  A large number of mergers of binary black holes (BHs) have been discovered by
gravitational wave observations since the first detection of gravitational
waves 2015. Binary BH mergers are the loudest events in the universe, however
their origin(s) have been under debate. There have been many suggestions for
merging binary BHs. Isolated binary stars are one of the most promising
origins. We have investigated the evolution of isolated binary stars ranging
from zero metallicity (Population III stars or Pop III stars) to the solar
metallicity by means of so-called rapid binary population synthesis simulation.
We have found that binary BHs formed from isolated binary stars reproduce the
redshift evolution of the merger rate density and the distribution of primary
BH masses and mass ratios inferred by Gravitational-Wave Transient Catalog 3
(GWTC-3). Pop III stars have a crucial role in forming merging binary BHs in
so-called the pair instability mass gap. Note that we choose the conventional
prescription of pair instability mass loss, based on the standard
$^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction rate. Finally, we have shown the
redshift evolution of the rate density of pair instability supernovae, and have
predicted that a few pair instability supernovae would be discovered in the
next few years. The discoveries would validate our results of merging binary
BHs.
