  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.
