Resonant and non-resonant relaxation of globular clusters
  Globular clusters contain a finite number of stars. As a result, they
inevitably undergo secular evolution (`relaxation') causing their mean
distribution function (DF) to evolve on long timescales. On one hand, this
long-term evolution may be interpreted as driven by the accumulation of local
deflections along each star's mean field trajectory -- so-called `non-resonant
relaxation'. On the other hand, it can be thought of as driven by non-local,
collectively dressed and resonant couplings between stellar orbits, a process
termed `resonant relaxation'. In this paper we consider a model globular
cluster represented by a spherical, isotropic isochrone DF, and compare in
detail the predictions of both resonant and non-resonant relaxation theories
against tailored direct $N$-body simulations. In the space of orbital actions
(namely the radial action and total angular momentum), we find that both
resonant and non-resonant theories predict the correct morphology for the
secular evolution of the cluster's DF, although non-resonant theory
over-estimates the amplitude of the relaxation rate by a factor ${\sim 2}$. We
conclude that the secular relaxation of hot isotropic spherical clusters is not
dominated by collectively amplified large-scale potential fluctuations, despite
the existence of a strong ${\ell = 1}$ damped mode. Instead, collective
amplification affects relaxation only marginally even on the largest scales.
The predicted contributions to relaxation from smaller scale fluctuations are
essentially the same from resonant and non-resonant theories.
