SIMBAD references

Context. The properties of open clusters such as metallicity, age, and morphology are useful tools in studies of the dynamic evolution of open clusters. The morphology of open clusters can help us better understand the evolution of such structures.
Aims. We aim to analyze the morphological evolution of 1256 open clusters by combining the shapes of the sample clusters in the proper motion space with their morphology in the two-dimensional spherical Galactic coordinate system, providing their shape parameters based on a member catalog derived from Gaia Second Data Release as well as data from the literature.
Methods. We applied a combination of a nonparametric bivariate density estimation with the least square ellipse fitting to derive the shape parameters of the sample clusters.
Results. We derived the shape parameters of the sample clusters in the two-dimensional spherical Galactic coordinate system and that of the proper motion space. By analyzing the dislocation of the sample clusters, we find that the dislocation, d, is related to the X-axis pointing toward the Galactic center, Y-axis pointing in the direction of Galactic rotation, and the Z-axis (log(|H|/pc)) that is positive toward the Galactic north pole. This finding underlines the important role of the dislocation of clusters in tracking the external environment of the Milky Way. The orientation (q_pm) of the clusters, with e_pm ≥ 0.4, presents an aggregate distribution in the range of -45° to 45°, comprising about 74% of them. This probably suggests that these clusters tend to deform heavily in the direction of the Galactic plane. NGC 752 is in a slight stage of expansion in the two-dimensional space and will become deformed, in terms of its morphology, along the direction perpendicular to the original stretching direction in the future if no other events occur. The relative degree of deformation of the sample clusters in the short-axis direction decreases as their ages increase. On average, the severely distorted sample clusters in each group account for about 26% ± 9%. This possibly implies a uniform external environment in the range of |H| ≥ 300 pc if the sample completeness of each group is not taken into account.