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 10 4 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 ∼ 10 4 kT to binaries that occur on the crossing timescale and outside of the periods of the homologous collapses.

A MODEST review

“…Fresh attention has been recently devoted to the study of the moment of core collapse in idealised Nbody models. Approaches for a new definition of core collapse based on self-similar solutions have been developed (Pavlík and Šubr 2018). Single component models of core collapse result in radial density profiles similar to those of previous simulations and in agreement with theoretical predictions.…”

A MODEST review

“…Fresh attention has been recently devoted to the study of the moment of core collapse in idealised N -body models. Approaches for a new definition of core collapse based on self-similar solutions have been developed (Pavlík and Šubr, 2018). Single component models of core collapse result in radial density profiles similar to those of previous simulations and in agreement with theoretical predictions.…”

New insights into star cluster evolution towards energy equipartition

“…We can even see a kinematic trace of core collapse as a local maximum in 𝑚 eq and 𝜂 at 𝑡 cc (cf. Bianchini et al 2018), which also demonstrates that their method and that of Pavlík & Šubr (2018), used here to determine 𝑡 cc , are compatible even in these kinematically distinct clusters. The top middle and top right panels show the evolution of 𝑚 eq and 𝜂 in the intermediate and outer shells, and demonstrate the differences between the rate of evolution towards EEP in both models that we discussed above.…”