Diffusion and mixing in globular clusters

TL;DR

This paper distinguishes between diffusion and mixing timescales in globular clusters, showing their variation and convergence behavior through simulations, which refines understanding of stellar orbital evolution.

Contribution

It introduces a clear distinction between diffusion times and mixing times in globular clusters and quantifies their relation to the half-mass relaxation time.

Findings

Diffusion timescales vary by a factor of 10-100 around the relaxation time.

Mixedness converges exponentially with a decay timescale about 10 times the relaxation time.

More than 20% of stars have diffusion times significantly different from the relaxation time.

Abstract

Collisional relaxation describes the stochastic process with which a self-gravitating system near equilibrium evolves in phase space due to the fluctuating gravitational field of the system. The characteristic timescale of this process is called the relaxation time. In this paper, we highlight the difference between two measures of the relaxation time in globular clusters: (i) the diffusion time with which the isolating integrals of motion (i.e. energy E and angular momentum magnitude L) of individual stars change stochastically and (ii) the asymptotic timescale required for a family of orbits to mix in the cluster. More specifically, the former corresponds to the instantaneous rate of change of a star's E or L, while the latter corresponds to the timescale for the stars to statistically forget their initial conditions. We show that the diffusion timescales of E and L vary systematically around the commonly used half-mass relaxation time in different regions of the cluster by a factor of ~10 and ~100, respectively, for more than 20% of the stars. We define the mixedness of an orbital family at any given time as the correlation coefficient between its E or L probability distribution functions and those of the whole cluster. Using Monte Carlo simulations, we find that mixedness converges asymptotically exponentially with a decay timescale that is ~10 times the half-mass relaxation time.