Correlation between mass segregation and structural concentration in relaxed stellar clusters

Abstract The level of mass segregation in the core of globular clusters has been previously proposed as a potential indicator of the dynamical constituents of the system, such as presence of a significant population of stellar-mass black holes (BHs), or even a central intermediate-mass black hole (IMBH). However, its measurement is limited to clusters with high-quality Hubble Space Telescope data. Thanks to a set of state-of-the-art direct N-body simulations with up to 200k particles inclusive of stellar evolution, primordial binaries, and varying BH/neutron stars, we highlight for the first time the existence of a clear and tight linear relation between the degree of mass segregation and the cluster structural concentration index. The latter is defined as the ratio of the radii containing 5 per cent and 50 per cent of the integrated light (R5/R50), making it robustly measurable without the need to individually resolve low-mass stars. Our simulations indicate that given R5/R50, the mass segregation Δm (defined as the difference in main-sequence median mass between centre and half-light radius) is expressed as Δm/M⊙ = −1.166R5/R50 + 0.3246, with a root-mean-square error of 0.0148. In addition, we can explain its physical origin and the values of the fitted parameters through basic analytical modelling. Such correlation is remarkably robust against a variety of initial conditions (including presence of primordial binaries and IMBHs) and cluster ages, with a slight dependence in best-fitting parameters on the prescriptions used to measure the quantities involved. Therefore, this study highlights the potential to develop a new observational tool to gain insight on the dynamical status of globular clusters and on its dark remnants.