Decoding the morphological evolution of open clusters

The morphology of open clusters can help us better understand the evolution of such structures. 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.

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. 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.