Enlightening the dynamical evolution of Galactic open clusters: an approach using Gaia DR3 and analytical descriptions $-$ Supplementary Material

Abstract

Most stars in our Galaxy form in stellar aggregates, which can become long-lived structures called open clusters (OCs). Along their dynamical evolution, their gradual depletion leave some imprints on their structure. In this work, we employed astrometric, photometric and spectroscopic data from the Gaia DR3 catalogue to uniformly characterize a sample of 60 OCs. Structural parameters (tidal, core and half-light radii, respectively, $r_{t}$, $r_{c}$ and $r_{h}$), age, mass ($M_{\textrm{clu}}$), distance, reddening, besides Jacobi radius ($R_{J}$) and half-light relaxation time ($t_{rh}$), are derived from radial density profiles and astrometrically decontaminated colour-magnitude diagrams. Ages and Galactocentric distances ($R_{G}$) range from 7.2$\,\lesssim\,$log($t.$yr^-1)$\,\lesssim\,$9.8 and 6$\,\lesssim\,R_{G}$(kpc)$\,\lesssim\,$12. Analytical expressions derived from $N$-body simulations, taken from the literature, are also employed to estimate the OC initial mass ($M_{\textrm{ini}}$) and mass loss due to exclusively dynamical effects. Both $r_{c}$ and the tidal filling ratio, $r_{h}/R_{J}$, tend to decrease with the dynamical age (=$t/t_{rh}$), indicating the shrinking of the OCs’ internal structure as consequence of internal dynamical relaxation. This dependence seems differentially affected by the external tidal field, since OCs at smaller $R_{G}$ tend to be dynamically older and have smaller $M_{\textrm{clu}}/M_{\textrm{ini}}$ ratios. In this sense, for $R_{G}\lesssim 8\,$kpc, the $r_{h}/R_{J}$ ratio presents a slight positive correlation with $R_{G}$. Beyond this limit, there is a dichotomy in which more massive OCs tend to be more compact and therefore less subject to tidal stripping in comparison to those less massive and looser OCs at similar $R_{G}$. Besides, the $r_{t}/R_{J}$ ratio also tends to correlate positively with $R_{G}$.