An Innovative Technique for Membership Identification in Open Star Clusters, Integrating pyUPMASK with the King Model

The probability cut-off threshold value represents one of the most substantial challenges in the study of open star clusters, notwithstanding its vital significance. There is ongoing debate on this matter, with some authors using a 50% value and others using a 70% value. Moreover, the probability cut-off threshold is altered even when only the field of view is modified, even when the same technique is used for the same cluster. So, we introduce a straightforward method that combines the probability with the King model. For every radial shell or ring, we assess the probability of yielding a number of stars that matches the number of stars estimated by the King model. This signifies that there is a probability threshold at each radius, rather than a single threshold that is applicable to the entire cluster. In this research, we utilized the pyUPMASK Python package alongside six distinct clustering algorithms. Each of these algorithms has been integrated with the King model, as previously mentioned. We employed our previous Gaia DR3 study of NGC 2158 as a case analysis to evaluate our methodology. Our key conclusion reveals that, initially, the Voronoi and HDBSCAN clustering algorithms exhibit significantly faster performance relative to other algorithms, requiring only minimal execution time. In contrast, the K-means and Gaussian Mixture Models are considerably slower, necessitating a longer execution time. Secondly, each method, when combined with the King model as mentioned earlier, yields identical values for the parameters of the NGC 2158 cluster, such as proper motion, distance, parallax, age, and others.