3 Data reduction

More than 350 CCD frames were taken during the four nights. The data reduction was performed by using the ESO-MIDAS image processing software. It evidently included a BIAS offset subtraction and a flat-field correction has also been performed for "cleaning'' the observations.

3.1 The used method of PSF fitting the data

Usually, only the two components of the visual binary observed were on the CCD frames. Obviously, the images of two components overlapped strongly. Therefore, we fitted simultaneously two MOFFAT profiles to both components in order to obtain the instrumental component magnitude difference and relative positions. This method is described by Cuypers (1997) in detail. Our FORTRAN programme used here for the data reduction makes use of this method. In addition, it detects the two components on the CCD frame automatically and calculates accurate initial values of the double MOFFAT function, needed for the least-square fitting, automatically as well.

Since the angular separation of the components is of a few arcseconds only, their images have identical shapes. So, the two fitted MOFFAT functions should have the following profile determining parameters in common: b -that is related to the FWHM-, e and f: parameters of the ellipticity, and q: the exponent of the MOFFAT function (see Cuypers 1997).

  

Figure 3: Correlation between seeing and the exponent of the MOFFAT function "q''

Figure 3 shows the strong correlation between seeing and the exponent of the MOFFAT function "q''. The symbols used in Fig. 3 have the same meaning as the ones of Fig. 1, corresponding to the four different nights. The corresponding slope of the linear regression was $0.70 \,\pm \,0.05$ for the second night, very significantly different from that of the third $(0.35\, \pm\, 0.04)$ and the fourth $(0.48 \pm 0.04)$.

3.2 CCD scale determination

We used the five HIPPARCOS (ESA, 1997) star pairs listed in Table 1 below in order to extract the CCD scale. The first two columns contain the two HIPPARCOS stars identification of the wide visual double star components. HIPPARCOS celestial $(\alpha,\delta)$ coordinates of these stars have been transformed first to actual ones of the epoch of observations (1998.48). Then, the corresponding angular separation of the pair in arcseconds has been calculated (third column). Column four contains the corresponding mean values of angular separation in pixels as resulted from the chip instrumental astrometry together with its uncertainty. Since atmospheric conditions (temperature and air pressure) were quite stable during observations, these values are mean standard deviations of all the individual separations measured in different nights. From column two and three the corresponding scale of the CCD chip has been calculated (column five). From these five individual scale values we obtained the final unweighted mean value of the scale $m = 0.30118 \pm 0.00056$ arcseconds/pixel.

  

Table 1: CCD scale determination using HIPPARCOS stars

One may remark that the uncertainies of angular separations due to the instrumental on CCD chip are around 0.02 pixels, equivalent to 0.006 arcseconds. Since our astrometric standard double stars have an angular separation of around 50 pixels, we expected an internal scale accuracy (due to the used CCD pixel size and the telescope focal length) around 0.00006 arcseconds/pixel. It is then clear that the resulted uncertainty of the scale (0.00056 arcseconds/pixel) is dominated by the HIPPARCOS catalogue uncertainties. This is mainly due to the rapid deterioration of the proper motion accuracies in this catalogue with time, which is the reason, in our case, for the relatively high uncertainty of the scale.

We calculated the same using data from the Brosche & Sinachopoulos (1988, 1989) catalogues and we found a scale $m = 0.3046\pm 0.0025$ arcseconds/pixel. This value is four times less accurate than the value of CCD scale based on the HIPPARCOS results and thus not used.

3.3 Position angle determination

Trails of up to ten stars near the celestial equator per night for defining the direction of the right ascension on the CCD chip were taken. We determined from them that this zero point is $\theta = -0.34 \,\pm \,0.02$ degrees. We added this value to the instrumental position angle.

The precision achieved in both the angular separation and the position angle has been often discussed in our previous papers of this series, especially by Sinachopoulos & Seggewiss (1990, Paper II), and by Nakos et al. (1995, Paper IV, and 1997).

It is nevertheless necessary to mention that we took $\sigma_{_{\rm r}}(z) = 0.004$ as an approximation of the mean error due to refraction for the used V filter. According to Herzsprung (1920), this value of $\sigma_{_{\rm r}}(z)$ is the expected difference in position $\delta(z)$ due to refraction between an A-type star and a K-type star at zenith distance $z=45^\circ$ for observations with yellow sensitive plates, which correspond to the V filter we used (see also in Sinachopoulos & Seggewiss 1990, for more details). Since we always observed at smaller zenith distances and the colour difference between the two components of our targets is probably not often that large, we consider the value of $\sigma_{_{\rm r}}(z)$ we adopted to be always larger than the correct value.