Properties of black hole-star binaries formed in \(N\)-body simulations of massive star clusters: implications for Gaia black holes

We investigate black hole-star binaries formed in \(N\)-body simulations of massive, dense star clusters. We simulate 32 clusters with varying initial masses (\(10^{4}~\rm M_{\odot}\) to \(10^{6}~\rm M_{\odot}\)), densities (\(1200~\rm M_{\odot}~pc^{-3}\) to \(10^{5}~\rm M_{\odot}~pc^{-3}\)), and metallicities \((Z = 0.01,~0.001,~0.0001)\). Our results reveal that star clusters produce a diverse range of BH-star binaries, with dynamical interactions leading to extreme systems characterised by large orbital separations and high black hole masses. Of the ejected BH-main sequence (BH-MS) binaries, \(20\%\) form dynamically, while the rest originate from the primordial binary population initially present in the cluster. Ejected BH-MS binaries that are dynamically formed have more massive black holes, lower-mass stellar companions, and over half are in a hierarchical triple system. All unbound BH-giant star (BH-GS) binaries were ejected as BH-MS binaries and evolved into the BH-GS phase outside the cluster. Due to their lower-mass companions, most dynamically formed binaries do not evolve into BH-GS systems within a Hubble time. Consequently, only 2 of the 35 ejected BH-GS binaries are dynamically formed. We explore the formation pathways of Gaia-like systems, identifying two Gaia BH1-like binaries that formed through dynamical interactions, and two Gaia BH2-like systems with a primordial origin. We did not find any system resembling Gaia BH3, which may however be attributed to the limited sample size of our simulations.