Revisiting relaxation in globular clusters

TL;DR

This paper revisits the theory of relaxation in globular clusters, proposing the Balescu-Lenard equation as a more rigorous alternative to classical theory, highlighting the role of self-gravity and collective fluctuations.

Contribution

It adapts the Balescu-Lenard equation to spherical clusters and compares its predictions with classical theory, revealing significant differences in relaxation flux estimates.

Findings

Balescu-Lenard fluxes differ markedly from classical fluxes.

Classical theory underestimates the impact of collective fluctuations.

Relaxation behavior varies with orbital anisotropy.

Abstract

The classical theory of cluster relaxation is unsatisfactory because it involves the Coulomb logarithm. The Balescu-Lenard (BL) equation provides a rigorous alternative that has no ill-defined parameter. Moreover, the BL equation, unlike classical theory, includes the cluster's self-gravity. A heuristic argument is given that indicates that relaxation does not occur predominantly through two-particle scattering and is enhanced by self-gravity. The BL equation is adapted to a spherical system and used to estimate the flux through the action space of isochrone clusters with different velocity anisotropies. A range of fairly different secular behaviours is found depending on the fraction of radial orbits. Classical theory is also used to compute the corresponding classical fluxes. The BL and classical fluxes are very different because (a) the classical theory materially under-estimates the impact of large-scale collectively amplified fluctuations and (b) only the leading terms in an infinite sum for the BL flux are computed. A complete theory of cluster relaxation likely requires that the sum in the BL equation be decomposed into a sum over a finite number of small wavenumbers complemented by an integral over large wavenumbers analogous to classical theory.