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.
