The importance of feedback (radiative and mechanical) from massive black holes at the centers of elliptical galaxies is not in doubt, given the well established relation among black hole mass and galaxy optical luminosity. Here, with the aid of high-resolution hydrodynamical simulations, we discuss how this feedback affects the hot ISM of isolated elliptical galaxies of different mass. The cooling and heating functions include photoionization plus Compton heating, the radiative transport equations are solved, and the mechanical feedback due to the nuclear wind is also described on a physical basis; star formation is considered. In the medium-high mass galaxies the resulting evolution is highly unsteady. At early times major accretion episodes caused by cooling flows in the recycled gas produced by stellar evolution trigger AGN flaring: relaxation instabilities occur so that duty cycles are small enough to account for the very small fraction of massive ellipticals observed to be in the QSO-phase, when the accretion luminosity approaches the Eddington luminosity. At low redshift all models are characterized by smooth, very sub-Eddington mass accretion rates. The mass accumulated by the central black hole is limited to range observed today, even though the mass lost by the evolving stellar population is roughly two order of magnitude larger than the black hole masses observed in elliptical galaxies.Comment: 20 pages, 4 (low-resolution) figures. Abbreviated version of the article to appear in book "Hot Interstellar Matter in Elliptical Galaxies", D.-W. Kim and S. Pellegrini eds., Astrophysics and Space Science Library (ASSL), Springe
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