next previous
Up: A proper motion study

3 On the astrometric accuracy of the Hoher List CCD frames

CCDs have been used in astrometry for several years, e.g. for the determination of parallaxes, double stars and for meridian circle observations (see references in Geffert 1998). However most of these observations are based on CCD observations with fields of $(10\hbox{$^\prime$ })^2$ and smaller. Since our study uses CCD observations of fields with a size at least 20$^\prime$ $\;\times\;$20$^\prime$ it seems necessary to evaluate the accuracy, which may be obtained with such telescope detector combinations. While the CCD frames of Calar Alto were already tested in an earlier study (Geffert et al. 1994), we will concentrate here on the Hoher List observations. In a first step we have compared positions of stars from pairs of CCD frames. The positions of one frame were transformed by an affine transformation to a second frame and the rms of the differences were calculated for each coordinate. Under the assumption that both frames contribute with equal weight to the differences, we have calculated from the rms the mean uncertainty of one position on one frame. These are given in Table 4 for several CCD pairs with nearly identical limiting magnitudes. In this comparison we included all stars which were detected on the CCD frames.

Table 4: Mean accuracy of the position of one star on a CCD frame determined from intercomparison of two CCD frames

$s_{\alpha}$ $s_{\delta}$ Lim. mag. No. of stars
  [mas] [mas] (V)  

62 64 16.5 1373
4238/4239 120 120 18.5 3378
4240/4241 63 67 16.2 1081
4242/4243 100 80 17.0 1980

In a second test we consider only the stars which contribute to the final catalogue of our investigation. These are stars at the brighter end of the magnitude distribution. Reducing the plates with one catalogue (ACT or Hipparcos) leads to positions of the stars of each plate/CCD frame in a common system. The position and proper motion of each star in our final solution described in Sect. 2 are determined by a fit to the positions and epochs of the different plates/CCD frames for each star. The mean position and proper motion of each star is then used to update the positions of each star for the epoch of the individual plates/CCD frames. For each plate the mean and rms of the positional differences from the initial positions are determined. The rms will give an indication of the accuracy of each individual plate/CCD frame. Table 5 summarizes for the Hoher List frames the mean and standard deviations for each frame.

Table 5: Mean deviation ( $\Delta _{\alpha }$, $\Delta _{\delta }$) and rms ( $\sigma _{\alpha }$, $\sigma _{\delta }$) of the positions of different CCD frames in the last step of the iteration. The data are based on the mean of about 270 stars

CCD frame
$\Delta _{\alpha }$ $\sigma _{\alpha }$ $\Delta _{\delta }$ $\sigma _{\delta }$ Colour
  [mas] [mas] [mas] [mas]  

+10 70 -7 90 B
4237 +6 70 -5 70 B
4238 +7 80 0 90 B
4239 +6 100 +2 50 B
4240 +7 80 0 50 V
4241 -2 40 -1 50 V
4242 -0 90 +5 50 V
4243 +3 40 +6 90 V

Table 5 shows a slight difference in the B and V frames of the order of a few mas. Nevertheless the systematic deviations between the B and V frames are small. The positional accuracy of each star is of the order of one tenth of a pixel. This value is a little bit larger with respect to other studies (e.g. Geffert 1998). The reason may be the crowding in the region of M 10. In general, the accuracy of one single frame is of the order of the accuracy of one refractor plate, which justfies the use of CCD frames for the second epoch observation.

  \begin{figure}\psfig{figure=ds1790f1.eps,height=70mm,bbllx=20mm,bblly=100mm,bburx=160mm,bbury=220mm}\end{figure} Figure 1: The vector-point-plot diagram of all stars in the field of M 10

next previous
Up: A proper motion study

Copyright The European Southern Observatory (ESO)