Dynamics of massive stellar black holes in young star clusters and the displacement of ultra-luminous X-ray sources

In low-metallicity environments, massive stars might avoid supernova explosions and directly collapse, forming massive (∼25-80 M_⊙) stellar black holes (MSBHs), at the end of their life. MSBHs, when hosted in young massive clusters, are expected to form binaries and to strongly interact with stars, mainly via three-body encounters. We simulate various realizations of young star clusters hosting MSBHs in hard binaries with massive stars. We show that a large fraction (∼44 per cent) of MSBH binaries are ejected on a short time-scale (≤10 Myr). The offset of the ejected MSBHs with respect to the parent cluster is consistent with observations of X-ray binaries and ultra-luminous X-ray sources. Furthermore, three-body encounters change the properties of MSBH binaries: the semimajor axis changes by ≤50 per cent and the eccentricity of the system generally increases. We shortly discuss the implications of our simulations on the formation of high-mass X-ray binaries hosting MSBHs.