The Binary Black Hole Merger Rate Deviates From the Cosmic Star Formation Rate: A Tug of War Between Metallicity and Delay Times

Gravitational-wave detectors are now making it possible to investigate how the merger rate of binary black holes (BBHs) evolves with redshift. In this study, we examine whether the BBH merger rate of isolated binaries deviates from a scaled star formation rate density (SFRD) -- a frequently used model in state-of-the-art research. To address this question, we conduct population synthesis simulations using COMPAS with a grid of stellar evolution models, calculate their cosmological merger rates, and compare them to a scaled SFRD. We find that our simulated rates deviate by factors up to $3.5\times$ at $z\sim0$ and $5\times$ at $z\sim 9$ due to two main phenomena: (i) The formation efficiency of BBHs is an order of magnitude higher at low metallicities than at solar metallicity; and (ii) BBHs experience a wide range of delays (from a few Myr to many Gyr) between formation and merger. Deviations are similar when comparing to a $\textit{delayed}$ SFRD, and even larger (up to $\sim 10\times$) when comparing to SFRD-based models scaled to the local merger rate. Interestingly, our simulations find that the BBH delay time distribution is redshift-dependent, increasing the complexity of the redshift distribution of mergers. We find similar results for simulated merger rates of BHNSs and BNSs. We conclude that the rate of BBH, BHNS, and BNS mergers from the isolated channel can significantly deviate from a scaled SFRD, and that future measurements of the merger rate will provide insights into the formation pathways of gravitational-wave sources.