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We present a numerical study, based on Monte Carlo simulations, aimed atdefining new empirical parameters measurable from observations and able totrace the different phases of star cluster dynamical evolution. As expected, acentral density cusp, deviating from the King model profile, develops duringthe core collapse (CC) event. Although the slope varies during the post-CCoscillations, the cusp remains a stable feature characterizing the centralportion of the density profile in all post-CC stages. We then investigate thenormalized cumulative radial distribution (nCRD) drawn by all the cluster starsincluded within one half the tridimensional half-mass radius (R<0.5 rh),finding that its morphology varies in time according to the cluster's dynamicalstage. To quantify these changes we defined three parameters: A5, the areasubtended by the nCRD within 5% of the half-mass radius, P5, the value of thenCRD measured at the same distance, and S2.5, the slope of the straight linetangent to the nCRD measured at R=2.5% rh. The three parameters evolvesimilarly during the cluster's dynamical evolution: after an early phase inwhich they are essentially constant, their values rapidly increase, reachingtheir maximum at the CC epoch and slightly decreasing in the post-CC phase,when their average value remains significantly larger than the initial one, inspite of some fluctuations. The results presented in the paper suggest thatthese three observable parameters are very promising empirical tools toidentify the star cluster's dynamical stage from observational data.

Searching for new observational signatures of the dynamical evolution of star clusters