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

Abstract

ABSTRACT 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 ΩGW ∼ 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 ΩGW ∝ f2/3 in the SKA band. The shape of the SGWB spectrum in the frequency range ∼[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 ∼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 ∼0.2 dex at z < ∼2, the amplitude of the SGWB in the frequency range ∼[1, 104] Hz may be underestimated by a similar factor at most.