The hunt for self-similar core collapse

Abstract

Context. Core collapse is a prominent evolutionary stage of self-gravitating systems. In an idealised collisionless approximation, the region around the cluster core evolves in a self-similar way prior to the core collapse. Thus, its radial density profile outside the core can be described by a power law, ρ ∝ r−α. Aims. We aim to find the characteristics of core collapse in N-body models. In such systems, a complete collapse is prevented by transferring the binding energy of the cluster to binary stars. The contraction is, therefore, more difficult to identify. Methods. We developed a method that identifies the core collapse in N-body models of star clusters based on the assumption of their homologous evolution. Results. We analysed different models (equal- and multi-mass), most of which exhibit patterns of homologous evolution, yet with significantly different values of α : the equal-mass models have α ≈ 2.3, which agrees with theoretical expectations, the multi-mass models have α ≈ 1.5 (yet with larger uncertainty). Furthermore, most models usually show sequences of separated homologous collapses with similar properties. Finally, we investigated a correlation between the time of core collapse and the time of formation of the first hard binary star. The binding energy of such a binary usually depends on the depth of the collapse in which it forms, for example from 100 kT to 104 kT in the smallest equal-mass to the largest multi-mass model, respectively. However, not all major hardenings of binaries happened during the core collapse. In the multi-mass models, we see large transfers of binding energy of ∼104 kT to binaries that occur on the crossing timescale and outside of the periods of the homologous collapses.