3 Membership and mean proper motion determination

In a sample of field stars in which an open cluster is present, a number of characteristics reveal the stars that are members of the cluster. These include the distance parameters (the members of the cluster are within a limited volume), the kinematics parameters (the cluster members present similar spatial velocities), or photometric parameters (the members have the same ages and same chemical composition). With the proper motion provided by the Tycho2 Catalogue it is possible segregate the members of the clusters simply using the knowledge that the stars of a cluster have similar spatial velocities (in our case, we use only the proper motion data). It is important to note that in this kind of investigation, the dispersion of proper motions of field stars is larger than that of the cluster. This happens because the dispersion of proper motions of field stars results from the dispersion of secular parallaxes, differential galactic rotation, peculiar motions and from observational errors, while the dispersion of proper motions of the cluster stars occur practically only due the observational errors, since the internal expansion of the cluster is negligible. When the proper motion distribution is almost bimodal in both coordinate axes, the statistical method is efficient to segregate the members of the clusters and is able to discover new members. Based on these considerations, we applied statistical methods to the Tycho2 data of individual stars in the regions of clusters to determine the probability of membership of each star. The methods were those described by Vasilevskis & Rach (1957) and Sanders (1971), also discussed by Slovak (1977). The method of Vasilevskis and Rach was used to estimate the initial values of the parameters used in the method of Sanders.

Following the suggestion of Zhao et al. (1982), proper motions different from the mean by more than three times the standard deviation were discarded.

In Table 2 (available in electronic form at the CDS) we present the parameters provided by the method of Sanders. The mean proper motions of the clusters ( $\mu_{\alpha} \cos \delta, \mu_{\delta}, \sigma$) and the results of the two-dimensional Gaussian fit to the population of field stars are given. With the frequency function parameters we could determine the individual probability of the membership of each star of the cluster. The number of stars of the clusters presented in Table 2 are the values that give the best results for the searched parameters, and correspond to membership probability greater than $51\%$. Tables 5 to 117, only available in electronic form at the CDS, list the stars in the limits of each cluster, with the membership probabilities calculated by our method. The distances of the clusters are also given in Table 2.