Determination of dynamical ages of open clusters through the A$^+$ parameter -- II

TL;DR

This study extends the use of the A+ parameter to estimate the dynamical ages of 23 open clusters using Gaia data, revealing diverse evolutionary stages and identifying the most and least evolved clusters.

Contribution

It applies the A+ parameter methodology to open clusters with Gaia data, classifies their dynamical stages, and compares their evolution to globular clusters, expanding previous research.

Findings

Open clusters show a wide range of dynamical ages.

NGC 2682 and King 2 are highly evolved clusters.

Berkeley 18 is the least evolved open cluster.

Abstract

Blue straggler stars (BSS), one of the most massive members of star clusters, have been used for over a decade to investigate mass segregation and estimate the dynamical ages of globular clusters (GCs) and open clusters (OCs). This work is an extension of our previous study, in which we investigated a correlation between theoretically estimated dynamical ages and the observed $A^+_{\mathrm{rh}}$ values, which represent the sedimentation level of BSS with respect to the reference population. Here, we use the ML-MOC algorithm on \textit{Gaia} EDR3 data to extend this analysis to 23 OCs. Using cluster properties and identified members, we estimate their dynamical and physical parameters. In order to estimate the $A^+_{\mathrm{rh}}$ values, we use the main sequence and main sequence turnoff stars as the reference population. OCs are observed to exhibit a wide range of degrees of dynamical evolution, ranging from dynamically young to late stages of intermediate dynamical age. Hence, we classify OCs into three distinct dynamical stages based on their relationship to $A^+_{\mathrm{rh}}$ and $N_{\text{relax}}$. NGC 2682 and King 2 are discovered to be the most evolved OCs, like Familly III GCs, while Berkeley 18 is the least evolved OC. Melotte 66 and Berkeley 31 are peculiar OCs because none of their dynamical and physical parameters correlate with their BSS segregation levels.