Resonant and non-resonant relaxation of globular clusters

TL;DR

This paper compares resonant and non-resonant relaxation theories in globular clusters using a spherical isotropic model and N-body simulations, finding both theories predict similar evolution morphology but differ in amplitude estimates.

Contribution

It provides a detailed comparison of resonant and non-resonant relaxation predictions against simulations, highlighting their similarities and differences in globular cluster evolution.

Findings

Both theories predict correct DF evolution morphology.

Non-resonant theory overestimates relaxation rate amplitude by ~2.

Collective amplification has minimal impact on relaxation.

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 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.