The fate of dense stellar systems

We investigate the fates of dense star clusters containing ∼ 10⁸ stars. If such systems have evolved to the stage when disruptive stellar collisions are important, the collisionally liberated gaseous debris may settle towards the centre. Spitzer and collaborators suggest that this gas condenses into a population of ‘new’ main sequence stars. Such a stellar subsystem commences an autonomous contraction, at a rate controlled by collisions among the ‘new’ stars themselves, when it attains a fraction ϵ = (ellipticity of original cluster)^1/2 of the total cluster mass. The gas liberated by stellar collisions can no longer recondense into stars when the concomitant luminosity rises to the Eddington limit for the subsystem: at this stage the subsystem must dissolve into an amorphous gas cloud. We discuss possible evolutionary tracks for the massive object thus formed. For a cluster of 10⁸N₈ solar-type stars, the maximum fraction of rest mass energy released before a massive object forms is only ∼ 3 × 10⁻⁴ϵ^13/9$$N^{4/7}_8$$. Before a cluster reaches the stage where stellar collisions are disruptive, runaway coalescence may already have led to the build-up of a central massive object. Alternatively, multiple supernovae could leave a post-coalescence cluster composed of compact stellar-mass remnants. Such a cluster sheds most of its members by evaporation before evolving to the stage where it collapses relativistically, unless sufficient gas is present to catalyse the contraction by interacting magnetically or gravitationally with the remnants. Dense star clusters may be responsible for some of the low-level manifestations of activity in galactic nuclei; but they are probably merely precursor stages of the more spectacular quasar-type phenomena, which develop after a massive object has formed.