Searching for new observational signatures of the dynamical evolution of
  star clusters
  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 star cluster dynamical evolution. 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 the tridimensional half-mass radius (R<0.5 rh),
finding that its morphology varies in time according to the cluster's dynamical
stage. To quantify these changes we defined three parameters: A5, the area
subtended by the nCRD within 5% of the half-mass radius, P5, the value of the
nCRD measured at the same distance, and S2.5, the slope of the straight line
tangent to the nCRD measured at R=2.5% rh. 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 the paper suggest that
these three observable parameters are very promising empirical tools to
identify the star cluster's dynamical stage from observational data.
