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 percent of Pop III binary remnants will fall into the centres (< 3 pc) of galaxies. About 5-50 percent 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 similar to 5-7 with similar to 0.4-10 yr(-1) Gpc(-3), leading to a promising detection rate of similar to 170-2700 yr(-1) for third-generation GW detectors that can reach z similar to 10. Low-mass (less than or similar to 10(6) M-circle dot) NSCs formed at high redshifts (z similar to 4.5) host most (greater than or similar to 90 per cent) of our mergers, which mainly consist of black holes (BHs) with masses of similar to 40-85 M-circle dot, 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 an MRD of similar to 0.01-0.09 yr(-1) Gpc(-3) at z similar to 1, consistent with that inferred by LIGO.