Investigating the retention of intermediate-mass black holes in star clusters using N-body simulations

Context. Unlike supermassive and stellar-mass black holes (SBHs), the existence of intermediate-mass black holes (IMBHs) with masses ranging between 102-5 M-circle dot has not yet been confirmed. The main problem in the detection is that the innermost stellar kinematics of globular clusters (GCs) or small galaxies, the possible natural loci to IMBHs, are very difficult to resolve. However, if IMBHs reside in the centre of GCs, a possibility is that they interact dynamically with their environment. A binary formed with the IMBH and a compact object of the GC would naturally lead to a prominent source of gravitational radiation, detectable with future observatories. Aims. We use N-body simulations to study the evolution of GCs containing an IMBH and calculate the gravitational radiation emitted from dynamically formed IMBH-SBH binaries and the possibility that the IMBH escapes the GC after an IMBH-SBH merger. Methods. We ran for the first time direct-summation integrations of GCs with an IMBH including the dynamical evolution of the IMBH with the stellar system and relativistic effects, such as energy loss in gravitational waves (GWs) and periapsis shift, and gravitational recoil. Results. We find in one of our models an intermediate mass-ratio inspiral (IMRI), which leads to a merger with a recoiling velocity higher than the escape velocity of the GC. The GWs emitted fall in the range of frequencies that a LISA-like observatory could detect, like the European eLISA or with mission options considered in the recent preliminary mission study conducted in China. The merger has an impact on the global dynamics of the cluster, as an important heating source is removed when the merged system leaves the GC. The detection of one IMRI would constitute a test of GR, as well as an irrefutable proof of the existence of IMBHs.