Relaxation-limited evaporation of globular clusters

Maurice H. P. M. van Putten

doi:10.1016/j.newast.2011.11.003

paper

Relaxation-limited evaporation of globular clusters

arXiv:1112.2006 · doi:10.1016/j.newast.2011.11.003

Abstract

Evaporative evolution of stellar clusters is shown to be relaxation limited when the number of stars satisfies $N >> N_{c}$ , where $N_{c} ≃ 1600$ . For a Maxwell velocity distribution that extends beyond the escape velocity, this process is {\em bright} in that the Kelvin-Helmholtz time scale, $f_{H}^{- 1} t_{r e l a x}$ , is shorter than the Ambartsumian-Spitzer time scale, $f_{N}^{- 1} t_{r e l a x}$ , where $f_{H} > f_{N}$ denote the fractional changes in total energy and number of stars per relaxation time, $t_{r e l a x}$ . The resulting evaporative lifetime $t_{e v} ≃ 20.5 t_{r e l a x}$ for isolated clusters is consistent with Fokker-Planck and N-body simulations, where $t_{r e l a x}$ 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 $d ln t_{e v} / d y ≃ - 1.9$ 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 $N = 1 0^{4} - 1 0^{6}$ 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 $3.4 σ /Ω$ in the radial direction of the orbit, where $Ω$ denotes the orbital angular velocity and $σ$ the stellar velocity dispersion in the cluster. These correlations may be tested by advanced wide field photometry and spectroscopy.

NewA, online 13 November 2011

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