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, $R_{\mathrm{BBH}}(z)$. 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 $30\rm{M}_{\odot}$ and short delay times ($t_{\rm delay} \lesssim
1$Gyr), while the stable RLOF channel primarily forms systems with BH masses
above $30\rm{M}_{\odot}$ and long delay times ($t_{\rm delay} \gtrsim 1$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
$30\rm{M}_{\odot}$ 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.
