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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.

Gravitational-wave detectors are starting to reveal the redshift evolution of the binary black hole (BBH) merger rate,R_BBH(z). We make predictions forR_BBH(z) as a function of black hole mass for systems originating from isolated binaries. To this end, we investigate correlations between the delay time and black hole mass by means of the suite of binary population synthesis simulations,COMPAS. We distinguish two channels: the common envelope (CE), and the stable Roche-lobe overflow (RLOF) channel, characterized by whether the system has experienced a common envelope or not. We find that the CE channel preferentially produces BHs with masses below about 30M_⊙and short delay times (t_delay≲ 1 Gyr), while the stable RLOF channel primarily forms systems with BH masses above 30M_⊙and long delay times (t_delay≳ 1 Gyr). We provide a new fit for the metallicity-dependent specific star formation rate density based on the Illustris TNG simulations, and use this to convert the delay time distributions into a prediction ofR_BBH(z). This leads to a distinct redshift evolution ofR_BBH(z) for high and low primary BH masses. We furthermore find that, at high redshift,R_BBH(z) is dominated by the CE channel, while at low redshift, it contains a large contribution (∼40%) from the stable RLOF channel. Our results predict that, for increasing redshifts, BBHs with component masses above 30M_⊙will become increasingly scarce relative to less massive BBH systems. Evidence of this distinct evolution ofR_BBH(z) for different BH masses can be tested with future detectors.