Recent observations show that the space density of luminous active galactic nuclei (AGNs) peaks at higher redshifts than that of faint AGNs. This downsizing trend in the AGN evolution seems to be contradictory to the hierarchical structure formation scenario. In this study, we present the AGN space density evolution predicted by a semi-analytic model of galaxy and AGN formation based on the hierarchical structure formation scenario. We demonstrate that our model can reproduce the downsizing trend of the AGN space density evolution. The reason for the downsizing trend in our model is a combination of the cold gas depletion as a consequence of star formation, the gas cooling suppression in massive halos, and the AGN lifetime scaling with the dynamical timescale. We assume that a major merger of galaxies causes a starburst, spheroid formation, and cold gas accretion onto a supermassive black hole (SMBH). We also assume that this cold gas accretion triggers AGN activity. Since the cold gas is mainly depleted by star formation and gas cooling is suppressed in massive dark halos, the amount of cold gas accreted onto SMBHs decreases with cosmic time. Moreover, AGN lifetime increases with cosmic time. Thus, at low redshifts, major mergers do not always lead to luminous AGNs. Because the luminosity of AGNs is correlated with the mass of accreted gas onto SMBHs, the space density of luminous AGNs decreases more quickly than that of faint AGNs. We conclude that the anti-hierarchical evolution of the AGN space density is not contradictory to the hierarchical structure formation scenario.
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