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4. Photometric data reduction

Photometric reduction consists of three parts: (a) the reduction in the instrumental photometric system (b) the data correction for the atmospheric extinction and (c) the transformation to the standard photometric system. For every new step of the reduction new errors are introduced and therefore the final accuracy of the results will decrease inevitably.

Two two-dimensional Moffat profiles were fitted simultaneously to the double star components on each CCD frame according to the classical least square technique (Cuypers 1994).

The components' magnitude difference resulted from this on chip instrumental photometry had always an accuracy of a few millimagnitudes. On the other hand, all nights proved to be of good photometric quality as well. These two factors enabled us to get nightly instrumental magnitudes of the components of the observed double stars with an accuracy of 0.004 mags or better.

The atmospheric extinction correction was derived according to the classical formulas
eqnarray284
where the ``0" index refers to the mangitude and the color indices outside the atmosphere. We should remind the v mangitude and the b-v and u-b color indices refer to the instrumental values.

For the determination of the first order extinction coefficients we used the A0 - type E408 standard star from the E regions (Graham 1982), which was observed each night, many times per night at different airmasses smaller than or equal to two. The first order extinction coefficients that we obtained are the following:
displaymath920

displaymath921

displaymath922

displaymath923

displaymath924

displaymath925

displaymath926

displaymath927

This list shows as well which filter was used each night for carrying out the observations.

Second-order extinction coefficients of the UBV system are fairly constant and can be calculated only twice per year for each observatory. For this reason, we used the values given by Gocherman et al. (1993) as updated by Grothues (1995).

For the transformation in the standard system, we used the average and the standard deviation values of the V extinction corrected magnitude and of the (b-v) extinction corrected colour. These were calculated from the two V and the two (b-v) extinction corrected values, which were obtained in the corresponding two pairs of two different nights of observations with the same filter. As we observed only one night in U filter, we calculated the error of the (u-b) extinction corrected colour according to the corresponding error equation.
The three standard deviation values of these extinction corrected magnitudes and colours, were around 0.01 mags.

The V magnitude and the B-V and U-B color indices, which refer to the standard system, can be obtained from the extinction corrected values v, (b-v) and (u-b) according to the following transformations:
displaymath928

For the estimation of tex2html_wrap_inline976 and tex2html_wrap_inline978 we used improved photometric values of 18 photometric standard stars from the E regions (Grenon 1991) observed in the night of the tex2html_wrap_inline980 to tex2html_wrap_inline982 of April. The values obtained for the transformation coefficients are the following:
displaymath929

displaymath930

displaymath931

  figure318
Figure 1: The two colour diagram

 

No ADS or DM tex2html_wrap_inline984 tex2html_wrap_inline986 tex2html_wrap_inline988 tex2html_wrap_inline990
1 -48 4325 5.345 0.593 0.068 0.236
2 -03 2577 5.509 1.062 0.170 0.210
3 -24 8146 2.168 1.010 0.058 0.057
4 -07 2793 4.286 0.445 0.090 0.044
5 -57 2434 2.559 0.038 0.102 0.318
6 -01 2347 2.731 0.059 -0.004 0.033
7 -58 2243 5.146 0.016 0.003 0.031
8 -40 6603 2.009 0.069 0.114 0.039
9 -40 6622 2.296 0.474 0.064 0.019
10 -74 804 1.545 0.244 -0.063 -0.153
11 -46 7356 3.757 1.327 0.071 0.087
12 -13 3466 3.301 0.203 0.029 0.030
13 -23 10415 6.574 1.845 -0.006 0.029
14 -34 7899 1.627 0.041 -0.008 -0.013
15 -62 2853 2.319 0.278 0.032 -0.025
16 -47 8078 3.779 0.056 0.023 0.003
17 -57 6065 3.153 0.040 -0.033 -0.001
18 -29 10446 2.230 0.121 0.043 -0.018
19 -26 9458 2.733 0.269 0.023 0.087
20 -27 9212 2.902 0.344 0.007 -0.028
21 -79 740 5.456 0.106 -0.092 0.078
22 -31 10930 4.415 0.302 0.261 0.334
23 +04 2864 2.737 0.042 0.040 -0.045
24 -16 3942 4.615 0.021 0.357 0.569
25 -14 4070 3.487 0.075 0.046 0.052
26 -25 10904 4.189 0.139 0.023 0.030
27 -31 12112 2.031 0.152 0.026 0.034
28 -38 10617 2.186 0.037 0.000 -0.007
29 -04 3976 3.704 0.072 0.045 0.056
30 -28 12218 2.506 0.185 0.070 -0.006
31 -65 3193 1.915 0.470 -0.533 0.801
32 -17 4630 3.404 0.195 0.009 0.064
33 -46 11189 2.264 0.332 0.064 0.059
34 -46 11604 2.918 0.138 0.003 -0.010
35 -13 4639 2.352 0.294 0.048 0.071
36 -52 10777 4.626 0.237 0.043 0.043
37 -04 4202 1.905 0.011 -0.013 -0.010
38 -57 8803 2.831 0.561 0.275 0.628
39 -32 15843 1.867 0.395 0.074 0.104
40 -32 13472 2.349 -0.648 -0.687
Table 3: Photometric differences and angular separation of the components

 

Table 2 contains the photometric results of the reduction that was performed on 40 visual binaries. Two lines per binary are given. The first corresponds to V magnitude and colours of the primary while the second one of the secondary. As in Table 1, the first column is an enumeration of the binaries, while the second column contains the Durchmusterung designation of the primaries. The next three columns contain the V magnitude and its error tex2html_wrap_inline1118 and the (B-V) and (U-B) color indices with their errors tex2html_wrap_inline1124 and tex2html_wrap_inline1126 respectively.

The error estimations in Table 2 resulted from the standard deviation values of the extinction corrected magnitudes and colours and the uncertainties of the transformation coefficients into the standard UBV system.


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