A novel look at energy equipartition in globular clusters
  Two-body interactions play a major role in shaping the structural and
dynamical properties of globular clusters (GCs) over their long-term evolution.
In particular, GCs evolve toward a state of partial energy equipartition that
induces a mass-dependence in their kinematics. By using a set of Monte Carlo
cluster simulations evolved in quasi-isolation, we show that the stellar mass
dependence of the velocity dispersion $\sigma(m)$ can be described by an
exponential function $\sigma^2\propto \exp(-m/m_\mathrm{eq})$, with the
parameter $m_\mathrm{eq}$ quantifying the degree of partial energy
equipartition of the systems. This simple parametrization successfully captures
the behaviour of the velocity dispersion at lower as well as higher stellar
masses, that is, the regime where the system is expected to approach full
equipartition. We find a tight correlation between the degree of equipartition
reached by a GC and its dynamical state, indicating that clusters that are more
than about 20 core relaxation times old, have reached a maximum degree of
equipartition. This equipartition$-$dynamical state relation can be used as a
tool to characterize the relaxation condition of a cluster with a kinematic
measure of the $m_\mathrm{eq}$ parameter. Vice versa, the mass-dependence of
the kinematics can be predicted knowing the relaxation time solely on the basis
of photometric measurements. Moreover, any deviations from this tight relation
could be used as a probe of a peculiar dynamical history of a cluster. Finally,
our novel approach is important for the interpretation of state-of-the-art
Hubble Space Telescope proper motion data, for which the mass dependence of
kinematics can now be measured, and for the application of modeling techniques
which take into consideration multi-mass components and mass segregation.
