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We investigate the evolution of supermassive binary black holes (BBHs) ingalaxies with realistic property distributions and the gravitational-wave (GW)radiation from the cosmic population of these BBHs. We incorporate acomprehensive treatment of the dynamical interactions of the BBHs with theirenvironments by including the effects of galaxy triaxial shapes and innerstellar distributions, and generate a large number of BBH evolution tracks. Bycombining these BBH evolution tracks, galaxy mass functions, galaxy mergerrates, and supermassive black hole-host galaxy relations into our model, weobtain the statistical distributions of surviving BBHs, BBH coalescence rates,the strength of their GW radiation, and the stochastic GW background (GWB)contributed by the cosmic BBH population. About ~1%-3% (or ~10%) ofsupermassive BHs at nearby galactic centers are expected to be binaries withmass ratio >1/3 (or >1/100). The characteristic strain amplitude of the GWB atfrequency 1/yr is estimated to be ~$2.0^{+1.4}_{-0.8}\times 10^{-16}$, and theupper bound of its results obtained with the different BH-host galaxy relationscan be up to $5.4\times 10^{-16}$, which await testing by future experiments(e.g., the Square Kilometer Array, FAST, Next-Generation Very Large Array). Theturnover frequency of the GWB spectrum is at ~0.25nHz. The uncertainties on theabove estimates and prospects for detecting individual sources are alsodiscussed. The application of the cosmic BBH population to the LaserInterferometer Space Antenna (LISA) band provides a lower limit to thedetection rate of BBHs by LISA, ~0.9/yr.

Dynamical evolution of cosmic supermassive binary black holes and their gravitational wave radiation