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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. 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 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 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 \ \ Hz) ^-2/3 for f \ 1 \ \ Hz 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 Interferometer Space Antenna (\ LISA) might detect intense gravitational wave bursts associated with coalescence of SMBH binaries with total mass M\ ₓ₎ₓ < 10⁷ M\ at z \ 2 at a rate \ 1. 0 \ yr^-1. Burst signals with a larger amplitude h\ ₁ₔₑₒₓ \ 10^-15 correspond to coalescence events of massive SMBH binary with total mass M\ ₓ₎ₓ \ 10⁸ M\ at low redshift z \ 1 at a rate \ 0. 1 \ yr^-1 whereas those with a smaller amplitude h\ ₁ₔₑₒₓ \ 10^-17 correspond to coalescence events of less massive SMBH binary with total mass M\ ₓ₎ₓ \ 10⁶ M\ at high redshift z \ 3.
Enoki et al. (Mon,) studied this question.