The redshift evolution of the binary black hole merger rate: a weighty matter

Abstract

Gravitational wave detectors are starting to reveal the redshift evolution of the binary black hole (BBH) merger rate, $R_{\mathrm{BBH}}(z)$. We make predictions for $R_{\mathrm{BBH}}(z)$ 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, characterised by whether the system has experienced a common envelope or not. We find that the CE channel preferentially produces BHs with masses below about $30{\mathrm{M}}_{\odot }$ and short delay times ($t_{\mathrm{delay}}\lesssim 1$Gyr), while the stable RLOF channel primarily forms systems with BH masses above $30{\mathrm{M}}_{\odot }$ and long delay times ($t_{\mathrm{delay}}\gtrsim 1$Gyr). We provide a new fit for the metallicity specific star-formation rate density based on the Illustris TNG simulations, and use this to convert the delay time distributions into a prediction of $R_{\mathrm{BBH}}(z)$. This leads to a distinct redshift evolution of $R_{\mathrm{BBH}}(z)$ for high and low primary BH masses. We furthermore find that, at high redshift, $R_{\mathrm{BBH}}(z)$ is dominated by the CE channel, while at low redshift it contains a large contribution ($\sim 40\%$) from the stable RLOF channel. Our results predict that, for increasing redshifts, BBHs with component masses above $30{\mathrm{M}}_{\odot }$ will become increasingly scarce relative to less massive BBH systems. Evidence of this distinct evolution of $R_{\mathrm{BBH}}(z)$ for different BH masses can be tested with future detectors.

20 pages + appendices, data is available at https://doi.org/10.5281/zenodo.5544170

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