The importance of the radiative feedback from SMBHs at the centers of elliptical galaxies is not in doubt, given the well established relations among electromagnetic output, black hole mass and galaxy optical luminosity. In addition, feedback due to mechanical and thermal deposition of energy from jets and winds emitted by the accretion disk around the central SMBH is also expected to occur. In this paper we improve and extend the accretion and feedback physics explored in our previous papers to include also a physically motivated mechanical feedback. We study the evolution of an isolated elliptical galaxy with the aid of a high-resolution 1-D hydrodynamical code, where the cooling and heating functions include photoionization and Compton effects, and restricting to models which include only radiative or only mechanical feedback. We confirm that for Eddington ratios above 0.01 both the accretion and radiative output are forced by feedback effects to be in burst mode, so that strong intermittencies are expected at early times, while at low redshift the explored models are characterized by smooth, very sub-Eddington mass accretion rates punctuated by rare outbursts. However, the explored models always fail some observational tests. If we assume the high mechanical efficiency of 10^{-2.3}, we find that most of the gas is ejected from the galaxy, the resulting X-ray luminosity is far less than is typically observed and little SMBH growth occurs. But models with low enough mechanical efficiency to accomodate satisfactory SMBH growth tend to allow too strong cooling flows and leave galaxies at z=0 with E+A spectra more frequently than is observed. We conclude that both types of feedback are required. Models with combined feedback are explored in a forthcoming paper [abridged]
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