Effect of feedback treatment on the M_BH − M_*, b relation. The relation predicted for galaxies at z ≤ 0.1 by our new two-dimensional model for AGN feedback (top panels) presented in Sect. 2.1 is compared with the predictions obtained with our previous isotropic treatment of feedback (bottom panels). For both AGN feedback models, we show the results with and without the selection effect discussed in Sect. 2.1, as indicated by the labels. In all panels, the color code corresponds to the logarithm of the fraction of galaxies with different M_BH in a given log M_*, b bin. The standard deviations ϵ for the new and previous treatment of AGN feedback is shown as a function of bulge stellar mass in the rightmost histograms. The horizontal strip represents the range of values obtained from different observational works: the upper bound is the intrinsic scatter ϵ derived by De Nicola et al. (2019), and the lower bound is the value of ϵ derived by the least-square fit analysis by Kormendy & Ho (2013) using individual errors in log σ, adding individual errors in log M_BH to the intrinsic scatter in quadrature, and iterating the intrinsic scatter until the reduced χ² = 1.