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_⊙ and short delay times (t_delay ≲ 1 Gyr), while the stable RLOF channel primarily forms systems with BH masses above 30 M_⊙ 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 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 (~40%) from the stable RLOF channel. Our results predict that, for increasing redshifts, BBHs with component masses above 30 M_⊙ 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.