The crucial part in the determination of the mean astrometric parameters of star clusters is the proper separation of members and non-members. This is especially important in the present case since we will typically have only a few stars per cluster (sometimes only one star), so that a single misclassified field star can already influence our final solution considerably. Since the information provided by Hipparcos is not sufficient to separate the cluster members from the field stars, we had to judge the membership by combining Hipparcos data with information provided by ground based studies. These include:
The following paragraphs will illustrate this approach.
Multicolour photometry and spectroscopy were our main criteria for the membership determination due to the fact that they are available for most stars and rule out membership for many of them. We performed a literature search for each cluster and noted the classification of our candidates in the various studies. We did not examine the membership on our own, since in most photometric studies the data was already carefully analysed by the authors themselves.
The main proper motion source is the Hipparcos Catalogue itself. If the proper motion of a cluster is already known from a few certain members in the Hipparcos Catalogue, it is possible to check the membership of the remaining stars with the proper motion of the cluster: new members are expected to have proper motions in agreement with the known members. However, the majority of our clusters do not have proper motions which clearly separate them from the field stars, therefore a matching proper motion in the Hipparcos Catalogue is a necessary but not a sufficient criterion for cluster membership.
In some cases we combined the Hipparcos proper motions with proper motions of additional members found in the TRC Catalogue (Høg et al. 1998). This was done for clusters where we could find no common motion among the Hipparcos stars or where only one member could be found in Hipparcos and we regarded it necessary to check its membership further. We also checked our proper motions against proper motions derived by Glushkova et al. (1999) from the TRC Catalogue.
Ground based proper motions were also used for the member determination. They are available for about 40 of the studied clusters. Ground based proper motions have generally the same or an even higher accuracy than the Hipparcos proper motions. Unfortunately, since they are not on the Hipparcos system, they cannot be directly compared with Hipparcos. Due to their accuracy, they were nevertheless a powerful tool to eliminate field stars from our sample.
High precision radial velocities are best suited to distinguish between members and non-members. Since they are available for relatively few stars only, their application is limited to a small number of clusters. They nevertheless give valuable information, since the studied stars are often giants or variable stars for which photometry and spectroscopy are of limited use.
Parallaxes are provided by the Hipparcos satellite. They put tight limits to the distances of nearby stars, but get less and less accurate the further the star is away. For most clusters they were able to eliminate a few foreground stars, but the majority of the field stars have parallaxes which would be compatible with the assumption of a cluster membership.
While the surface density of a star cluster drops from the inner to the outer parts, the density of the background remains essentially constant. Thus, a star seen close to the cluster centre is more likely a member than a star near the tidal radius. The angular distance therefore gives some hints for the classification of stars.
Our final classification was made by taking into account all the information we could get. Stars were divided into three categories (members, possible members and non-members) according on how well they fulfilled the membership criteria.
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