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3 Proper motions

3.1 Data and reduction


Table 3: Plate Material for proper motion study of Stock 2

Plate Id.
$\alpha$ $\delta$ Epoch Emulsion Filter Medium

2:19 60:02 1952.708 103AE 2444 Glass Copy
POSSII R114 1:54 60:00 1989.965 IIIaF RG 630 Film Copy
POSSII B114 1:54 60:00 1987.744 IIIaJ GG 395 Film Copy

The proper motion survey of Stock 2 is based on Super COSMOS scans (Hambly et al. [1998]) of three POSS plates listed in Table 3. A region of $3^{\circ}\times 3^{\circ}$ has been scanned about the nominal cluster centre with a positional accuracy of $\sim 1~\mu$m. The scans were performed in the so-called Image Analysis Mode (Beard et al. [1990]), which automatically deblends objects and rejects extended objects like galaxies. A transformation from plate to equatorial coordinates in the FK5 system has been performed using PPM stars on the plate. Using software provided by the Royal Observatory of Edinburgh, the following reduction steps were performed:

The first task is to pair up the objects on the first and second epoch plate (E597 and R114, respectively). This involves identifying common objects, determining and applying a transformation from the coordinate system of the first epoch plate to the second epoch plate, and pairing up objects that lie at the same position (allowing for some small margin of error).

1000 bright stars in common are used to fit and apply a linear coordinate transformation of the form

$\displaystyle x_{\rm e}$ = a + bxm + cym (1)
$\displaystyle y_{\rm e}$ = $\displaystyle d + ex_{\mathrm m} + fy_{\mathrm m} \,$ (2)

to the plates. Here x and y refers to the plate coordinates, subscript e denotes the expected coordinate from the second epoch plate, and subscript m the measured coordinate on the first epoch plate. A transformation of this form will correct for differences in plate origin, scale, orientation, shear and squash. Including shear and squash did not improve our fit, so we constrained the fit by b=-f and c=e. The root mean square error of the fit was $5~\mu$m which corresponds to 0.34 arcsec.

Stars with equal coordinates on both plates (i.e. the nearest star within $50~\mu$m) were considered as identical, and relative proper motions were derived. However, two more systematic effects have to be accounted for.

Distortion of the plate emulsion can have serious effects on the position of stars when large areas of the plate are analysed. To avoid having to fit these complicated distortions, the plates were subdivided into smaller regions ( $12\times12 = 144$ boxes), and proper motions determined independently within each region. Secondly, stellar positions are magnitude dependent due to the non-linearity of the plate emulsions.

The plate coordinate transformation was re-applied to stars of the first epoch plate in each of the 144 sub-regions independently. This was done in the same way as described above. Reference stars to fit the transformation equations were chosen automatically within a suitable magnitude range to avoid too faint or too bright and saturated stars. The residual positions were fitted as a function of magnitude and the residuals of this fit subtracted from the first epoch plate positions. This fit was re-iterated, until the fit converged. The remaining positional differences are the actual proper motions.

Within each of the 144 subregions, a background field distribution is visible in vector point diagrams (VPDs), centered around zero proper motion. More precisely, the average centre coordinate of the proper motion distributions of all 144 subregions is (-0.09, 0.37) $\pm$ (0.60, 0.37) arcsec per year. Each subfield has thus the same zero point in proper motion, and the results of all subregions are merged to one VPD in Fig. 3.

3.2 Plate photometry

The method of separating cluster members from background objects by means of a proper motion analysis is to identify a group of common proper motion stars that are distinct from the background population. However, plotting a VPD of the stellar proper motions at this stage would reveal very little, as the cluster stars are masked by the overwhelming majority of some 105 background objects. It is first necessary to preselect background stars by means of a colour magnitude diagram of the plate photometry, calibrated using the new CCD photometry.

Since our plate material supplies magnitudes in the photographic system, the CCD photometry has first to be transformed to the natural photographic system using the equations

B-BJ = $\displaystyle \left(0.32\pm0.03\right)\left(B-V\right)$ (3)
R-R63F = $\displaystyle 0.013 +0.204\left(R-I\right) -0.100\left(R-I\right)^{2}$  
    $\displaystyle -0.0295\left(R-I\right)^{3}$ (4)

from Blair & Filmore ([1982]), and Bessell ([1986]) respectively, where BJ and R63F denote magnitudes in the photographic system and BVRI are CCD measured magnitudes in the standard system. A cubic spline function was fitted to transform CCD BVRI magnitudes to photographic BJ and R63F magnitudes; points for this fit were chosen interactively so as to allow for some extrapolation beyond the bright and faint limit of the CCD photometry. Finally, the fit was applied to all stars on the plate. The residuals of the fit of naturalized CCD and calibrated plate photometry have a scatter of $\approx$ 0.15 magnitudes both for BJ and R63F.

Unfortunately, the CCD photometry covers only a small central region of the scanned plate. Further investigation suggested that there was a position dependent colour-shift across the plate. If colour-magnitude diagrams were plotted for different sub-regions of the plate, the position of the density distribution of background field stars in the colour-magnitude plane varied by up to 0.1 magnitudes in colour. Whether this is due to problems with the photometric calibration or the effect of differential reddening across the field (due to the low Galactic latitude, $b \sim 1.9^{\circ}$, of the cluster) is unclear. The shifts are consistent with an increased reddening towards the Galactic plane, but also with a colour-effect towards the edge of the plate. In the absence of more photometry with which to calibrate the photographic data, the plate material was used with the calibration determined from the central region.

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