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4 Separation of cluster and field stars

Figure 1 gives the vector-point-plot diagram of all our proper motions indicating the concentration of the cluster stars. For the separation of cluster and field stars we have concentrated our investigation on stars up to the limiting radius of 14 $\hbox{$^\prime$ }$ (Webbink 1988) around the cluster centre. 284 stars remained in the data sample. For these stars a bivariate Gaussian fitting to the proper motions was performed using the method of Sanders (1971). Table 6 gives the result of the analysis. The cluster standard deviations are larger than the internal errors of the proper motion. This difference is clearly not an indication of a possible detection of internal motions of stars in the cluster. More likely these differences are caused by crowding effects and undetected systematic errors of the different telescopes used in this investigation.

M 10 is a globular cluster with three slow variable stars (Clement et al. 1985) and several UV bright stars (Zinn et al. 1972; Harris et al. 1983). Our sample contains only the variable stars V2 and V3 (see references in Clement et al. 1985). The other special stars are located in crowded regions, below the limiting magnitude, or exhibit too large proper motion errors. Both variable stars V2, V3 have according to our investigation a membership probability of 97%. This confirms the earlier suggestion (Clement et al. 1985) that these stars are of W-Virginis type, although V3 has a very unusual period of 7.8 days.

Table 6: Parameters of the fit to the bivariate Gaussian distribution of the proper motions of stars with $R<14\hbox {$^\prime $ }$ around M 10. $n_{\rm c}$ and $n_{\rm f}$ denote the number of the cluster and field stars, $x_{\rm c}$, $y_{\rm c}$ the mean cluster proper motion in $\alpha $ and $\delta $, respectively, $x_{\rm f}$, $y_{\rm f}$ the mean proper motion of field stars, $\sigma _{x{\rm c}}$, $\sigma _{y{\rm c}}$ the Gaussian widths of the cluster distribution, and $\sigma _{x{\rm f}}$, $\sigma _{y{\rm f}}$ the widths of the field star distribution. The x-direction is the direction of right ascension, the y direction is the declination axis. The units are mas/yr

Value Parameter Value

$n_{\rm c}$
193 $n_{\rm f}$ 88
$x_{\rm c}$ -4.9 $x_{\rm f}$ -3.5
$y_{\rm c}$ -5.3 $y_{\rm f}$ -3.3
$\sigma _{x{\rm c}}$ 1.8 $\sigma _{x{\rm f}}$ 7.0
$\sigma _{y{\rm c}}$ 2.0 $\sigma _{y{\rm f}}$ 7.1

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