Gravitational Waves from Mergers of Population III Binary Black Holes: Roles Played by Two Evolution Channels

The gravitational wave (GW) signal from binary black hole (BBH) mergers is a promising probe of Population III (Pop III) stars. To fully unleash the power of the GW probe, one important step is to understand the relative importance and features of different BBH evolution channels. We model two channels, isolated binary stellar evolution (IBSE) and nuclear star cluster-dynamical hardening (NSC-DH), in one theoretical framework based on the semi-analytical code A-SLOTH, under various assumptions on Pop III initial mass function (IMF), initial binary statistics and high-z nuclear star clusters (NSCs). The NSC-DH channel contributes ∼ 8-95% of Pop III BBH mergers across cosmic history, with higher contributions achieved by initially wider binary stars, more top-heavy IMFs, and more abundant high-z NSCs. The dimensionless stochastic GW background (SGWB) produced by Pop III BBH mergers has peak values Ω^ peak_ GW∼ 10^-11-8× 10^-11 around observer-frame frequencies ν∼ 10-100 Hz. The Pop III contribution can be a non-negligible (∼ 2-32%) component in the total SGWB at ν≲ 10 Hz. The estimated detection rates of Pop III BBH mergers by the Einstein Telescope are ∼ 6-230 yr^-1 and ∼ 30-1230 yr^-1 for the NSC-DH and IBSE channels, respectively. Pop III BBH mergers in NSCs are more massive than those from IBSE, so they dominate the Pop III SGWB below 20 Hz in most cases. Besides, the detection rate of Pop III BBH mergers involving at least one intermediate-mass BH above 100 M_⊙ by the Einstein Telescope is ∼ 0.5-200 yr^-1 in NSCs but remains below 0.1 yr^-1 for IBSE.