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.

Motivated by the presence of numerous dark matter clumps in the Milky Way's halo, as expected from the cold dark matter cosmological model, we conduct numerical simulations to examine the heating of the disk. We construct a fairly realistic initial Galaxy model with a stable thin disk. The disk interacts with dark matter clumps for about 5 Gyr. Three physical effects are examined: the mass spectrum of the dark matter clumps, the initial thickness of the galactic disk, and the spatial distribution of the clumps. We find that the massive end of the mass spectrum determines the amount of disk heating. Thicker disks suffer less heating. There is a certain thickness at which the heating due to the interaction with the clumps is saturated. The spatial distribution of the clumps plays an important role in disk heating. We adopt two different spatial distributions of the clumps. The first, which mimics the primordial distribution of the clumps at the epoch of the collapse of the halo, is proportional to the underlying halo density distribution. Recent cosmological simulations, however, yield depletion of the clumps within the extent of the disk in the present-day galaxies. Therefore, we construct the second distribution, which has the same number density of the clumps as the prediction for the cosmological simulations within the disk region. Our numerical simulations show that the first distribution produces considerable disk heating, while the latter does not. These results suggest that at early epochs, or in cases where many clumps are surviving until the present, the disk should have suffered considerable heating in the earlier epochs of their evolution.

We have investigated the effect of initial mass segregation on the runaway merging of stars. The evolution of multi-mass, dense star clusters was followed by means of direct N-body simulations of up to 131.072 stars. All clusters started from King models with dimensionless central potentials of 3.0 ≤ W 0 ≤ 9.0. Initial mass segregation was realized by varying the minimum mass of a certain fraction of stars whose either (1) distances were closest to the cluster center or (2) total energies were lowest. The second case is more favorable to promote the runaway merging of stars by creating a high-mass core of massive, low-energy stars.Initial mass segregation could decrease the central relaxation time and thus help the formation of a high-mass core. However, we found that initial mass segregation does not help the runaway stellar merger to happen if the overall mass density profile is kept constant. This is due to the fact that the collision rate of stars is not increased due to initial mass segregation. Our simulations show that initial mass segregation is not sufficient to allow runaway merging of stars to occur in clusters with central densities typical for star clusters in the Milky Way.