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Astron. Astrophys. 327, 145-154 (1997)

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3. Results

Before starting the analysis of the observational data we should take into account that RR Tau is associated with a weak S-shaped reflecting nebulosity (Herbig 1960). In this connection it is important to estimate what the influence of the nebulosity is on the background radiation. Moreover, the radiation of such nebulae is usually polarized and contributes in some cases appreciably to the intrinsic polarization of young stars (Vrba et al. 1979). To estimate the possible influence of the associated nebulosity we have observed RR Tau during moonless nights through two diaphragms: 10arc sec and 20arc sec. A comparison of these polarimetric measurements shows that they agree within the observational errors. We have estimated that the maximum of the background radiation through the 20arc sec diaphragm is [FORMULA] at the V pass-band. This means that the background radiation is negligible compared to the stellar flux over the whole range of the brightness variations of RR Tau and can, therefore, be neglected both in the polarimetric and photometric measurements.

3.1. The photometric activity of RR Tau

The UBVRI histograms presented in Fig. 1 give a general notion of the photometric activity of RR Tau. They are based on the following data: 46 UBV points by Zajtseva & Lyuty (1979), 45 UBVR points by Shaimieva & Shutiomova (1985), 17 UBVR points by Kardopolov & Rspaev (1989), 372 UBVR points from Herbst et al.'s (1994) catalogue and 80 UBVRI + 36 UBVR points from Tables 1 and 2 of the present paper. Each point corresponds to one observation per night. In those cases when a few measurements were made during one night we have used the average value of the stellar magnitudes. The general asymmetry of the RR Tau activity histograms is typical for stars with non-periodic Algol-type minima (Parenago 1954).

[FIGURE] Fig. 1. Normalized histograms of the photometric activity of RR Tau in the UBVRI pass-bands based on published data and data of the present paper. See text for details.

In Fig. 2 we show the variations of the RR Tau stellar magnitudes, the degree and position angle of the linear polarization in the V pass-band based on data of the present paper. One can see from this figure that the observations at CAO and at Dodaira complement each other well. A comparison of photometric data obtained at the same nights at CAO and Dodaira shows no significant differences. As we have noted above RR Tau has a very large amplitude of variability: [FORMULA]. Sometimes its magnitude changed rather rapidly from night to night. The maximum rate of brightness variability was registered on J.D. 8948/8949 to be [FORMULA] per day at the V pass-band (here and below the initial part (244) of the Julian date is omitted).

[FIGURE] Fig. 2. Variations of the RR Tau stellar magnitude, the degree and position angle of the linear polarization at the V pass-band based on data of the present paper. Circles represent Crimean data, and squares those obtained at Dodaira.

During the observations we have registered when the star is both at its brightest and at its faintest states. The brightest states were observed on J.D. = 9224.5, 9225.6 and 9245.5 (Fig. 2). These three points are well above the values observed at any other given time (Fig. 1) and suggest the occurance of flares. The amplitude of the variation with respect to the "normal bright state (V=10.m86)" is the same in the two epochs:

J.D. = 9225: [FORMULA] = 1.37, [FORMULA] = 0.82, [FORMULA] = 0.67, [FORMULA] = 0.59, [FORMULA] = 0.44

J.D. = 9245: [FORMULA] = 1.35, [FORMULA] = 0.87, [FORMULA] = 0.71, [FORMULA] = 0.60, [FORMULA] = 0.44

The flare-like events at the light curve of RR Tau can also be seen in Fig. 1 of the paper by Zajtseva & Lyuty (1979). However, Goransky (1995) whose data were used in that light curve did not confirm the reality of that "flare". Analysis of the AAVSO long-term (from 1926 to 1958) observations collected by Mayer (1982) shows that such "flares" are very rare events, and have been observed only few times in all previous observations of RR Tau.

The deepest minimum of brightness of RR Tau (V = 14.m2) has been observed at J.D. = 9372.24 at the Dodaira Observatory. The accuracy of the measurements at that night was quite low due to poor seeing conditions (the star was observed at a zenith angle of about [FORMULA]): about [FORMULA] in V and about [FORMULA], [FORMULA] and [FORMULA] in the colours [FORMULA] and [FORMULA], respectively.

