Targeting black holes from metal-poor progenitors with next-generation gravitational-wave detectors

Abstract

Next-generation gravitational-wave detectors such as the Einstein Telescope and Cosmic Explorer will be able to detect binary black-hole mergers out to the cosmic dawn. Mergers observed in the local Universe represent a mixture of systems formed across the entire cosmic history, spanning a wide range of astrophysical environments. Iron-group elements govern metallicity effects on stellar evolution, making metallicity a key tracer that leaves a strong imprint on the black-hole population. We introduce the concept of a &#34;target&#34; redshift, $z_t$, defined as the epoch at which more than 90% of stars form with metallicity $Z < 0.1\,Z_\odot$. This provides a straightforward way to isolate mergers originating from metal-poor environments. The determination of $z_t$ relies on the reconstruction of the cosmic star-formation rate density as a function of iron abundance. This reconstruction is not unique, as it depends on the combination of different empirical scaling relations. Consequently, $z_t$ spans a broad range, from $z_t \sim 4$ to $z_t > 10$, depending on the adopted model variation. We present a statistical framework that enables rapid tests of astrophysical predictions against forecasted observations from next-generation gravitational-wave detectors. By quantifying variations in the binary black-hole merger-rate density between the target redshift and the local Universe, our approach maps evolutionary trends across parameter space and estimates the detection statistics required to distinguish genuine astrophysical variations from statistical fluctuations.