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3. Astrometric data reduction

The night of April 26 was chosen for the astrometric part of this work, due to the good seeing value at Cerro La Silla of far below one arcsecond. Good seeing produces stable star traces of high quality, which enable an accurate determination of the right ascension direction. As it has been already mentioned, the angular separation (tex2html_wrap_inline862) as well as the position angle (tex2html_wrap_inline864) for every binary was calculated in the V filter only on frames taken in this night.

In order to define the right ascension direction on the CCD chip, several trails of stars in M 16 open cluster were taken during this night using the V filter. Obviously, all the CCD surface was used for taking these traces. In an earlier work, Sinachopoulos (1988) presented the technique of star traces for CCD cameras. Using several star trails per frame on six different frames taken one after the other, we determined the zero point of the position angle with an accuracy of tex2html_wrap_inline870 degrees.

In order to estimate the scale of the CCD we used several stars on images of M 16 taken in the same night of April 26 through the V filter as well. A detailed astrometric work on this cluster has been published in the paper of Tucholke et al. (1986). According to it the typical internal errors of tex2html_wrap_inline874 and tex2html_wrap_inline876 positions are both tex2html_wrap_inline878. The minimum accuracy (for tex2html_wrap_inline880) in the position of one star, is
Since the error in the angular separation of two stars of the M 16 cluster depends on the accuracy in the position of each one of them, the standard deviation will be
According to the same paper, the mean error in the proper motion for the stars observed is tex2html_wrap_inline882 in both components. Since the difference of time between the epoch of the observations and the epoch to which the paper refers is tex2html_wrap_inline884, the error in both components is
and as we are interested in the angular separation of two stars, the error due to the proper motion uncertainty will be
Moreover the error in the difference in the position of two stars does not depend on the error in the proper motion, the standard deviation in the angular separation will be
We used several star pairs in M16 having angular separation around 600 pixels on the CCD chip, in order to determine the telescope scale with high accuracy. The error we derived for the scale factor in that way is

By comparing the positions of the stars detected by DAOPHOT with the values presented in the paper mentioned above we calculated the scale factor of our optical system, which was tex2html_wrap_inline886 (tex2html_wrap_inline888). This agrees with the scale calculated for this telescope by van Dessel & Sinachopoulos (1993).

For the error of the angular separation tex2html_wrap_inline890 due to the atmospheric refraction we took tex2html_wrap_inline892. However, this is a rather poor assumption, since this error can be up to a few hundredths of an arcsecond for observations made at airmasses tex2html_wrap_inline894 if the V filter is used and even higher for the B and U ones. Nevertheless, tex2html_wrap_inline902 was never the case of our astrometric observations, as they carried out near minimum possible airmasses (usually tex2html_wrap_inline904).

A discussion of the calculation of the final accuracy achieved in the angular separation was presented by Nakos et al. (1995) and a detailed one by Sinachopoulos & Seggewiss (1990).

Although the method of star traces was used for the determination of the right ascencion direction, the good quality of the M 16 astrometry would enable us to use it for this purpose as well. A comparison of the two methods would be very interesting.

Table 1 contains the astrometric results. The first column is an enumeration of the visual binaries. The next four columns contain the coordinates of the primaries for epoch 2000. Next column contains the Durchmusterung designation of the primaries. The next four columns contain the angular separation (tex2html_wrap_inline906), its accuracy (tex2html_wrap_inline908) in arcsecs and the position angle (tex2html_wrap_inline910) with its accuracy (tex2html_wrap_inline912) in degrees. The last column contains the epoch of the observations. It must be taken into account that the very small values of tex2html_wrap_inline914 errors are due to the assumption of tex2html_wrap_inline916. Realistic values of tex2html_wrap_inline918 are probably one order of magnitude higher.

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