Probing the physics of dense stellar systems in the Large Magellanic Cloud

In the context of studies of star clusters in the Large Magellanic Cloud (LMC), we investigated the long-standing size–age conundrum, characterized by the fact that young clusters are all compact while old systems display a broad range of core radii despite comparable chronological ages. To explore its origin, we analyzed the massive, old, and compact clusters NGC 1835, NGC 1754, and NGC 1916. We performed a homogeneous analysis of high-resolution Hubble Space Telescope observations, constructing deep color–magnitude diagrams and star-count density profiles, deriving structural parameters through King-model fits, and estimating chronological ages via isochrone fitting. We then applied the “dynamical clock” method, which exploits the radial distribution of blue straggler stars (BSSs), whose degree of mass segregation, quantified by the parameter A+, provides a fully empirical measure of dynamical age. The results confirm that NGC 1835, NGC 1754, and NGC 1916 are extremely compact clusters, with core radii of 0.84 pc, 0.84 pc, and 0.46 pc, respectively, and very short central relaxation times, indicating advanced dynamical states. For NGC 1835 and NGC 1754, the measured A+ values (0.30 and 0.31) are among the largest found in LMC clusters, providing clear evidence of strong mass segregation. Both systems follow the correlation between A+ and central relaxation time and the anti-correlation between A+ and core radius defined by Galactic and Magellanic Cloud clusters. For NGC 1916, A+ could not be reliably determined because of contamination and incompleteness, and its dynamical age was therefore inferred solely from the central relaxation time. These findings indicate that the observed spread of core radii among old LMC clusters reflects differences in their internal dynamical evolution, with the most compact systems being the most dynamically evolved, thereby providing a natural explanation for the size–age conundrum.