Using GMM in open cluster membership: An insight

The unprecedented precision of Gaia has led to a paradigm shift in membership determination of open clusters where a variety of machine learning (ML) models can be employed. In this paper, we apply the unsupervised Gaussian Mixture Model (GMM) to a sample of thirteen clusters with varying ages ($logt\approx$ 6.38-9.64) and distances (441-5183 pc) from Gaia DR3 data to determine membership. We use ASteca to determine parameters for the clusters from our revised membership data. We define a quantifiable metric Modified Silhouette Score (MSS) to evaluate its performance. We study the dependence of MSS on age, distance, extinction, galactic latitude and longitude, and other parameters to find the particular cases when GMM seems to be more efficient than other methods. We compared GMM for nine clusters with varying ages but we did not find any significant differences between GMM performance for younger and older clusters. But we found a moderate correlation between GMM performance and the cluster distance, where GMM works better for closer clusters. We find that GMM does not work very well for clusters at distances larger than 3 kpc.