Gravitational waves from mergers of Population III binary black holes: roles played by two evolution channels

TL;DR

This study models two channels of Population III binary black hole evolution, assessing their contributions to gravitational wave signals and background, with implications for detection by future observatories like the Einstein Telescope.

Contribution

It introduces a unified semi-analytical framework to compare isolated binary evolution and nuclear star cluster channels for Pop III BBH mergers, highlighting their relative importance and GW signatures.

Findings

NSC-DH channel contributes 8-95% of Pop III BBH mergers.

Pop III BBH mergers produce a stochastic GW background peaking at 10-100 Hz.

Detection rates by the Einstein Telescope range from 6 to 1230 per year.

Abstract

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 $\sim 8-95\%$ 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 $\Omega^{\rm peak}_{\rm GW}\sim 10^{-11}-8\times 10^{-11}$ around observer-frame frequencies $\nu\sim 10-100\ \rm Hz$. The Pop III contribution can be a non-negligible ($\sim 2-32\%$) component in the total SGWB at $\nu\lesssim 10\ \rm Hz$. The estimated detection rates of Pop III BBH mergers by the Einstein Telescope are $\sim 6-230\ \rm yr^{-1}$ and $\sim 30-1230\ \rm yr^{-1}$ 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 $100\ \rm M_\odot$ by the Einstein Telescope is $\sim 0.5-200\ \rm yr^{-1}$ in NSCs but remains below $0.1\ \rm yr^{-1}$ for IBSE.