Gravitational Radiation from Coalescing Supermassive Black Hole Binaries in a Hierarchical Galaxy Formation Model

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We investigate the expected gravitational wave emission from coalescing supermassive black hole (SMBH) binaries resulting from mergers of their host galaxies. We employ a semi-analytic model of galaxy and quasar formation based on the hierarchical clustering scenario to estimate the amplitude of the expected stochastic gravitational wave background owing to inspiraling SMBH binaries and bursts rates owing to the SMBH binary coalescence events. We find that the characteristic strain amplitude of the background radiation is hc(f) 10⁻¹⁶ (f/1 μ Hz)⁻²/³ for f 1 μ Hz. 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 (LISA) might detect intense gravitational wave bursts associated with coalescence of SMBH binaries with total mass M tot < 10⁷ M at z 2 at a rate 1.0 yr⁻¹. Our model predicts that burst signals with a larger amplitude h burst 10⁻¹⁵ correspond to coalescence events of massive SMBH binary with total mass M tot 10⁸ M at low redshift z 1 at a rate 0.1 yr⁻¹ whereas those with a smaller amplitude h burst 10⁻¹⁷ correspond to coalescence events of less massive SMBH binary with total mass M tot 10⁶ M at high redshift z 3.