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New observational facilities are probing astrophysical transients such as stellar explosions and gravitational-wave sources at ever-increasing redshifts, while also revealing new features in source property distributions. To interpret these observations, we need to compare them to predictions from stellar population models. Such models require the metallicity-dependent cosmic star formation history ($\mathit{}(Z,z)$) as an input. Large uncertainties remain in the shape and evolution of this function. In this work, we propose a simple analytical function for$\mathit{}(Z,z)$. Variations of this function can be easily interpreted because the parameters link to its shape in an intuitive way. We fit our analytical function to the star-forming gas of the cosmological TNG100 simulation and find that it is able to capture the main behavior well. As an example application, we investigate the effect of systematic variations in the$\mathit{}(Z,z)$parameters on the predicted mass distribution of locally merging binary black holes. Our main findings are that (i) the locations of features are remarkably robust against variations in the metallicity-dependent cosmic star formation history, and (ii) the low-mass end is least affected by these variations. This is promising as it increases our chances of constraining the physics that govern the formation of these objects (https://github.com/LiekeVanSon/SFRD_fit/tree/7348a1ad0d2ed6b78c70d5100fb3cd2515493f02/).

Gravitational-wave (GW) detections are starting to reveal features in the mass distribution of double compact objects. The lower end of the black hole (BH) mass distribution is especially interesting as few formation channels contribute here and because it is more robust against variations in the cosmic star formation than the high-mass end. In this work we explore the stable mass transfer channel for the formation of GW sources with a focus on the low-mass end of the mass distribution. We conduct an extensive exploration of the uncertain physical processes that impact this channel. We note that, for fiducial assumptions, this channel reproduces the peak at ∼9M_☉in the GW-observed binary BH mass distribution remarkably well and predicts a cutoff mass that coincides with the upper edge of the purported neutron star–black hole (NS–BH) mass gap. The peak and cutoff mass are a consequence of the unique properties of this channel; namely (1) the requirement of stability during the mass transfer phases, and (2) the complex way in which the final compact object masses scale with the initial mass. We provide an analytical expression for the cutoff in the primary component mass and show that this adequately matches our numerical results. Our results imply that selection effects resulting from the formation channel alone can provide an explanation for the purported NS–BH mass gap in GW detections. This provides an alternative to the commonly adopted view that the gap emerges during BH formation.