GW energy spectrum Ω_GW and the fractional circular polarization 𝒫_circ calculated from 1600 Monte Carlo realizations of the SMBH binary population. In the left panels, the black solid curve shows the mean and the gray bands the 68% and 95% CL regions of the Monte Carlo realizations, and the red curve corresponds to one of the realizations shown in Fig. 3. In the upper left panel the green line shows the mean GW energy density (8). The distributions of Ω_GW and 𝒫_GW at 1 nHz (blue) and at 30 nHz (orange) calculated from the Monte Carlo realizations are shown in the right panels. In the upper right panel, the dashed lines show , and in the lower right panel, the dashed curves show Gaussian fits to these distributions of width σ = 0.13 (blue) and σ = 0.23 (orange). In this figure, p_BH = 0.17 is assumed.