Massive Black Holes in Star Clusters. II. Realistic Cluster Models

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Abstract
We have followed the evolution of multimass star clusters containing massive central black holes through collisional N-body simulations done on GRAPE6. Each cluster is composed of between 16,384 and 131,072 stars together with a black hole with an initial mass of MBH = 1000 M☉. We follow the evolution of the clusters under the combined influence of two-body relaxation, stellar mass loss, and tidal disruption of stars by the massive central black hole. We find that the (three-dimensional) mass density profile follows a power-law distribution ρ ~ r-α with slope α = 1.55 inside the sphere of influence of the central black hole. This leads to a constant-density profile of bright stars in projection, which makes it highly unlikely that core-collapse clusters contain intermediate-mass black holes (IMBHs). Instead, globular clusters containing massive central black holes can be fitted with standard King profiles. Because of energy generation in the cusp, star clusters with IMBHs expand. The cluster expansion is so strong that clusters that start very concentrated can end up among the least dense clusters. The amount of mass segregation in the core is also smaller compared to postcollapse clusters without IMBHs. Most stellar mass black holes with masses MBH > 5 M☉ are lost from the clusters within a few gigayears through mutual encounters in the cusp around the IMBH. Black holes in star clusters disrupt mainly main-sequence stars and giants and no neutron stars. The disruption rates are too small to form an IMBH out of a MBH ≈ 50 M☉ progenitor black hole even if all material from disrupted stars is accreted onto the black hole, unless star clusters start with central densities significantly higher than what is seen in present-day globular clusters. We also discuss the possible detection mechanisms for IMBHs. Our simulations show that kinematical studies can reveal 1000 M☉ IMBHs in the closest clusters. IMBHs in globular clusters are weak X-ray sources, since the tidal disruption rate of stars is low and the star closest to the IMBH is normally another black hole, which prevents other stars from undergoing stable mass transfer. For globular clusters, dynamical evolution can push compact stars near the IMBH to distances small enough that they become detectable sources of gravitational radiation. If 10% of all globular clusters contain IMBHs, extragalactic globular clusters could be one of the major sources of gravitational wave events for LISA.
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