由恒星自行确定疏散星团半径的一种方法
A method for determining the radius of an open cluster from stellar proper motions
摘要：
本文提出了一种从至少包含位置和自行的天体测量星表中客观地计算疏散星团半径的方法。它利用自行空间中的最小生成树（Minimum Spanning Tree，以下简称MST）来区分星团星和场星，并首次定义了一个统计参数来量化星团-场分离的强度。这是针对一系列不同的采样半径来完成的，从这些采样半径中获得簇半径作为实现最佳簇场分离的大小。这种策略的新颖之处在于，星团半径的获得与恒星的空间分布无关。我们测试的可靠性和鲁棒性的方法与模拟和真实的数据，从一个良好的研究疏散星团（NGC 188），并将其应用到UCAC 4数据的其他五个疏散星团具有不同的编目半径值。NGC 188、NGC 1647、NGC 6603和Ruprecht 155的半径值分别为15.2+/-1.8，29.4 +/-3.4，4.2 +/-1.7和7.0+/-0.3弧分。ASCC 19和Collinder 471显示了不止一种可能的解决方案，但不可能知道这是由于所涉及的不确定性，还是由于它们的自行分布中存在复杂的模式，这可能是物理对象固有的，或者由于目录采样的方式。
英文摘要：
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 (hereinafter MST) 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 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.
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