The Mass Density of Merging Binary Black Holes over Cosmic Time

The connection between the binary black hole (BBH) mergers observed by LIGO-Virgo-KAGRA and their stellar progenitors remains uncertain. Specifically, the fraction ϵ of stellar mass that ends up in BBH mergers and the delay time τ between star formation and merger carry information about the astrophysical processes that produce merging BBHs. We model the merger rate in terms of cosmic star formation, coupled with a metallicity-dependent efficiency ϵ and a distribution of delay times τ , and infer these parameters with data from the Third Gravitational-Wave Transient Catalog. The progenitors to merging BBHs preferentially form in low-metallicity environments with a low-metallicity efficiency of log 10 ϵ < Z t = − 3.99 − 0.87 + 0.68 and a high-metallicity efficiency of log 10 ϵ < Z t = − 4.60 − 0.34 + 0.30 at 90% credibility. The data also prefer short delay times. For a power-law distribution p ( τ ) ∝ τ α , we find τ min < 1.9 Gyr and α < −1.32 at 90% credibility. Our model allows us to extrapolate the mass density in BBHs to high redshifts. We cumulatively integrate our density rate over time to get the total density of merging stellar-mass BBHs as a function of redshift. Today, BBH mergers are only ∼0.01% of the total stellar-mass density created by >10 M ⊙ progenitors. However, because massive stars are short lived, there may be more mass in merging BBHs than in living massive stars as early as ∼2.5 Gyr ago. We also compare to the mass in supermassive black holes, finding that the densities were comparable ∼12.5 Gyr ago, but their densities quickly increased to ∼75 times the density in merging stellar-mass BBHs by z ∼ 1.