A simple two-component description of energy equipartition and mass segregation for anisotropic globular clusters

Abstract

In weakly-collisional stellar systems such as some globular clusters, partial energy equipartition and mass segregation are expected to develop as a result of the cumulative effect of stellar encounters, even in systems initially characterized by star-mass independent density and energy distributions. In parallel, numerical simulations have demonstrated that radially-biased pressure anisotropy slowly builds up in realistic models of globular clusters from initial isotropic conditions, leading to anisotropy profiles that, to some extent, mimic those resulting from incomplete violent relaxation known to be relevant to elliptical galaxies. In this paper, we consider a set of realistic simulations realized by means of Monte Carlo methods and analyze them by means of self-consistent, two-component models. For this purpose, we refer to an underlying distribution function originally conceived to describe elliptical galaxies, which has recently been truncated and adapted to the context of globular clusters. The two components are supposed to represent light stars (combining all main sequence stars) and heavy stars (giants, dark remnants, and binaries). We show that this conceptually simple family of two-component truncated models provides a reasonable description of simulated density, velocity dispersion, and anisotropy profiles, especially for the most relaxed systems, with the ability to quantitatively express the attained levels of energy equipartition and mass segregation. In contrast, two-component isotropic models based on the King distribution function do not offer a comparably satisfactory representation of the simulated globular clusters. With this work, we provide a new reliable diagnostic tool applicable to nonrotating globular clusters that are characterized by significant gradients in the local value of the mass-to-light ratio, beyond the commonly used one-component dynamical models. In particular, these models are supposed to be an optimal tool for the clusters that underfill the volume associated with the boundary surface determined by the tidal interaction with the host galaxy.