Gravitational Waves from Supermassive Black Hole Coalescence in a Hierarchical Galaxy Formation Model

Abstract

We investigate the expected gravitational wave emission from coalescing supermassive black hole (SMBH) binaries resulting from mergers of their host galaxies. When galaxies merge, the SMBHs in the host galaxies sink to the center of the new merged galaxy and form a binary system. We employ a semianalytic model of galaxy and quasar formation based on the hierarchical clustering scenario to estimate the amplitude of the expected stochastic gravitational wave background due to inspiraling SMBH binaries and bursts due to the SMBH binary coalescence events. We find that the characteristic strain amplitude of the background radiation is hc(f) ~ 10-16(f/1 μHz)-2/3 for f ≲ 1 μHz just below the detection limit from measurements of the pulsar timing provided that SMBHs coalesce simultaneously when host galaxies merge. The main contribution to the total strain amplitude of the background radiation comes from SMBH coalescence events at 0 < z < 1. We also find that a future space-based gravitational wave interferometer such as the planned Laser Interferometer Space Antenna might detect intense gravitational wave bursts associated with coalescence of SMBH binaries with total mass Mtot < 107 M☉ at z ≳ 2 at a rate ~1.0 yr-1. Our model predicts that burst signals with a larger amplitude hburst ~ 10-15 correspond to coalescence events of massive SMBH binary with total mass Mtot ~ 108 M☉ at low redshift (z ≲ 1) at a rate ~0.1 yr-1, whereas those with a smaller amplitude (hburst ~ 10-17) correspond to coalescence events of less massive SMBH binaries with total mass Mtot ~ 106 M☉ at high redshift (z ≳ 3).