Relaxation-limited evaporation of globular clusters

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.