The Metallicity Dependence and Evolutionary Times of Merging Binary Black Holes: Combined Constraints from Individual Gravitational-wave Detections and the Stochastic Background

Abstract

The advent of gravitational-wave astronomy is now allowing for the study of compact binary merger demographics throughout the Universe. This information can be leveraged as tools for understanding massive stars, their environments, and their evolution. One active question is the nature of compact binary formation: the environmental and chemical conditions required for black hole birth and the time delays experienced by binaries before they merge. Gravitational-wave events detected today, however, primarily occur at low or moderate redshifts due to current interferometer sensitivity, therefore limiting our ability to probe the high-redshift behavior of these quantities. In this work, we circumvent this limitation by using an additional source of information: observational limits on the gravitational-wave background from unresolved binaries in the distant Universe. Using current gravitational-wave data from the first three observing runs of LIGO–Virgo–KAGRA, we combine catalogs of directly detected binaries and limits on the stochastic background to constrain the time-delay distribution and metallicity dependence of binary black hole evolution. Looking to the future, we also explore how these constraints will be improved at the Advanced LIGO A+ sensitivity. We conclude that, although binary black hole formation cannot be strongly constrained with today’s data, the future detection (or a nondetection) of the gravitational-wave background with Advanced LIGO A+ will carry strong implications for the evolution of binary black holes.

The Mass Density of Merging Binary Black Holes over Cosmic Time

“…The joint posterior on α and t min follows the expected correlation, so that larger (less negative) values of α are more strongly ruled out for larger values of t min and vice versa. These results are consistent with previous findings that short delay times are preferred, driven by the fact that the shape of the BBH merger rate resembles the SFR at z < 1 (Fishbach & Kalogera 2021;Fishbach & van Son 2023;Vijaykumar et al 2023;Turbang et al 2024). These results can also be compared to predictions from population synthesis previously mentioned.…”

“…We assume that the metallicity threshold is  = -Z Z log 0.5 10 t ( ) , consistent with many theoretical predictions (see Figure 7 of Fishbach & van Son 2023). While one could fit for the metallicity threshold alongside >Z t  and <Z t  , we find that the current data are unable to provide meaningful constraints, in agreement with previous work (Turbang et al 2024).…”

“…The progenitor formation rate and the delay time distribution set the BBH merger rate as a function of cosmic time. Thus, measurements of the redshift evolution of the BBH merger rate inform the SFR, the cosmic chemical history, and the delay time distribution (Fishbach & Kalogera 2021;Mukherjee & Dizgah 2022;Fishbach & van Son 2023;Vijaykumar et al 2023;Turbang et al 2024). Additionally, by fitting the observed BBH merger rate in terms of these astrophysical parameters, we can infer what the rate should be at higher redshifts, beyond the current LVK detection horizon at z ∼ 1.…”

“…We use the 69 confident BBH events with false alarm rate < 1 yr and both masses above 3 M e from GWTC-3. We do not consider the nondetection of the stochastic GW background as previous work has shown it has a negligible effect compared to resolved coalescences (Turbang et al 2024). We assume masses, spins, and merger redshifts follow independent distributions, so that the merger rate density (number of mergers per comoving volume per source-frame time) follows…”