Stellar Open Clusters' Membership Probabilities: an N-Dimensional Geometrical Approach

Abstract

We present a new geometrical method aimed at determining the members of open clusters. The methodology estimates, in an N-dimensional space, the membership probabilities by means of the distances between every star and the cluster central overdensity. It can handle different sets of variables, which have to satisfy the simple condition of being more densely distributed for the cluster members than for the field stars (as positions, proper motions, radial velocities and/or parallaxes are). Unlike other existing techniques, this fact makes the method more flexible and so can be easily applied to different datasets. To quantify how the method identifies the clus- ter members, we design series of realistic simulations recreating sky regions in both position and proper motion subspaces populated by clusters and field stars. The re- sults, using different simulated datasets (N = 1, 2 and 4 variables), show that the method properly recovers a very high fraction of simulated cluster members, with a low number of misclassified stars. To compare the goodness of our methodology, we also run other existing algorithms on the same simulated data. The results show that our method has a similar or even better performance than the other techniques. We study the robustness of the new methodology from different subsamplings of the ini- tial sample, showing a progressive deterioration of the capability of our method as the fraction of missing objects increases. Finally, we apply all the methodologies to the real cluster NGC 2682, indicating that our methodology is again in good agreement with preceding studies.