3 Results and discussions

Table 1 (available in electronic form) presents our final results for the clusters and fields parameters, determined by the method of Sanders. The mean proper motion of the studied open clusters are also available in DAML2002. Tables 2 to 95, only available in electronic form, list the stars in the limits of each cluster, with the membership probabilities calculated by our method.

As performed in Paper I, we checked our mean absolute proper motions against the mean proper motions derived by BDW and other recent papers. In a comparison with BDW's results we found 39 common objects. A Gaussian fit to the differences (Fig. 1) gives a mean proper motion difference of -0.6 in $\mu_{\alpha}\cos{\delta}$ and -0.1 in $\mu _{\delta }$;

Figure 1: Comparison of our mean proper motions with those determined by BWD. The differences are presented as a function of the results of BWD. The open circles represent the values in $\mu_{\alpha}\cos{\delta}$, and the stars in $\mu _{\delta }$.

the standard deviations are 1.6 mas/yr in $\mu_{\alpha}\cos{\delta}$ and 1.8 mas/yr in  $\mu _{\delta }$.

3.1 NGC 2360, NGC 2244, NGC 6531 and Trumpler 15

A few open clusters marked in Fig. 1 present differences with BDW greater than the maximum expected value (about 2.5 mas/yr, which is the typical error in Tycho2 proper motions of single stars).

In the cases of the clusters NGC 2360, NGC 2244, NGC 6531 and Trumpler 15 it seems that our method is unable to distinguish the members from the background, which has approximately the same proper motion (see the VPDs in Fig. 2).

Figure 2: Vector proper motion diagram of the stars in the region of the open clusters NGC 2360, NGC 2244, NGC 6531 and Trumpler 15. The axes present $\mu_{\alpha}\cos{\delta}$ and $\mu _{\delta }$, in mas/yr.

Based on the bad segregation of the two populations (field and cluster) in the VPD, we suggest that the results given by BDW are the correct ones.

However, it is important to pay close attention to the fact that the proper motions provided by the Tycho2 catalogue differs from the Hipparcos ones, specially for the stars used by BDW for the cluster NGC 6531.

3.2 NGC 1893 and NGC 5138

The proper motion provided by BDW for these two clusters were based on only one star.

For the NGC 1893 the star considered is HIP 25103 ( $\mu_{\alpha}\cos{\delta} = -1.3$ mas/yr and $\mu_{\delta}= +0.21$ mas/yr). This star is present in the Tycho2 catalogue ( $\mu_{\alpha}\cos{\delta} = -1.1$ mas/yr and $\mu_{\delta}= -1.8$ mas/yr), so that the proper motion is a little different from the Hipparcos one in  $\mu _{\delta }$. Note that the radial velocity of HIP 25103 (V=-7.5 km s^-1, Crampton & Fisher 1974) is compatible with the mean radial velocity of the cluster ( $-4.7~ \pm~ 4.4$ km s^-1) provided by Rastorguev et al. (1999). From a photometric point of view, the spectral type of this star (O5) suggests that it belongs to the cluster.

The difference found in $\mu _{\delta }$ for that star explains partly the difference in the mean proper motion of the cluster in the two works. Since we used a dozen stars to segregate the members, we believe that our result is the more correct one, considering also that our result maintains the membership of the star HIP 25103.

For the NGC 5138 the star considered by BDW is HIP 65618. This star is present in the Tycho2 sample and our analysis shows that this star has high membership probability ($P=85\%$). The difference obtained is due to the difference between Tycho2 ( $\mu_{\alpha}\cos{\delta} = -3.00$ mas/yr and $\mu_{\delta}= +3.10$ mas/yr) and Hipparcos ( $\mu_{\alpha}\cos{\delta} = -1.73$ mas/yr and $\mu_{\delta}= -4.79$ mas/yr) proper motions. To corroborate that our result is correct we note that Dias (2000) determined the mean proper motion of this cluster, obtaining components ( $\mu_{\alpha}\cos{\delta} = -4.2$ mas/yr and $\mu_{\delta}= +1.9$ mas/yr) compatible with those derived in the present paper.

Based on this analysis we suggest that our proper motion determinations, which rely on a large number of stars, are the correct ones for the clusters NGC 1893 and NGC 5138.