New Parameters for Star Cluster Dynamics: The Role of Clusters' Initial Conditions

We recently introduced three new parameters that describe the shape of the normalized cumulative radial distribution (nCRD) of the innermost stars in globular clusters (GCs) and trace the clusters' dynamical evolution. Here, we extend our previous investigations to the case of a large set of Monte Carlo simulations of GCs, started from a broad range of initial conditions. All the models are analyzed at the same age of 13 Gyr when they have reached different evolutionary phases. The sample of models is well representative of the structural properties of the observed population of Galactic GCs. We confirm that the three nCRD parameters are powerful tools to distinguish systems in the early stages of dynamical evolution from those that have already experienced core collapse. They might also help disentangle clusters hosting a low-mass intermediate-mass black hole of a few hundred solar masses from cases with large concentrations of dark remnants in their centers. With respect to other dynamical indicators, the nCRD parameters offer the advantage of being fully empirical and easier to measure from observational data.