Resonant relaxation in globular clusters

Abstract

Resonant relaxation has been discussed as an efficient process that changes the angular momenta of stars orbiting around a central supermassive black hole due to the fluctuating gravitational field of the stellar cluster. Other spherical stellar systems, such as globular clusters, exhibit a restricted form of this effect where enhanced relaxation rate only occurs in the directions of the angular momentum vectors, but not in their magnitudes; this is called vector resonant relaxation (VRR). To explore this effect, we performed a large set of direct N-body simulations, with up to 512k particles and ~500 dynamical times. Contrasting our simulations with Spitzer-style Monte Carlo simulations, that by design only exhibit 2-body relaxation, we show that the temporal behavior of the angular momentum vectors in $N$-body simulations cannot be explained by 2-body relaxation alone. VRR operates efficiently in globular clusters with $N>10^4$. The fact that VRR operates in globular clusters may open way to use powerful tools in statistical physics for their description. In particular, since the distribution of orbital planes relaxes much more rapidly than the distribution of the magnitude of angular momentum and the radial action, the relaxation process reaches an internal statistical equilibrium in the corresponding part of phase space while the whole cluster is generally out of equilibrium, in a state of quenched disorder. We point out the need to include effects of VRR in Monte Carlo simulations of globular clusters.