A method for determining the radius of an open cluster from stellar proper motions

摘要

We propose a method for calculating the radius of an open cluster in anobjective way from an astrometric catalogue containing, at least, positions andproper motions. It uses the minimum spanning tree (hereinafter MST) in theproper motion space to discriminate cluster stars from field stars and itquantifies the strength of the cluster-field separation by means of astatistical parameter defined for the first time in this paper. This is donefor a range of different sampling radii from where the cluster radius isobtained as the size at which the best cluster-field separation is achieved.The novelty of this strategy is that the cluster radius is obtainedindependently of how its stars are spatially distributed. We test thereliability and robustness of the method with both simulated and real data froma well-studied open cluster (NGC 188), and apply it to UCAC4 data for fiveother open clusters with different catalogued radius values. NGC 188, NGC 1647,NGC 6603 and Ruprecht 155 yielded unambiguous radius values of 15.2+/-1.8,29.4+/-3.4, 4.2+/-1.7 and 7.0+/-0.3 arcmin, respectively. ASCC 19 and Collinder471 showed more than one possible solution but it is not possible to knowwhether this is due to the involved uncertainties or to the presence of complexpatterns in their proper motion distributions, something that could be inherentto the physical object or due to the way in which the catalogue was sampled.