Gravitational waves from the remnants of the first stars in nuclear star
  clusters
  We study Population III (Pop III) binary remnant mergers in nuclear star
clusters (NSCs) with a semi-analytical approach for early structure formation.
Within this framework, we keep track of the dynamics of Pop III binary (compact
object) remnants during cosmic structure formation, and construct the
population of Pop III binary remnants that fall into NSCs by dynamical friction
of field stars. The subsequent evolution within NSCs is then derived from
three-body encounters and gravitational-wave (GW) emission. We find that 7.5%
of Pop III binary remnants will fall into the centres ($< 3\ \rm pc$) of
galaxies. About $5-50\%$ of these binaries will merge at $z>0$ in NSCs,
including those with very large initial separations (up to 1~pc). The merger
rate density (MRD) peaks at $z\sim 5-7$ with $\sim 0.4-10\ \rm yr^{-1}\ \rm
Gpc^{-3}$, leading to a promising detection rate $\sim 170-2700\ \rm yr^{-1}$
for 3rd-generation GW detectors that can reach $z\sim 10$. Low-mass ($\lesssim
10^{6}\ \rm M_{\odot}$) NSCs formed at high redshifts ($z\gtrsim 4.5$) host
most ($\gtrsim 90\%$) of our mergers, which mainly consist of black holes (BHs)
with masses $\sim 40-85\ \rm M_{\odot}$, similar to the most massive BHs found
in LIGO events. Particularly, our model can produce events like GW190521
involving BHs in the standard mass gap for pulsational pair-instability
supernovae with a MRD $\sim 0.01-0.09\ \rm yr^{-1}\ Gpc^{-3}$ at $z\sim 1$,
consistent with that inferred by LIGO.
