually restricted to the data obtained in the V band To calculate a spectral albedo A(Ȝ) we used the [e.g. 1, 2, 3, 4], since most of the data have been accu- mid-infrared asteroid survey [11] and the eight-color mulated by observations in this bandpass. It is clear the spectra of asteroids [12]. So that A(Ȝ) = AV × R(Ȝ), parameters of asteroid polarimetric and photometric where the visual geometric albedo AV and spectral re- functions vary depending on the wavelength of light flectance R(Ȝ) normalized to unity at the visual wave- diffusely reflected by an asteroid surface. However, the length were taken from [11] and [12], respectively. following question remains open: will correlations be- 2.5 U band Ȝ y = 48.87x - 0.221

tween asteroid polarimetric and photometric parameters c 2 R² = 0.992 be different at different wavelengths? To investigate B band

this topic we used the polarimetric and photometric 1.5 V band databases available now at PDS [5, 6]. These catalogs 1 R band contain the high-accuracy polarimetric and photometric I band measurements of asteroids in the UBVRI bandpasses 0.5 Fig. 3

against the phase angle, Į, at the time of observations. Photometric roughness [1] 0 0 0 0.01 0.02 0.03 0.04 0.05 0.06 U band -0.2 Phase coefficient b(Ȝ), mag/deg -0.4 B band

) 0.7

Ȝ -0.6 V band ( U band

A y = 1.004x 0.6 -0.8 Lg R band R² = 0.994 B band -1 0.5 I band V band -1.2 Fig. 1 0.4 2

[13] ı R band -1.4 0.3 -0.6 -0.4 -0.2 0 0.2 0.4 0.2 I band

Lg Pmin Ȝ 0.1 Fig. 4 0 0 00.20.40.60.8 -0.2 U band B band aOE -0.4 V band ) The interrelations between various optical charac- Ȝ

( -0.6 R band A teristics of asteroids are shown in Figs. 1 – 7. The data -0.8

Lg I band measured in the different bandpasses are marked by [14] -1 colors, whereas crossers and dashed lines denote inter- -1.2 Fig. 2 relations, which have been already known [1, 2, 13, 14] -1.4 owing to observations in the V band. On the plots, solid -2 -1.5 -1 -0.5 0 lines demonstrate the regression relationships calculat- Lg h(Ȝ) ed on the base of multispectral data. We calculated the attributes of asteroid negative Figures 1 and 2 demonstrate interdependences be- polarization branch (i.e., its depth P (Ȝ), at Į , and min min tween A(Ȝ) and P (Ȝ), h(Ȝ) parameters in logarithmic slope h(Ȝ) at Į ,) in the above bandpasses using the min inv coordinates. Despite the scatter of the points on these approximating formula introduced in [7]. In the case of plots, the linear correlations, found previously for the asteroid photometric functions observed in the same V-band data [13, 14], more or less specifies the multi- bandpasses, we used the empiric formula [8] to calcu- spectral data. However, there are no specific correla- late the amplitude of opposition effect a (Ȝ) and the OE tions between parameters in question for the low-, phase coefficient b(Ȝ). We also utilized the theoretic moderate-, and high-albedo asteroids. This, in particu- phase function [9, 10] to estimate certain physical char- lar, implies that the inverse ratio between spectral albe- acteristics of asteroid surfaces such as the surface pho- do A(Ȝ) and P (Ȝ), h(Ȝ) parameters may be absent for tometric roughness c(Ȝ) as well as the a(Ȝ) and ı2(Ȝ) min certain asteroids. parameters that were entered in practice [10] to specify 47th Lunar and Planetary Science Conference (2016) 1068.pdf

A very close correlation between phase coeffi- 0.8 cient b(Ȝ) and surface photometric roughness c(Ȝ) is U band

shown in Fig. 3. Moreover, the regression lines for 0.6 B band Ȝ multispectral data and those for the V band actually 2

