Non-resonant relaxation of anisotropic globular clusters

TL;DR

This paper adapts Chandrasekhar's non-resonant relaxation theory to anisotropic globular clusters, demonstrating its effectiveness in predicting orbital diffusion and isotropization, with implications for understanding cluster evolution.

Contribution

The study explicitly tailors non-resonant relaxation theory to anisotropic clusters and compares it with N-body simulations, highlighting its accuracy and limitations.

Findings

NR theory accurately predicts orbital diffusion in anisotropic clusters

Isotropization occurs rapidly during initial contraction phases

Long-range resonant relaxation may be needed for extreme anisotropies

Abstract

Globular clusters are dense stellar systems whose core slowly contracts under the effect of self-gravity. The rate of this process was recently found to be directly linked to the initial amount of velocity anisotropy: tangentially anisotropic clusters contract faster than radially anisotropic ones. Furthermore, initially anisotropic clusters are found to generically tend towards more isotropic distributions during the onset of contraction. Chandrasekhar's "non-resonant" (NR) theory of diffusion describes this relaxation as being driven by a sequence of local two-body deflections along each star's orbit. We explicitly tailor this NR prediction to anisotropic clusters, and compare it with $N$-body realisations of Plummer spheres with varying degrees of anisotropy. The NR theory is shown to recover remarkably well the detailed shape of the orbital diffusion and the associated initial isotropisation, up to a global multiplicative prefactor which increases with anisotropy. Strikingly, a simple effective isotropic prescription provides almost as good a fit, as long as the cluster's anisotropy is not too strong. For these more extreme clusters, accounting for long-range resonant relaxation may be necessary to capture these clusters' long-term evolution.