  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% and 50% of the integrated light ($R_5/R_\mathrm{50}$), making it
robustly measurable without the need to individually resolve low-mass stars.
Our simulations indicate that given $R_5/R_\mathrm{50}$, the mass segregation
$\Delta m$ (defined as the difference in main sequence median mass between
center and half-light radius) is expressed as $\Delta m/M_\odot = -1.166
R_5/R_\mathrm{h} + 0.3246$, 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 modeling. 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-fit 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.
