A family picture: tracing the dynamical path of the structural properties of multiple populations in globular clusters

We studied the spatial distributions of multiple stellar populations (MPs) in a sample of 20 globular clusters (GCs) spanning a broad range of dynamical ages. The differences between first-population (FP) and second-population (SP) stars were measured by means of the parameter $A^+$, defined as the area enclosed between their cumulative radial distributions. We provide the first purely observational evidence of the dynamical path followed by MPs from initial conditions toward a complete FP-SP spatial mixing. Less dynamically evolved clusters have SP stars more centrally concentrated than FPs, while in more dynamically evolved systems the spatial differences between FP and SP stars decrease and eventually disappear. By means of an appropriate comparison with a set of numerical simulations, we show that these observational results are consistent with the evolutionary sequence expected by the long-term dynamical evolution of clusters forming with an initially more centrally concentrated SP sub-system. This result is further supported by the evidence of a trend between $A^+$ and the stage of GC dynamical evolution inferred by the ratio between the present-day and the initial mass of the cluster.