Diffusion and mixing in globular clusters
  Collisional relaxation describes the stochastic process with which a
self-gravitating system near equilibrium evolves in phase space due to the
fluctuating gravitational field of the system. The characteristic timescale of
this process is called the relaxation time. In this paper, we highlight the
difference between two measures of the relaxation time in globular clusters:
(i) the diffusion time with which the isolating integrals of motion (i.e.
energy E and angular momentum magnitude L) of individual stars change
stochastically and (ii) the asymptotic timescale required for a family of
orbits to mix in the cluster. More specifically, the former corresponds to the
instantaneous rate of change of a star's E or L, while the latter corresponds
to the timescale for the stars to statistically forget their initial
conditions. We show that the diffusion timescales of E and L vary
systematically around the commonly used half-mass relaxation time in different
regions of the cluster by a factor of ~10 and ~100, respectively, for more than
20% of the stars. We define the mixedness of an orbital family at any given
time as the correlation coefficient between its E or L probability distribution
functions and those of the whole cluster. Using Monte Carlo simulations, we
find that mixedness converges asymptotically exponentially with a decay
timescale that is ~10 times the half-mass relaxation time.
