Resonant and non-resonant relaxation of globular clusters

Abstract

ABSTRACT 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 time-scales. 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’ (NR). 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’ (RR). In this paper, we consider a model globular cluster represented by a spherical, isotropic isochrone DF, and compare in detail the predictions of both RR and NR 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 RR and NR theories predict the correct morphology for the secular evolution of the cluster’s DF, although the NR theory overestimates the amplitude of the relaxation rate by a factor of ∼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 ℓ = 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 RR and NR theories.