Dynamical Evolution of Four Old Galactic Open Clusters Traced by Their Constituent Stars with Gaia DR3

We investigate the evolutionary stages of four open clusters Berkeley 39, Collinder 261, NGC 6819, and NGC 7789 of ages ranging from 1.6 to 6 Gyr. These clusters have previously been classified into dynamically young and intermediate age groups based on the segregation level of BSS with respect to red-giant-branch stars and mainsequence stars, respectively. We identify members of these four clusters using the ML-MOC algorithm on Gaia DR3 data. To examine the relative segregation of cluster members of different evolutionary stages, we utilize cumulative radial distributions, proper motion distributions, and spatial distributions in galactocentric coordinates. Our analysis shows that Berkeley 39 and NGC 6819 exhibit moderate signs of population-wise segregation from evolved to less-evolved members. NGC 7789 shows signs of mass segregation only in the cumulative radial distributions. On the other hand, Collinder 261 exhibits high segregation of BSS in the cumulative radial distribution, while other populations show the same level of segregation.