Cluster radius and sampling radius in the determination of cluster membership probabilities

We analyze the dependence of the membership probabilities obtained from kinematical variables on the radius of the field of view around open clusters (the sampling radius, ). From simulated data, we show that optimal discrimination between cluster members and non-members is achieved when the sampling radius is very close to the cluster radius. At higher values, more field stars tend to be erroneously assigned as cluster members. From real data of two open clusters (NGC 2323 and NGC 2311), we infer that the number of identified cluster members always increases with increasing . However, there is a threshold value above which the identified cluster members are severely contaminated by field stars and the effectiveness of membership determination is relatively small. This optimal sampling radius is 14 arcmin for NGC 2323 and 13 arcmin for NGC 2311. We discuss the reasons for this behavior and the relationship between cluster radius and optimal sampling radius. We suggest that, independently of the method used to estimate membership probabilities, several tests using different sampling radius should be performed to evaluate possible biases.