Clusterix 2.0: a virtual observatory tool to estimate cluster membership probability

Clusterix 2.0 is a web-based, Virtual Observatory compliant, interactive tool for the determination of membership probabilities in stellar clusters based on proper-motion data using a fully non-parametric method. In an area occupied by a cluster, the frequency function is made up of two contributions: cluster and field stars. The tool performs an empirical determination of the frequency functions from the vector point diagram without relying on any previous assumption about their profiles, Clusterix 2,0 allows us to search the appropriate spatial areas in an interactive way until an optimal separation of the two populations is obtained. Several parameters can be adjusted to make the calculation computationally feasible without interfering with the quality of the results, The system offers the possibility to query different catalogues, such as Gala, or upload a user's own data, The results of the membership determination can be sent via Simple Application Messaging Protocol (SAMP) to Virtual Observatory (VO) tools such as Tool for OPerations on Catalogues And Tables (TOPCAT), We apply Clusterix 2,0 to several open clusters with different properties and environments to show the capabilities of the tool: an area of live degrees radius around NGC 2682 (M67), an old, well-known cluster; a young cluster NGC 2516 with a striking elongated structure extended up to four degrees; NGC 1750 and NGC 1758, a pair of partly overlapping clusters; the area of NGC 1817, where we confirm a little-known cluster, Juchert 23; and an area with many clusters, where we disentangle two overlapping clusters situated where only one was previously known: Ruprecht 26 and the new CLUSTERIX 1.