We investigate the evolution of supermassive binary black holes ( BBHs ) in galaxies with realistic property distributions and the gravitational wave ( GW ) radiation from the cosmic population of these BBHs .
We incorporate a comprehensive treatment of the BBH dynamical interactions with their environments by including the effects of galaxy triaxial shapes and inner stellar distributions , and generate a large number of BBH evolution tracks .
By combining these BBH evolution tracks , galaxy mass functions , galaxy merger rates , and supermassive black hole–host galaxy relations into our model , we obtain the statistical distributions of surviving BBHs , BBH coalescence rates , the strength of their GW radiation , and the stochastic GW background contributed by the cosmic BBH population .
About \sim 1 % –3 % ( or \sim 10 \% ) of supermassive BHs at nearby galactic centers are expected to be binaries with mass ratio > 1 / 3 ( or > 1 / 100 ) .
The characteristic strain amplitude of the GW background at frequency 1 { yr ^ { -1 } } are estimated to be \sim 2.0 ^ { +1.4 } _ { -0.8 } \times 10 ^ { -16 } , and its upper bound of the results obtained with the different BH–host galaxy relations can be up to 5.4 \times 10 ^ { -16 } , which wait to be tested by future experiments ( e.g. , SKA , FAST , ngVLA ) .
The turnover frequency of the GW background spectrum is at \sim 0.25 { nHz } .
The uncertainties to the above estimates and prospects for detecting individual sources are also discussed .
The application of the cosmic BBH population to the LISA band provides a lower limit to the detection rate of BBHs by LISA , { \sim } 0.9 { yr ^ { -1 } } .