The Binary Black Hole Merger Rate Deviates from a Simple Delayed Cosmic Star Formation Rate: The Impact of Metallicity and Delay Times*

Gravitational-wave detectors are making it possible to investigate how the merger rate of binary black holes (BBHs) evolves with redshift (z). We examine whether the merger rate R_merge(z) of isolated binaries deviates from the form assumed in state-of-the-art research: a scaled star formation rate density (SFRD). To address this, we conduct population synthesis simulations using COMPAS for a two-dimensional grid of stellar evolution prescriptions, convolve results with a metallicity-dependent SFRD, and compare the simulated R_merge(z)'s to "toy models" of R_merge(z) in the form of scaled SFRDs. We find that simulated R_merge(z)'s deviate from toy model rates by factors up to 5× for BBHs. Deviations are caused by two effects:

(i) The formation efficiency of BBHs is an order of magnitude higher at lower metallicity (Z < Z_⊙/5), corresponding to high z, due to weaker stellar winds.

(ii) BBH mergers can be significantly delayed (e.g., >1 Gyr) from BBH formation.

Combined, these effects cause R_merge(z) to be up to 3.5× higher at z=0 and 5× lower at z~9 compared to a scaled SFRD. We also find that scaling toy models to the inferred local R_merge causes deviations from simulated R_merge(z)'s beyond factors 10× at z~9. Interestingly, some of our simulations find z-dependence in BBH delay time distributions, increasing the complexity of delay time effects on R_merge(z).