Dependence of the old star clusters' dynamical clock on the host galaxy gravitational field

I report outcomes of the analysis of the $A^+$ parameter, which measures the level of radial segregation of blue straggler stars in old star clusters, commonly known as the dynamical clock for the long-term internal dynamical evolution. I used $A^+$ values available in the literature for 48 Milky Way globular clusters. I found that the relationship of $A^+$ and the number of central relaxation times which have elapsed ($N_{relax}$) shows a non negligible dependence on the strength of the host galaxy gravitational potential, in addition to depending on the two-body relaxation mechanism. Indeed, a measured $A^+$ value corresponds to relatively smaller or larger $N_{relax}$ values for star clusters located farther or closer to the galaxy center. From an observational point of view, this finding reveals the possibility of disentangling for the first time the dynamical evolutionary stage due to two-body relaxation and tidal effect, that affect the whole star clusters' body concurrently.