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3. Standard transformation. Photometric accuracy

What follows refers to the 18 observing campaigns carried out to obtain the light curves of the six binary systems selected, including the eight runs in which we observed ZZ UMa.

First of all, atmospheric extinction coefficients were computed for each night by the "Bouguer method" (Hardie 1962), using the comparison stars as well as the photometric standards observed several times during the night, covering a typical range in air masses from 1 to 2.

Following the method described by Grønbech et al. (1976), after extinction correction, we determined night corrections for each observing period, in order to define magnitudes in the instrumental system.

For the observing periods at Calar Alto, the mean extinction coefficients obtained were: 0.142, 0.061, 0.051, 0.148 with RMS of 0.021, 0.010, 0.012, 0.021 for V, (b-y), tex2html_wrap_inline928 and tex2html_wrap_inline930 respectively. We can appreciate their stability over the 5 years of observations. These results are in good agreement with previously published ones, Fabregat et al. (1991).

The extinction coefficients obtained for the two runs performed at La Silla are also very stable, with mean values of 0.161, 0.056, 0.051, 0.132 and RMS of 0.017, 0.006, 0.003, 0.003 for V, (b-y), tex2html_wrap_inline936 and tex2html_wrap_inline938 respectively for the 24 nights in the two periods.

Next we transformed the observations to the uvby and tex2html_wrap_inline942 standard systems, (Strömgren 1966; Crawford & Barnes 1970), following the procedure described by Fabregat & Reglero (1990). For that purpose a set of 38 standard stars from the compilation of Olsen (1991), was observed on selected nights with good atmospheric conditions. For each period independent transformation coefficients were computed and used to transform the magnitudes of the comparisons and program objects to the standard system.

For the campaigns where the number and type of standard stars measured allowed it, we computed the transformation coefficients separately for stars with (b-y)<0.410 (A-F "blue" stars) and (b-y)>0.410 (G-K ``red" stars), in order to take into account the difference in colours for these stars in the transformation of the indices tex2html_wrap_inline948 and tex2html_wrap_inline950. The colour effect is not seen in the y and (b-y) transformations, Fabregat (1989).

tex2html_wrap_inline956 photometry has been transformed following the method described by Crawford & Mander (1966). The mean transformation cofficients obtained for the mono-channel photometer used at the 1.5 m telescope at Calar Alto were:

for the multi-channel photometer at Calar Alto:


and for the multi-channel photometer at La Silla:


These values and their dispersions reflect the stability of the equipment during the 6 years of observations and its closeness to the standard system, as seen by scale transformation coefficients very close to unity.

Table 1: standard photometry for ZZ UMa and the comparisons

In Table 2 we list the mean magnitudes and indices obtained for the 38 standards used, indicating the number of campaigns in which they were observed, the number of points averaged, and the difference between standard values and observed values. Only HD 143107A shows residuals on the tex2html_wrap_inline1016 and tex2html_wrap_inline1018 indices that clearly deviate from the mean values. HD 81997A also deviates on the tex2html_wrap_inline1020 index.

An estimation of the internal error of the photometry can be made by using the RMS dispersion of the differences between the standard value and the computed value for the standard set observed.

The average dispersions for the 11 photometric periods in which we could calculate the transformation were: 0.009 and 0.004 in V magnitude and (b-y) colour, and 0.005, 0.006, 0.005 in the tex2html_wrap_inline1026, tex2html_wrap_inline1028 and tex2html_wrap_inline1030 indices.

These values are in good agreement with the mean RMS dispersions for the whole standard set of 0.010, 0.005, 0.005, 0.006, 0.005 magnitudes for V, (b-y), tex2html_wrap_inline1036, tex2html_wrap_inline1038 and tex2html_wrap_inline1040 respectively.

We assume as an error of our photometry the larger of these two estimations, namely: 0.010 mag in V, 0.005 mag in (b-y), and 0.005, 0.006, 0.005 in tex2html_wrap_inline1046, tex2html_wrap_inline1048 and tex2html_wrap_inline1050 indices.

SAO 15242, (V=10.13, G0V) and SAO 15251 (V=10.00, G2V), were used as comparison and check stars for ZZ UMa, their magnitudes and spectral types being similar to ZZ UMa itself.

The constancy of the comparison star was checked every night. The internal RMS error for the 135 differences (tex2html_wrap_inline1056) 0.007, 0.007, 0.014, 0.021, 0.019 in magnitude for V, (b-y), tex2html_wrap_inline1062, tex2html_wrap_inline1064 and tex2html_wrap_inline1066 respectively, is of the same order of that obtained for main-program stars.

Average standard magnitudes and colour indices for the comparisons of ZZ UMa are given in Table 1 (click here) with an indication of their accuracy measured through the RMS dispersion of the observed values. In Table 1 (click here) are also given averaged magnitudes and colour indices for the binary system in the eclipses and first quadrature.

Figure 1 (click here) presents the ZZ UMa differential light curve in the y filter. The light curve including the eclipses has been covered in eight different epochs, from March 1990 to May 1996. The apparent scatter of the light curve outside eclipses is mainly induced by activity. The 294 differential magnitude (tex2html_wrap_inline1070) values in the standard system are given in Table 3. The analysis of this binary, including activity effects, will be published soon.

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