Dynamical double black holes and their host cluster properties
  We investigate the relationship between the global properties of star
clusters and their double black hole (DBH) populations. We use the code {\tt
NBODY6} to evolve a suite of star cluster models with an initial mass of
$\mathcal{O}(10^4)$M$_\odot$ and varying initial parameters. We conclude that
cluster metallicity plays the most significant role in determining the lifespan
of a cluster, while the initial half-mass radius is dominant in setting the
rate of BH exchange interactions in the central cluster regions. We find that
the mass of interacting BHs, rather than how frequently their interactions with
other BHs occur, is more crucial in the thermal expansion and eventual
evaporation of the cluster. We formulate a novel approach to easily quantify
the degree of BH-BH dynamical activity in each model. We report 12 in-cluster
and three out-of-cluster (after ejection from the cluster) DBH mergers, of
different types (inspiral, eccentric, hierarchical) across the ten $N$-body
models presented. Our DBH merger efficiency is 3--4$\times10^{-5}$ mergers per
M$_\odot$. We note the cluster initial density plays the most crucial role in
determining the number of DBH mergers, with the potential presence of a
transitional density point (between 1.2-3.8$\times10^3$M$_\odot$/pc$^3$) below
which the number of in-cluster mergers increases with cluster density and above
which the increased stellar density acts to prevent in-cluster BH mergers. The
importance of the history of dynamical interactions within the cluster in
setting up the pathways to ejected DBH mergers is also discussed. Our findings
show a broad match with observed LIGO-Virgo DBH mergers.
