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

N. Sánchez, E. J. Alfaro, F. López Martínez

Abstract
We propose a method for calculating the radius of an open cluster in an objective way from an astrometric catalogue containing, at least, positions and proper motions. It uses the minimum spanning tree in the proper motion space to discriminate cluster stars from field stars and it quantifies the strength of the cluster-field separation by means of a statistical parameter defined for the first time in this paper. This is done for a range of different sampling radii from where the cluster radius is obtained as the size at which the best cluster-field separation is achieved. The novelty of this strategy is that the cluster radius is obtained independently of how its stars are spatially distributed. We test the reliability and robustness of the method with both simulated and real data from a well-studied open cluster (NGC 188), and apply it to UCAC4 data for five other 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 Collinder 471 showed more than one possible solution, but it is not possible to know whether this is due to the involved uncertainties or due to the presence of complex patterns in their proper motion distributions, something that could be inherent to the physical object or due to the way in which the catalogue was sampled.

Keywords
stars: kinematics and dynamics; open clusters and associations: general; open clusters and associations: individual: ASCC 19; open clusters and associations: individual: Collinder 471; open clusters and associations: individual: NGC 1647; open clusters an

Monthly Notices of the Royal Astronomical Society
Volume 475, Issue 3, Page 4122
2018 April

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Instituto de Astrofísica e Ciências do Espaço Universidade do Porto Faculdade de Ciências da Universidade de Lisboa
Fundação para a Ciência e a Tecnologia COMPETE 2020 PORTUGAL 2020 União Europeia