On the Origin of GW190521-like events from repeated black hole mergers
  in star clusters
  LIGO and Virgo have reported the detection of GW190521, from the merger of a
binary black hole (BBH) with a total mass around $150$ M$_\odot$. While current
stellar models limit the mass of any black hole (BH) remnant to about $40 - 50$
M$_\odot$, more massive BHs can be produced dynamically through repeated
mergers in the core of a dense star cluster. The process is limited by the
recoil kick (due to anisotropic emission of gravitational radiation) imparted
to merger remnants, which can escape the parent cluster, thereby terminating
growth. We study the role of the host cluster metallicity and escape speed in
the buildup of massive BHs through repeated mergers. Almost independent of host
metallicity, we find that a BBH of about $150$ M$_\odot$ could be formed
dynamically in any star cluster with escape speed $\gtrsim 200$ km s$^{-1}$, as
found in galactic nuclear star clusters as well as the most massive globular
clusters and super star clusters. Using an inspiral-only waveform, we compute
the detection probability for different primary masses ($\ge 60$ M$_\odot$) as
a function of secondary mass and find that the detection probability increases
with secondary mass and decreases for larger primary mass and redshift. Future
additional detections of massive BBH mergers will be of fundamental importance
for understanding the growth of massive BHs through dynamics and the formation
of intermediate-mass BHs.
