A direct N-body model of core-collapse and core oscillations

TL;DR

This study presents a detailed N-body simulation of a star cluster demonstrating core-collapse, core oscillations, and the impact of black hole binaries, confirming previous scaling relations for larger N clusters.

Contribution

First direct N-body simulation with N=200,000 including stellar and binary evolution, confirming core oscillations and their halting by black hole binary ejection.

Findings

Core-collapse occurs at 10.5 Gyr with subsequent oscillations.

Ejection of black hole binary halts core oscillations.

Scaling relations from smaller N studies hold for larger N.

Abstract

We report on the results of a direct N-body simulation of a star cluster that started with N = 200 000, comprising 195 000 single stars and 5 000 primordial binaries. The code used for the simulation includes stellar evolution, binary evolution, an external tidal field and the effects of two-body relaxation. The model cluster is evolved to 12 Gyr, losing more than 80% of its stars in the process. It reaches the end of the main core-collapse phase at 10.5 Gyr and experiences core oscillations from that point onwards -- direct numerical confirmation of this phenomenon. However, we find that after a further 1 Gyr the core oscillations are halted by the ejection of a massive binary comprised of two black holes from the core, producing a core that shows no signature of the prior core-collapse. We also show that the results of previous studies with N ranging from 500 to 100 000 scale well to this new model with larger N. In particular, the timescale to core-collapse (in units of the relaxation timescale), mass segregation, velocity dispersion, and the energies of the binary population all show similar behaviour at different N.