Title:Structural parameters, chronological age and dynamical age of the LMC globular cluster NGC 1754

Abstract:In the context of a new systematic study of the properties of the most compact and massive star clusters in the Large Magellanic Cloud (LMC), here we present the determination of the chronological age, the structural parameters, and the dynamical age of NGC 1754. We used high-resolution images taken with the WFC3/HST instrument, both in optical and near-ultraviolet filters. The high quality of the images made it possible to construct the star density profile from resolved star counts, and to fit the observed profile with an appropriate King model to obtain the structural parameters (e.g. core, half-mass, and tidal radii). Our findings confirm that NGC 1754 is a very compact globular cluster with a core radius of only 0.84 pc. The analysis of the same dataset allowed us to confirm a very old age ($t=12.8\pm0.4$ Gyr) for this system, thus further consolidating the indication that the process of globular cluster formation started at the same cosmic time both in the LMC and in the Milky Way, independently of the characteristics of the host environment. We have also used the empirical method called ``dynamical clock'' to estimate the dynamical age of the system. This consists of quantifying the degree of central segregation of blue straggler stars (BSSs) using the $A^+_{rh}$ parameter, which is defined as the area enclosed between the cumulative radial distribution of BSSs and that of a reference (lighter) population. This method yielded a value of $A^+_{rh}=0.31\pm0.07$, which is the highest measured so far for LMC clusters, pointing to an advanced dynamical age for the cluster, possibly on the verge of core collapse. The results presented here for NGC 1754 confirm that the natural dynamical evolution of globular clusters plays a role in shaping the age-core radius distributions observed in the LMC.