Comparison of the M_h − L_X scaling relation with the observational data from Koutoulidis et al. (2012). To capture the redshift range of majority of AGN used in this analysis, we have plotted the model scaling relations for three redshifts: z = 0.5,1.0,1.5. The dotted lines with surrounding gray bands display the results from the semianalytic galaxy–AGN co-evolution model of Fanidakis et al. (2012), as presented in Koutoulidis et al. (2012), showing their “hot-halo” (dark gray region) and “all AGN” case, i.e., the sum of “hot-halo” and “starburst” modes (light gray region). The long-dashed line shows the M_h − L_X scaling one obtains once converting the amplitude-adjusted M_h − M_BH relation of Bandara et al. (2009) by using the fixed Eddington ratio f_Edd ≡ L_X/L_Edd(M_BH) = 3 × 10^-4.