Relaxation-limited evaporation of globular clusters

TL;DR

This paper demonstrates that the evaporation of globular clusters is limited by relaxation processes when the number of stars is large, providing a theoretical framework consistent with simulations and predicting observable stellar stream features.

Contribution

It introduces a relaxation-limited evaporation model for globular clusters, deriving lifetime estimates, tidal sensitivities, and stream morphologies, supported by analytical calculations and simulations.

Findings

Evaporative lifetime approximately 20.5 times the relaxation time.

Derived tidal sensitivity of evaporation time as a function of cluster-to-tidal radius ratio.

Predicted star stream shapes and separations related to orbital parameters.

Abstract

Evaporative evolution of stellar clusters is shown to be relaxation limited when the number of stars satisfies $N>>N_c$, where $N_c\simeq 1600$. For a Maxwell velocity distribution that extends beyond the escape velocity, this process is {\em bright} in that the Kelvin-Helmholtz time scale, $f_H^{-1}t_{relax}$, is shorter than the Ambartsumian-Spitzer time scale, $f_N^{-1}t_{relax}$, where $f_H>f_N$ denote the fractional changes in total energy and number of stars per relaxation time, $t_{relax}$. The resulting evaporative lifetime $t_{ev}\simeq 20.5 t_{relax}$ for isolated clusters is consistent with Fokker-Planck and N-body simulations, where $t_{relax}$ is expressed in terms of the half-mass radius. We calculate the grey body factor by averaging over the anisotropic perturbation of the potential barrier across the tidal sphere, and derive the tidal sensitivity ${d\ln t_{ev}}/{dy}\simeq -1.9$ to -0.7 as a function of the ratio $y$ of the virial-to-tidal radius. Relaxation limited evaporation applies to the majority of globular clusters of the Milky Way with $N=10^4-10^6$ that are in a pre-collapse phase. It drives streams of stars into the tidal field with a mean kinetic energy of 0.71 relative to temperature of the cluster. Their $S$ shape morphology leads in sub-orbital and a trails in super-orbital streams separated by $3.4\sigma/\Omega$ in the radial direction of the orbit, where $\Omega$ denotes the orbital angular velocity and $\sigma$ the stellar velocity dispersion in the cluster. These correlations may be tested by advanced wide field photometry and spectroscopy.