The colour-magnitude diagrams of RR Tau are given in Fig. 3. They demonstrate the complex behaviour of the colour-indices [FORMULA] and [FORMULA] with the changes of brightness. These are similar to those observed by Rössiger & Wenzel (1974), Zajtseva (1986) and Kardopolov & Rspaev (1989): the initial reddening of the star stops at some brightness level and the star becomes bluer again with further decrease of the visual flux. This "blueing effect" is one of the most interesting photometric properties of many UXORs. It is caused by the scattered radiation due to CS dust, which dominates in the blue region of the spectrum at the times of deep minima (Grinin 1986). If this radiation arises in a large CS volume 4 it has to be constant and will determine a natural limitation to the amplitudes of Algol-type minima.

[FIGURE] Fig. 3. The RR Tau colour-magnitude diagrams based on data in Tables 1 and 2. The meaning of the symbols is the same as in Fig. 2. The model fits are shown by solid (model 1) and dashed (model 2) lines (see text for more details).

Using the upper (rectilinear) parts of the colour-magnitude diagrams we have estimated from the reddening of RR Tau the extinction law in the CS dust clouds revolving around this star: [FORMULA] = 4.4. This value is larger than the mean value of the interstellar (IS) reddening (R = 3.0 - 3.2), which indicates that the grain sizes in the CS clouds are larger compared to those in the IS matter (see also Sect. 4).

3.2. The polarimetric activity of RR Tau

The brightness variations of RR Tau at all UBVRI pass-bands were accompanied by significant changes of the polarization parameters. The anti-correlation between the degree of linear polarization and the stellar brightness is clearly seen in Figs. 2 and 5. The maximum degree of polarization in the V pass-band (P [FORMULA] with [FORMULA]) has been observed on J.D. 9653.4 when the star was at a deep minimum. Another deep minimum was observed near J.D. 9372.2 (Fig. 2). However due to poor seeing conditions the accuracy of the measurements on that night was low, therefore, we did not use them in our analysis.

Despite the strong variations of the degree of linear polarization observed during the deep minimum at J.D. 9653, the position angle did not change significantly. Since the observed polarization is the sum of the variable intrinsic component and the constant component of the IS matter, this means that the position angles of both components are about the same. This suggestion is supported by the polarization map of the region around RR Tau (Fig. 4): the mean value of the position angle of the IS polarization in this region is: [FORMULA] which coincides within about [FORMULA] with the position angle of the polarization of RR Tau at deep minimum.

[FIGURE] Fig. 4. Polarization map of the RR Tau neighbourhood based on the data of Shakhovskaya et al.'s (1986) paper. The observed polarization of RR Tau itself (open circle) is given for the normal state of the star and for the deep minimum.

From Fig. 5 one can see that the dependence of the percentage of the observed polarization at all five pass-bands on the stellar magnitudes is non-linear and agrees well with those determined theoretically using the model of CS screening, explained below. A comparison with the data of Kardopolov and Rspaev (1989) shows that they agree well with our data observed at the same brightness of the star. This means that the Stokes parameters of the radiation scattered in the CS dust envelope of RR Tau did not change significantly within the time interval of about 7 years. It is interesting to note also that according to Figs. 2 and 5 the intrinsic polarization of the star did not change during the flare-like events which were observed near J.D. 9224 and 9245.

[FIGURE] Fig. 5. RR Tau polarization degree vs. UBVRI magnitudes. The solid lines show the theoretical dependence [FORMULA] from Eqs. 2-3. Symbols as in Fig. 2

The wavelength dependences of the RR Tau linear polarization observed at different levels of its brightness are shown in Fig. 6. They resemble those observed in another UXOR WW Vul (see Fig. 2 in the paper by Grinin et al. 1988). Such a behaviour of [FORMULA] is the result of selective weakening of the direct (non-polarized) stellar radiation in the sum of the radiation of the star and the CS dust.

[FIGURE] Fig. 6. The wavelength dependence of the linear polarization of RR Tau for the different V stellar magnitudes.

Fig. 7 shows the behaviour of the Stokes parameters of the RR Tau radiation at the V pass-band in the [FORMULA], [FORMULA] plane. At the bright state of the star the intrinsic polarization is small and the observed polarization is determined almost completely by the interstellar component (see below). At the deep minima it is almost entirely caused by scattered radiation in the CS dust envelope.

[FIGURE] Fig. 7. Behavior of the parameters [FORMULA] and [FORMULA] of the polarization of RR Tau in the V pass-band. Open dots are Crimean data, open squares are Dodaira data. For reference, we show the values of the IS component ([FORMULA]) and the intrinsic component of linear polarization ([FORMULA]) of the star in the brightest state (V = 10.m153) from Table 3.
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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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