A&A 408, 379-385 (2003)
F. A. Tupieva
Institute of Astrophysics, Tajik Academy of Sciences, and Isaac Newton Institute of Chile, Tajikistan Branch, Bukhoro Str. 22, Dushanbe 734042, Tajikistan
Received 10 June 2002 / Accepted 30 April 2003
The color curves of Nysa connected to the rotation and phase angle were obtained from observations for the first time in 1982. The color curves showed the U-B change with rotation. The value of this change was 0.2 mag. Color variation indicates that the extended color spot is on the surface of 44 Nysa. The U-B color index decreases with the increase of the phase angle (the phase coefficient is 0.011 mag/deg). This decrease is stronger for the surface with color spots. Phase functions of the brightness for opposite sides of Nysa are different. The value of the opposition effect of 44 Nysa decreases as reflectance decreases.
Key words: minor planets, asteroids - star system: general - techniques: photometric
Beginning in 1949, when the first electrophotometric measurements of the brightness of Nysa were obtained, this asteroid has been observed photometrically during more then ten oppositions. Individual measurements of U-B and B-V color indices of Nysa are given by Groeneveld & Kuiper (1954), Zappala & van Houten-Groeneveld (1979), Piironen (1982), Taylor & Tedesco (1983). However, data of color variations during a rotational cycle and dependence of color on the phase angle have not been obtained. Phase color curves are useful for the interpretation of the opposition effect (Helfenstein et al. 1997) and color variations with rotation for the definition of Nysa's surface homogeneity.
In this paper, phase color curves and color variation of 44 Nysa, obtained with UBV broadband photometry, are discussed.
In July-August 1982 the photoelectric measurements of the brightness of 44 Nysa were carried out with the 70-cm reflector of the Gissar Observatory of Tajikistan at UBV standard spectral bands. Conditions of observation of the asteroid were difficult: the airmass of the asteroid was close to 2, the observations were made at full Moon and there were nights affected by the presence of dust in the Earth's atmosphere. Therefore, comparison stars were selected close to the asteroid position and they were often compared with photometric standards and among themselves. Observations were carried out with the help of a photometer, working in the regime of the count of photons. Counting time of the signal was 30 s. 2 to 4 measurements of the asteroid's brightness were made between two measurements of a star's brightness. The stability of operation of the photometer was controlled by the sample, the brightness of which was measured for 40 min on average. The accuracy of single measurement of the asteroid's brightness was of in the V band, in B-V and in U-B.
The data of comparison stars are given in Table 1.
Table 1: The data of comparison stars.
Table 2: The aspect data for Nysa in 1982.
Table 3: Brightness and colors of 44 Nysa in 1982.
Their coordinates were determined by the Stellar atlas of Vehrenberg (1970). Their brightness and color indices were determined by comparison with photometric standards IC 4275 ( , ) and SA112 ( , , ) (Kazanasmas et al. 1981; Moffett & Barnes 1979).
Table 2 summarises the aspect data for Nysa in the opposition of 1982. The date and universal time of the middle observation (UT) corrected for light-time are given in the first column. The equatorial (, ) and ecliptic (, ) coordinates of the asteroid at 2000.0, the heliocentric (r) and geocentric () distances and the solar phase angle ( ) are given in the following columns.
Table 3 lists the V magnitudes and color indices
(B-V and U-B) derived for Nysa with the standard UBV system for the individual measurements of brightness of the
asteroid. The first column lists
universal time corrected for light time. The final column
lists the comparison stars used (see Table 1).
|Figure 1: Composite lightcurves of 44 Nysa: upper - for the interval of phase angles from to ( - , - , - , - , - , - ); lower - from to ( - , - , - , - ).|
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|Figure 2: Composite color curves of 44 Nysa. For B-V on the upper color curve: - , - , - , -, - , - , - ; on the lower color curve: - , - , - , - . The U-B data from each different night are not distinguished by different plot symbols. Phases of rotation of U-B data correspond to the ones of B-V data.|
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Table 4: The photometric data for 44 Nysa in 1982.
The identification of the extrema of the lightcurves in Fig. 1 corresponds to the definition of Birch et al. (1983). M1 is the maximum that precedes the flat-bottom minimum. There is a notch in the right side of this minimum, which clearly appears on the lightcurves in the opposition of 1979. The amplitude of the obtained lightcurves is 0.22 mag; levels of maxima of the lower lightcurve differ by and that of the upper lightcurve by In Fig. 1 the positions of the maxima of these lightcurves are shifted from each other.
The composite U-B and B-V curves are given in Fig. 2. They were received as lightcurves of Fig. 1, but only for the mean values of color indices in U-B and B-V. The mean values of the color indices were calculated as four-point or two-point floating averages of individual color indices from Table 3. In Fig. 2, vertical lines show the errors of the U-B mean values. The errors of the B-V mean values do not exceed
Figure 2 shows the considerable color change over the surface of Nysa in U-B and the faint change in B-V. For the interval phase angles from to the U-B change (the upper curve in Fig. 2) is different to that for the interval from to (the lower curve).
The U-B change is seen for the long interval of rotation phase, including the regions of the secondary maximum and both minima of the lightcurve. The amplitude of the change in U-B is At the region of the secondary maximum of the lightcurve (M2), Nysa is more red than at M1, and at the minima Nysa is more blue.
