Deciphering Star Cluster Evolution by Shape Morphology
  We analyze the morphological evolution of open clusters and provide shape
parameters for 265 open clusters. The results show that the overall shape of
sample clusters becomes more elliptical as they grow older, while their core
remains circular or slightly trend to circularize. There is a negative
correlation of the ellipticities with the number of members of the sample
clusters. A significant negative correlation between the overall ellipticities
and masses is also detected for the sample clusters with log(age/year) $\geq$
8, suggesting that the overall shapes of the clusters are possibly influenced
by the number of members and masses, in addition to the external forces and the
surrounding environment. For most young sample clusters, the radial
stratification degree of the short axis direction is greater than that of the
long, implying that the radial stratification degree in the two directions
within the young sample cluster may be unevenly affected by an internal
evolutionary process. Older sample clusters exhibit lower stratification in the
tangential direction, which possibly means those clusters may continue to
survive for a long time at a low level of stratification. Our analysis shows
that the overall shape of the sample clusters may be more susceptible to the
influence of Galactic tides toward the Galactic center than the shear forces
embedded in Galactic differential rotation. By analyzing the distribution of
the ages and number of members of star clusters, we suggest that NGC 6791 may
originate from superclusters.
