AGN feedback in numerical simulations

The passively evolving stellar populations in elliptical galaxies provide a continuous source of fuel for the SMBH accretion, which is 1) linearly proportional to the stellar mass of the host spheroid, 2) extended over the entire galaxy life (but declining with cosmic time), 3) available independently of merging events, 4) summing up to a total gas mass a factor 10-100 larger than the currently observed SMBH masses. The main results obtained from numerical simulations of elliptical galaxies with central SMBHs, in which a physically based implementation of radiative and mechanical feedback effects is considered, are presented. The successful theoretical and observational predictions of the models, as well as the unsolved problems, are also presented.