Ratio of the predicted flux from our BH population and the observed limits in the soft band (0.3–2 keV; shown by the color bar). The y-axis shows the possible values for $k=f_{\mathrm{occupation}}^{\mathrm{BH}}{U}_{\mathrm{duty}}{ϵ}_{\mathrm{Edd}}{ϵ}_X$ assuming a metallicity equal to Z = 0.01 Z_⊙ (top panel) and Z = 0.1 Z_⊙ (bottom panel). The x-axis is the average column density N_ave in units of cm⁻². The solid red line denotes the curve where the transition from overprediction occurs.