The relation between the mass-to-light ratio and the relaxation state of globular clusters

The internal dynamics of globular clusters (GCs) is strongly affected by two-body interactions that bring the systems to a state of partial energy equipartition. Using a set of Monte Carlo clusters simulations, we investigate the role of the onset of energy equipartition in shaping the mass-to-light ratio (M/L) in GCs. Our simulations show that the M/L profiles cannot be considered constant and their specific shape strongly depends on the dynamical age of the clusters. Dynamically younger clusters display a central peak up to M/L $\simeq25$ $M_\odot/L_\odot$ caused by the retention of dark remnants; this peak flattens out for dynamically older clusters. Moreover, we find that also the global values of M/L correlate with the dynamical state of a cluster quantified as either the number of relaxation times a system has experienced $n_{rel}$ or the equipartition parameter $m_{eq}$: clusters closer to full equipartition (higher $n_{rel}$ or lower $m_{eq}$) display a lower M/L. We show that the decrease of M/L is primarily driven by the dynamical ejection of dark remnants, rather than by the escape of low-mass stars. The predictions of our models are in good agreement with observations of GCs in the Milky Way and M31, indicating that differences in relaxation state alone can explain variations of M/L up to a factor of $\simeq3$. Our characterization of the M/L as a function of relaxation state is of primary relevance for the application and interpretation of dynamical models.