Gravitational waves from the remnants of the first stars in nuclear star clusters

Abstract

ABSTRACT 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 per cent of Pop III binary remnants will fall into the centres ($\lt 3\ \rm pc$) of galaxies. About 5–50 per cent 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 ∼ 5–7 with ${\sim} 0.4\!-\!10\ \rm yr^{-1}\ \rm Gpc^{-3}$, leading to a promising detection rate of ${\sim} 170\!-\!2700\ \rm yr^{-1}$ for third-generation GW detectors that can reach z ∼ 10. Low-mass (${\lesssim} 10^{6}\ \rm M_{\odot }$) NSCs formed at high redshifts (z ≳ 4.5) host most (≳90 per cent) of our mergers, which mainly consist of black holes (BHs) with masses of ${\sim} 40\!-\!85\ \rm M_{\odot }$, 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 an MRD of ${\sim} 0.01\!-\!0.09\ \rm yr^{-1}\ Gpc^{-3}$ at z ∼ 1, consistent with that inferred by LIGO.