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2 Observations and the reduction

Table 1 lists the photographic plates used in this work, while Table 2 indicates the observational data of the CCD frames. The plates were taken either with the ($D=0.3\;$m, $f=5.1\;$m) double refractor of Bonn, now located at Hoher List observatory, or with the ($D=0.4\;$m, $f=7\;$m) refractor of Shanghai. The CCD frames were taken with the WWFPP camera (Reif et al. 1994) at the 1.23 m telescope at Calar Alto and with a similar camera (HoLiCam) at Hoher List observatory. The use of the complete material allows a nearly uniform coverage of the epoch difference of 92 years. The limiting magnitude of the plates is of the order of $V = 15.5\;$mag, while the corresponding one of the CCD frames ranges from V = 16 to 19 mag. The refractor plates of Bonn were mainly scanned at the PDS 2020GM of University of Münster. The plates R1874 and R1875 with lower limiting magnitude have been measured at the ASCORECORD of Hoher List observatory. On these plates only 80 stars for each plate were measured. Stars were extracted and rectangular coordinates x and y were determined from the PDS measurements using standard procedures (e.g. Tucholke 1994). The first epoch plates of the Bonn refractor contained scratches and reseau lines, which led to problems for a significant number of the stars. Therefore for some of these stars no rectangular coordinates could be obtained. The plates from Shanghai were scanned at the PDS 1010MS of the Purple Mountain Observatory, Chinese Academy of sciences (see also Wang et al. 1999).

The determination of the rectangular coordinates x, y of the stars on the CCD frames was performed for the observations from Hoher List by standard CCD reduction techniques (DAOPHOT, IRAF) routines. Magnitudes, x and y positions were determined via PSF fit. The observations from Calar Alto were reduced earlier (Geffert et al. 1994) by the IMEX routine of the IRAF program package.

The astrometric reduction was performed by a central overlap algorithm. Due to the small field of the CCD frames we had to use only the plates in the first step of the reduction. A catalogue of positions and proper motions of 450 stars was established in this first step. In the following steps of the reduction the CCD frames were included. While for the plates only quadratic polynomials of the rectangular coordinates had to be taken into account, third order polynomials were necessary for the reduction of the CCD frames. The third order polynomials for the reduction of the CCD frames had to be used due to the distortion of the optics of the focal reducer of the WWFPP camera (Geffert et al. 1994). From the different position and time pairs we determined for each star for a certain epoch the mean position and the proper motion using least squares technique. All stars with proper motion errors larger than 4 mas/yr were omitted. The final catalogue contains 532 positions and proper motions of stars in the region of M 10. The median of the internal errors was about $\mbox{ $\pm$\space }1\;$mas/yr. From a plot of the proper motions versus magnitude no magnitude equation was found in our data.

Table 2: CCD observations used in this work. All CCD observations were made with the WWFPP camera (Reif et al. 1994)

Epoch Filter No. of frames

1 m Hoher List
1996 V, B 10
1.23 m Calar Alto 1994 R 5


Table 3: The catalogue of positions and proper motions of 532 stars in the field of M 10. Four lines are given as an example. The complete catalogue is available in electronic form at VizieR (CDS; see Ochsenbein et al. 2000). The epoch of the positions is 1950

$\alpha_{2000}$ $\delta_{2000}$ $\sigma _{\alpha }$ $\sigma _{\delta }$ $\mbox{$\mu_{\alpha}\cos\delta$ }$ $\mbox{$\mu_{\delta}$ }$ $\sigma_{\mbox{$\mu_{\alpha}\cos\delta$ }}$ $\sigma_{\mbox{$\mu_{\delta}$ }}$
  [$^{\rm h}$$^{\rm m}$$^{\rm s}$] [$^\circ$'''] [$^{\rm s}$] [''] [mas/yr] [mas/yr] [mas/yr] [mas/yr]

165434.488 -44520.57 0.004 0.04 -33.2 -27.5 1.7 1.2
2 165446.910 -35253.73 0.006 0.02 3.5 5.8 3.3 0.6
3 165447.085 -42306.77 0.002 0.01 -5.5 4.4 1.1 0.3
4 165448.326 -41334.70 0.002 0.03 -4.3 -2.2 0.7 0.7
$\;$ $\stackrel{\displaystyle .}{\displaystyle .}$ $\stackrel{\displaystyle .}{\displaystyle .}$ $\stackrel{\displaystyle .}{\displaystyle .}$ $\stackrel{\displaystyle .}{\displaystyle .}$ $\stackrel{\displaystyle .}{\displaystyle .}$ $\stackrel{\displaystyle .}{\displaystyle .}$$\;\:\:$ $\stackrel{\displaystyle .}{\displaystyle .}$$\;\:\:$ $\stackrel{\displaystyle .}{\displaystyle .}$$\;\:\:$ $\stackrel{\displaystyle .}{\displaystyle .}$$\;\:\:$

We have performed two independent reductions of the M 10 data with reference stars from Hipparcos (ESA 1997) and the ACT catalogue (Urban et al. 1998). Although the Hipparcos stars proper motions are more accurate, they seemed to be of only limited usefulness for our work, since the majority of the plates contained only four Hipparcos stars, while about 17 stars could be used from the ACT catalogue. Therefore we consider both solutions as equivalent. Table 3 (the complete table is available in electronic form) gives the catalogue of our positions and proper motions for the complete field with respect to the ACT catalogue. The limiting magnitude of this catalogue is about $V = 15.5\;$mag, which corresponds to the limiting magnitude of the first epoch plates. The size of the field is approximately $75\;\times\;75\;{\rm arcmin}^2$centered on M 10. We chose the ACT solution for the catalogue in Table 3. The proper motions may be transfered to the Hipparcos system by adding $\Delta\mbox{$\mu_{\alpha}\cos\delta$ }= -1.5\;$mas/yr and $\Delta\mbox{$\mu_{\delta}$ }= +0.1\;$mas/yr to the proper motions from Table 3. For the determination of the membership we will also use the solution based on the ACT catalogue, while for the determination of the absolute proper motion of M 10 we will take the mean of both solutions.

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