From Cosmological Simulations to Binary Black Hole Mergers: The Impact of Using Analytical Star Formation History Models on Gravitational-wave Source Populations

Abstract Observations of binary black hole (BBH) mergers provide a unique window into the lives of massive stars across cosmic time. Connecting redshift-dependent merger properties to massive star progenitors requires accurate models of cosmic star formation and chemical enrichment histories. Analytical fits for the metallicity-specific cosmic star formation rate density S ( Z , z ) are commonly used as proxies for the complex underlying star formation history, yet they remain unconstrained. Using the IllustrisTNG cosmological simulations, we evaluate the accuracy of these analytical S ( Z , z ) prescriptions. By coupling the simulated and analytical S ( Z , z ) to the population synthesis code COMPAS , we investigate the resulting BBH merger rates and mass distributions. We find that analytical S ( Z , z ) prescriptions can overestimate BBH merger rates at high redshift ( z ≳ 6) by up to a factor of 10–10 4 , depending on cosmological simulation resolution, and can introduce spurious features in the BBH mass distribution. For example, they can produce an artificial feature near 8 M ⊙ in the primary mass distribution at z ≲ 2, which is absent when using the full simulation-based S ( Z , z ) , while simultaneously suppressing high-mass features. These discrepancies arise because simple analytical models fail to capture a high-metallicity bump and a more flattened low-metallicity tail in the simulated S ( Z , z ) metallicity distribution. Our results highlight the importance of accurate star formation histories for modeling BBH populations, demonstrate the limitation of widely used analytical S ( Z , z ) fits, and underscore the need for careful integration of cosmological simulations, analytical fits, and population synthesis when interpreting gravitational-wave observations.