Star clusters with primordial binaries – III. Dynamical interaction between binaries and an intermediate-mass black hole

We present the first study of the dynamical evolution of an isolated star cluster that combines a significant population of primordial binaries with the presence of a central black hole. We use equal-mass direct N-body simulations, with N ranging from 4096 to 16 384 and a primordial binary ratio of 0-10 per cent; the black hole mass is about 1 per cent of the total mass of the cluster. The evolution of the binary population is strongly influenced by the presence of the black hole, which gives the cluster a large core with a central density cusp. Starting from a variety of initial conditions (Plummer and King models), we first encounter a phase, that last approximately 10 half-mass relaxation times, in which binaries are disrupted faster compared to analogous simulations without a black hole. Subsequently, however, binary disruption slows down significantly due to the large core size. The dynamical interplay between the primordial binaries and the black hole thus introduces new features with respect to the scenarios investigated so far, where the influence of the black hole and of the binaries have been considered separately. A large core to half-mass radius ratio appears to be a promising indirect evidence for the presence of an intermediate-mass black hole in old globular clusters.