Gravitational Waves and Intermediate-mass Black Hole Retention in
  Globular Clusters
  The recent discovery of gravitational waves has opened new horizons for
physics. Current and upcoming missions, such as LIGO, VIRGO, KAGRA, and LISA,
promise to shed light on black holes of every size from stellar mass (SBH)
sizes up to supermassive black holes which reside in galactic nuclei. The
intermediate mass black hole (IMBH) family has not been detected beyond any
reasonable doubt neither directly nor indirectly. Recent analyses suggest
observational evidence for the presence of IMBHs in the centers of two Galactic
globular clusters. In this paper, we investigate the possibility that globular
clusters were born with a central IMBH, which undergo repeated merger events
with SBHs in the cluster core. By means of a semi-analytical method, we follow
the evolution of the primordial cluster population in the galactic potential
and the Gravitational Wave (GW) mergers of the binary IMBH-SBH systems. Our
models predict $\approx 1000$ IMBHs within $1$ kpc from the Galactic Center.
Our results show that the IMBH-SBH merger rate density changes from
$\mathcal{R}\approx 1000$ Gpc$^{-3}$ yr$^{-1}$ beyond $z\approx 2$ to
$\mathcal{R}\approx 1-10$ Gpc$^{-3}$ yr$^{-1}$ at $z\approx 0$. The rates at
low redshifts may be significantly higher if young massive star clusters host
IMBHs. The merger rates are dominated by IMBHs with masses between $10^3$ and
$10^4\,\mathrm{M}_{\odot}$. Currently there are no LIGO/VIRGO upper limits for
GW sources in this mass range, but our results show that at design sensitivity
these instruments may detect these IMBH-SBH mergers in the coming years.
\textit{LISA} and the Einstein Telescope will be best suited to detect these GW
events. The inspirals of IMBH-SBH systems may also generate an unresolved GW
background.
