2022ApJ...926..118B

We present a numerical study, based on Monte Carlo simulations, aimed at defining new empirical parameters measurable from observations and able to trace the different phases of the dynamical evolution of star clusters. As expected, a central density cusp, deviating from the King model profile, develops during the core collapse (CC) event. Although the slope varies during the post-CC oscillations, the cusp remains a stable feature characterizing the central portion of the density profile in all post-CC stages. We then investigate the normalized cumulative radial distribution (nCRD) drawn by all the cluster stars included within one half of the tridimensional half-mass radius (R <= 0.5r _ h _), finding that its morphology varies in time according to the cluster's dynamical stage. To quantify these changes we defined three parameters: A ₅, the area subtended by the nCRD within 5% of the half-mass radius, P ₅, the value of the nCRD measured at the same distance, and S _2.5, the slope of the straight line tangent to the nCRD measured at R = 2.5%r _ h _. The three parameters evolve similarly during the cluster's dynamical evolution: after an early phase in which they are essentially constant, their values rapidly increase, reaching their maximum at the CC epoch and slightly decreasing in the post-CC phase, when their average value remains significantly larger than the initial one, in spite of some fluctuations. The results presented in this paper suggest that these three observable parameters are very promising empirical tools to identify the star cluster's dynamical stage from observational data.