Exploring the multiband gravitational wave background with a semi-analytic galaxy formation model

An enormous number of compact binary systems, spanning from stellar to supermassive levels, emit substantial gravitational waves during their final evolutionary stages, thereby creating a stochastic gravitational wave background (SGWB). We calculate the merger rates of stellar compact binaries and massive black hole binaries using a semi-analytic galaxy formation model Galaxy Assembly with Binary Evolution (GABE) - in a unified and self-consistent approach, followed by an estimation of the multiband SGWB contributed by those systems. We find that the amplitudes of the principal peaks of the SGWB energy density are within one order of magnitude Omega(GW) similar to 10(-9)-10(-8). This SGWB could easily be detected by the Square Kilometre Array (SKA), as well as by the planned interferometric detectors, such as the Einstein Telescope and the Laser Interferometer Space Antenna (LISA). The energy density of this background varies as Omega(GW) proportional to f(2/3) in the SKA band. The shape of the SGWB spectrum in the frequency range similar to[10(-4),1] Hz could allow the LISA to distinguish the black hole seed models. The amplitude of the SGWB from merging stellar binary black holes at similar to 100 Hz is approximately 10 and 100 times greater than those from merging binary neutron stars and neutron-star-black-hole mergers, respectively. Note that, since the cosmic star formation rate density predicted by GABE is somewhat lower than the observational results by similar to 0.2 dex at z < similar to 2, the amplitude of the SGWB in the frequency range similar to[1, 10(4)] Hz may be underestimated by a similar factor at most.