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

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 (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.

arXiv comment12 pages including 14 figures and 1 table. Accepted for publication in MNRAS

References in corpus (37)

• The VizieR database of Astronomical Catalogues
• The Fourth US Naval Observatory CCD Astrograph Catalog (UCAC4)
• New catalogue of optically visible open clusters and candidates
• The PPMXL catalog of positions and proper motions on the ICRS. Combining USNO-B1.0 and 2MASS
• A Spitzer Survey of Young Stellar Clusters within One Kiloparsec of the Sun: Cluster Core Extraction and Basic Structural Analysis
• Global survey of star clusters in the Milky Way II. The catalogue of basic parameters
• Astrophysical parameters of Galactic open clusters
• The statistical Analysis of Star Clusters
• UPMASK: unsupervised photometric membership assignment in stellar clusters
• Direct determination of the spiral pattern rotation speed of the Galaxy
• Clustered and Triggered Star Formation in W5: Observations with Spitzer
• 109 new Galactic open clusters
• ASteCA - Automated Stellar Cluster Analysis
• Evolving structures of star-forming clusters
• The spatial distribution of stars in open clusters
• Global survey of star clusters in the Milky Way I. The pipeline and fundamental parameters in the second quadrant
• The structures of embedded clusters in the Perseus, Serpens and Ophiuchus molecular clouds
• Towards absolute scales of radii and masses of open clusters
• Spatial dependence of 2MASS luminosity and mass functions in the old open cluster NGC 188
• Cluster membership probabilities from proper motions and multiwavelength photometric catalogues: I. Method and application to the Pleiades cluster
• Structure and mass segregation in Galactic stellar clusters
• A Multi-Membership Catalogue for 1876 Open Clusters using UCAC4 data
• A Census of Large-Scale ($\ge$ 10 pc), Velocity-Coherent, Dense Filaments in the Northern Galactic Plane: Automated Identification Using Minimum Spanning Tree
• On the recent star formation history of the Milky Way disk
• Observational constraints on star cluster formation theory - I. The mass-radius relation
• A comparative study on the reliability of open cluster parameters
• Statistical fractal analysis of 25 young star clusters
• Statistical comparison of clouds and star clusters
• Open clusters and associations in the Gaia era
• ${\mathcal{Q}}^{+}$: Characterising the structure of young star clusters
• 2MASS photometry and kinematical studies of open cluster NGC 188
• Looking for phase-space structures in star-forming regions: An MST-based methodology
• Cluster radius and sampling radius in the determination of cluster membership probabilities
• Source clustering in the Hi-GAL survey determined using a minimum spanning tree method
• NGC 2548: clumpy spatial and kinematic structure in an intermediate-age galactic cluster
• PPMXL photometric study of four open cluster candidates (Ivanov 2, Ivanov 7, Ivanov 9 and Harvard 9)
• Improved proper motion determinations for 15 open clusters based on the UCAC4 catalog

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• A Gaia DR2 view of the Open Cluster population in the Milky Way
• Clusters and mirages: cataloguing stellar aggregates in the Milky Way
• A catalogue of open cluster radii determined from Gaia proper motions
• Visualizing the pulsar population using graph theory
• Exploration of morphological coherence in open clusters with a "core-shell'' structure
• Study of the open cluster Alessi-Teutsch 9 (ASCC 10) using multiband photometry and Gaia EDR3