The ISM evolution of elliptical galaxies experiencing feedback from accretion onto a central black hole was studied recently with high-resolution 1D hydrodynamical simulations including radiative heating and pressure effects, a RIAF-like radiative efficiency, mechanical input from AGN winds, and accretion-driven starbursts. Here we focus on the observational properties of the models in the X-ray band (nuclear luminosity; hot ISM luminosity and temperature; temperature and brightness profiles during quiescence and during outbursts). The nuclear bursts last for ~10^7 yr, with a duty-cycle of a few X (10^-3-10^-2); the present epoch bolometric nuclear emission is very sub-Eddington. The ISM thermal luminosity lx oscillates in phase with the nuclear one; this helps reproduce statistically the observed large lx variation. In quiescence the temperature profile has a negative gradient; thanks to past outbursts, the brightness profile lacks the steep shape typical of inflowing models. Outbursts produce disturbances in these profiles. Most significantly, a hot bubble from shocked hot gas is inflated at the galaxy center; the bubble would be conical in shape, and show radio emission. The ISM resumes a smooth appearance on a time-scale of ~200 Myr; the duty-cycle of perturbances in the ISM is of the order of 5-10%. From the present analysis, additional input physics is important in the ISM-black hole coevolution, to fully account for the properties of real galaxies, as a confining external medium and a jet. The jet will reduce further the mass available for accretion (and then the Eddington ratio $l$), and may help, together with an external pressure, to produce flat or positive temperature gradient profiles (observed in high density environments). Alternatively, $l$ can be reduced if the switch from high to low radiative efficiency takes place at a larger $l$ than routinely assumed.
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