In 1982, observations of the asteroid 44 Nysa covered the
interval of the solar phase angles from
the aspect angle (the angle between the rotation axes and
the line of sight) was changing slightly, not more than
The photometric data for 44 Nysa are given in Table 4, where V(M1) and V(0.25) denote the asteroid's
brightness reduced to the primary maximum and to the
rotation phase f=0.25 of the lightcurves in Fig. 1. These
magnitudes were corrected for unit distances r and .
are the values of mean
color indices during the night. U-B(M1) and U-B(0.25)
are the reduced color V(M1) and V(0.25) values.
|Figure 3: Phase functions of brightness and colors of Nysa.|
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The phase functions of brightness and color were determined by the data of Table 4. These functions are given in Fig. 3. Figures 3a, b show the reduced brightness V(M1) and V(0.25) as a function of the phase angle (). Figures 3c, d show the average colors for each night and as a function of . In Figs. 3e, g are given the phase functions of the reduced color U-B(M1) and U-B(0.25).
It is seen from Figs. 3a, b that both functions show a nonlinear increase of the brightness of the asteroid at small phase angles, i.e. an opposition effect. This effect is larger and wider for the phase function which was obtained for V(0.25). Near phase f=0.25 Nysa is more blue and less bright than it is at the primary maximum (see Figs. 1 and 2). For the phase coefficient (), which determines the linear change of the brightness of the asteroid with phase angle, was calculated for this functions and it is 0.026 mag/deg for V(M1) values and 0.018 mag/deg for V(0.25).
The mean color indices do not change with phase angle (Fig. 3c), while decrease with the increase of (Fig. 3d). The scatter of the points in Fig. 3d was caused by the change of the color U-B with the rotation phase (Fig. 2). After color U-B was reduced to the certain rotation phase this scatter of the points was removed (Figs. 3e, g). In Figs. 3e, g the non-linear change of the U-B color is present for and the linear decrease of the color with the increase in phase angle is present for . For the U-B(M1) values phase coefficient is 0.002 mag/deg (Fig. 3e) and 0.011 mag/deg for the U-B(0.25) (Fig. 3g).
The obtained U-B color change with rotation covers almost of the surface of Nysa and has the value of 0.2 mag. Nysa is more blue at the minima of its lightcurve than at the secondary maximum (M2), and it is bluer at the primary minimum (m1) than at the secondary minimum (m2). The secondary maximum (M2) is slightly redder than the primary maximum (M1). The extended color variation over the surface of Nysa can be caused by the difference in composition or by the difference in surface texture.
In 1977, Nysa was investigated polarimetrically, in order to find an albedo change with rotation (Degewij et al. 1979), but the result was negative. Unfortunately, in 1977 observations were done in other ways than in 1982. In 1977, Nysa's south surface (32 to the south of the equator) and in 1982 its northern surface (30 to the north of the equator) were observed.
Table 5: Aspect and color index of 44 Nysa.
Note that all other observations of Nysa were done either on the equatorial or the south surface. Only in two oppositions (1982 and 1986) the aspect of the observation was 60. Pole coordinates of Nysa are taken from Magnussion (1986). Aspect data and color indices for 44 Nysa are summarized in Table 5.
Color indices obtained up to 1982 are smaller than our results. Excluding the possible systematic error of our color indexes, this difference can be explained by the different color of Nysa's two hemispheres. This is possible if Nysa originated from a differentiated parent body, and if there are regions containing different matter on its surface. For example, this effect was observed for the asteroid 15 Eunomia (Reed et al. 1997), which is member of the Eunomia family, like 44 Nysa.
Further interesting results are connected to the phase functions of the brightness and color, which were obtained for different sides of Nysa, namely for the region of the primary maximum (M1) and for the opposite region, which corresponds to the rotation phase 0.25. Phase functions of the brightness (Figs. 3a, b) have different phase coefficients () and different values of the opposition effect. Possibly, this is connected to the extended color spot on Nysa's surface. Most of the asteroids for which phase color functions were obtained showed a reddening with phase. Nysa showed an unusual decrease of the U-B color with phase, which differs for the two regions.
Mishchenko & Dlugach (1993) interpreted Nysa's opposition effect in the V band (Harris et al. 1989) by the coherent backscattering of the light. If coherent backscattering of the light dominates the reflections, then the value of the opposition effect is expected to increase as reflectance increases (Nelson et al. 1998). Nysa shows a strong linear decrease of U-B with increase of the phase angle ( mag/deg) for the surface where the color spot is present (f=0.25) and the observed value of the opposition effect in the U band is smaller than that in B and V bands. Thus, my results confirm that coherent backscattering of the light is the cause of the opposition effect of Nysa.
The opposite side of Nysa (f=0.8) gives a nonlinear change of U-B for small phase angles and a slight linear decrease for . The opposition effect was not observed in the U band.
The color curves connected with the rotation and phase angle were obtained from observations of Nysa in 1982. The color curves show the U-B change with rotation and the value of this change was 0.2 mag. These color variations may be connected to the extended color spot on the surface of 44 Nysa.
The U-B color index decreases with the increase in phase angle. A strange U-B decrease is observed for the surface with the color spot.
Phase functions of the brightness, which were obtained for opposite sides of Nysa, differ from each other.
The value of the opposition effect of 44 Nysa decreases as reflectance decreases.
I thank Dr. A. W. Harris for the critical comments and suggestions which improved the paper and Dr. P. B. Babadzhanov for assistance and many helpful discussions.