Realistic models for evolving globular clusters: core collapse with a mass spectrum

We present models for evolving globular clusters with realistic stellar mass spectra, generated by direct numerical integration of the Fokker–Planck equation. The goal of this study is to compute surface brightness and projected velocity dispersion profiles that can be directly compared with observations. We use an evolved power-law mass function containing non-luminous objects of up to 1.2 Mʘ, red giants and horizontal branch stars of 0. 7 Mʘ, and main-sequence stars extending down to 0.1 Mʘ. The heavy non-luminous objects settle to the centre of the cluster and dominate the core within a half-mass relaxation time which corresponds to ~3 Gyr for our standard model resembling a Salpeter mass function. We follow the simulation until core collapse is well established at 10 Gyr. The surface density profile of the heavy non-luminous objects in the core at this time is |$\sigma\propto{r}^{-1.2}$|⁠. The other less massive components have significantly flatter power-law surface density profiles in the core, with the power-law index depending on the individual stellar mass of each mass group. Since red giants and horizontal branch stars dominate the luminosity of the cluster, the resulting composite surface brightness profiles are substantially flatter than for single component models. This is consistent with the recent finding by Lugger et al. that the central power-law slopes of several candidate post-core-collapse clusters are flatter than the value of –1 expected for binary post-collapse expansion in a one-component cluster. Our models should place significant constraints on the stellar population in globular clusters, particularly the non-luminous remnant component.