The Redshift Evolution of the Binary Black Hole Merger Rate: A Weighty Matter

Gravitational-wave detectors are starting to reveal the redshift evolution of the binary black hole (BBH) merger rate, R (BBH)(z). We make predictions for R (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 30 M (circle dot) and short delay times (t (delay) less than or similar to 1 Gyr), while the stable RLOF channel primarily forms systems with BH masses above 30 M (circle dot) and long delay times (t (delay) greater than or similar to 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 of R (BBH)(z). This leads to a distinct redshift evolution of R (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 (similar to 40%) from the stable RLOF channel. Our results predict that, for increasing redshifts, BBHs with component masses above 30 M (circle dot) will become increasingly scarce relative to less massive BBH systems. Evidence of this distinct evolution of R (BBH)(z) for different BH masses can be tested with future detectors.

Automated summary

This study predicts and investigates the correlation between binary black hole (BBH) merger rate, R (BBH)(z), and black hole mass for systems originating from isolated binaries. The results show that the common envelope (CE) channel tends to produce smaller black holes with shorter delay times, while the stable Roche-lobe overflow (RLOF) channel primarily forms larger black hole systems with longer delay times. By using metallicity-dependent specific star formation rate density, the redshift evolution of R (BBH)(z) is predicted. It is found that at high redshift, the CE channel dominates R (BBH)(z), while at low redshift, the stable RLOF channel contributes about 40% to R (BBH)(z). The results also suggest that as redshift increases, binary black holes with component masses above 30 solar masses will become increasingly rare.