Decoding Morphological Evolution of Open Clusters

Base on {\it Gaia} Second Data Release and the combination of nonparametric bivariate density estimation with the least square ellipse fitting, we derive the shape parameters of the sample clusters. By analyzing the dislocation of the sample clusters, 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 $e_{pm}$~$\geq$~0.4 presents an aggregate distribution in the range of -45$\degr$ to 45$\degr$, 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 deform itself 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\%~$\pm$~9\%. This possibly implies a uniform external environment in the range of $|$H$|$~$\leq$~300~pc if the sample completeness of each group is not taken into account.