We have followed the evolution of multi-mass star clusters containing massive central black
holes through
collisional $N$-body simulations done on GRAPE6. Each cluster is composed of between
16,384 to 131,072 stars together with a black hole with an initial mass of $M_{BH}=1000
M_\odot$.
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 (3D) mass density profile follows a power-law distribution
$\rho \sim r^{-\alpha}$ with
slope $\alpha=1.55$ 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. Instead globular clusters containing massive
central black
holes can be fitted with standard King profiles. Due to energy generation in the
cusp, star clusters with intermediate-mass black holes (IMBHs) expand. The cluster
expansion is so
strong
that clusters which start very concentrated can end up among the least dense clusters.
The amount of mass segregation in the core is also smaller
compared to post-collapse clusters without IMBHs.
Most stellar mass black holes with masses $M_{BH}>5 M_\odot$ are lost from the clusters within
a few Gyrs 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 $M_{BH} \approx 50$ $M_{BH}$ 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.
Complete paper: pdf file (654 KBytes)