3D projection analysis: Characterizing the morphological stability of nearby open clusters

Context. The study of open cluster morphology is pivotal for exploring their formation and evolutionary processes.Aims. We manage to assess the morphological stability of 105 nearby open clusters within tidal radii on the X-Y, X-Z, and Y-Z planes of the heliocentric Cartesian coordinate system, utilizing member catalogs from the literature. Meanwhile, we also delve into factors potentially impacting the clusters’ morphological stability on these projection planes.Methods. We used the rose diagram method by constructing the 3D projected morphology of sample clusters to quantify the morphological stability of their 3D projected morphology.Results. Our analysis indicates there is a demonstrated linear positive correlation between the number of sample clusters’ member stars within tidal radii and their morphological stability in different 3D projection planes. This may suggest that the more member stars there are within the tidal radius of a cluster, the stronger its own gravitational binding capacity is, resulting in strong morphological stability. We find a direct link between the clusters’ morphological stabilities in the X-Z plane within tidal radii and their velocity dispersion in the same plane, suggesting that the morphological stabilities in the X-Z plane may be dependent on internal dynamics. Moreover, the morphological stability of the clusters’ 3D projection is influenced by their spatial positions along the Y axis, but not linearly, indicating that the environmental changes at the clusters’ location may affect their morphological stability. Likewise, specific external forces can have an effect on their morphological stability.Conclusions. This research introduces a novel perspective for understanding the morphological stability of open clusters, with a particular focus on their 3D projected morphologies.