ı V band coincide. The physical meaning of the phase coefficient 0.4 R band

becomes more transparent: in the visible spectral range, pattern 0.2 I band variations in the slope of the linear part of the asteroid Fig. 7 magnitude-phase dependences are caused by variations [2] Brightness variation of speckle 0 in the photometric roughness of asteroid surfaces. In 0 0.10.20.30.40.50.6

turn other parameter of the empiric photometric func- Geometric Albedo A(Ȝ) 2 tion [6], aOE(Ȝ), is closely related to ı (Ȝ) parameter. As follows from Fig.4 the amplitude of brightness op- Returning to the question raised above, we can position spike at different wavelength is induced by a argue in favor of the following statistical regularity. brightness contrast of a patchy pattern that could be Every one of the interrelations under study remains generated by surface semitransparent particles with statistically invariable with respect to different wave- different refractive index m(Ȝ) [10]. lengths in the visible spectral range. This may be a con- 2.5 sequence of the facts that (i) the V and B data predom-

) U band Ȝ

( y = -0.47ln(x) + 0.532 inant in Figs. 1 – 7, and (ii) all the multispectral data c 2 R² = 0.768 B band have approximately the same random spread relative to 1.5 the regression lines shown on these plots. V band We use the results obtained here to interpret the 1 R band multispectral polarimetric observations of asteroids (part VII, this volume). 0.5 I band Fig. 5

Photometric roughness References: 0 [1,2] [1] Shustarev P.N. et al. (2013) 44th LPS, 0 0.1 0.2 0.3 0.4 0.5 0.6 Abstract #1064. [2] Golubeva L.F. et al. (2013) 44th Geometric Albedo A(Ȝ) LPS, Abstract #1063. [3] Rosenbush V. et al. (2002) 2.50 Proc. of NATO Adv. Res. Workshop, 191–224. [4] y=0.40x2 + 0.1x |Pmin| Golubeva L.F. and Shestopalov D.I. (1983) Sov. 2.00 2

)|, % R =0.984

Ȝ Astron. 27, 351–357. [5] Lupishko D.F. and Vasilyev ( U band 1.50 S.V. (2012) NASA PDS, Asteroid Polarimetric Data- Pmin B band base V7.0. EAR-A-3-RDR-APD-POLARIMETRY- 1.00 V band V7.0. [6] Shevchenko V.G. et al. (2010) NASA PDS, 0.50 R band Fig. 6 Kharkiv Asteroid Magnitude-Phase Relations V1.0. Polarization | [2] EAR-A-COMPIL-3-MAGPHASE-V1.0. [7] Shesto- 0.00 0 0.5 1 1.5 2 2.5 palov D. (2004) JQSRT 88, 351–356. [8] Shevchenko Photometric roughness c(Ȝ) V.G. (1996) LPS XXVII, 1193–1194. [9] Akimov L. A. (1982) Vestn. Kharkov Univ. 232, 12–22. [10] Shku- Interrelations between the surface photometric ratov Yu. G. (1983) Sov. Aston. 27, 581– 583. [11] roughness c(Ȝ) on the one hand and A(Ȝ), Pmin(Ȝ) pa- Usui F. et al. (2011) Publ. Astron. Soc. Jpn. 63, 1117– rameters on the other hand are presented in Figs. 5 and 1138. [12] Zellner B. et al. (1985) Icarus 61, 355–416. 6. The roughness c(Ȝ) stands in closer relation to [13] Lupishko D.F. and Mohamed R.A. (1996) Icarus Pmin(Ȝ) than to A(Ȝ). For the present, we cannot explain 119, 209–213. [14] Shestopalov D.I. and Golubeva why this occurs. As before, regression lines obtained L.F. (2015) Adv. Space. Res. 56, 2254–2274. for multispectral data prove to be close to those ob- Acknowledgements: The asteroid observation tained only for the V band (shown by the crossers). data utilized in our work were taken from databases )LJXUHVKRZVWKHXQXVXDOŀ-like dependence of avalible now at NASA PDS. ı2(Ȝ) parameter on albedo A(Ȝ). We have become ac- customed to the fact that dependences between multispectral parameters and those obtained in the V band are similar, and the last case is no exception. This implies that the interpretation of this dependence found previously in [2] for the parameters at the visual wavelength are also valid for the given set of these multispectral characteristics.