By using high-resolution 1D hydrodynamical simulations, we investigate the effects of purely mechanical feedback from super massive black holes (SMBHs) in the evolution of elliptical galaxies for a broad range of feedback efficiencies and compare the results to four major observational constraints. In particular, we focus on 1) the central black hole to stellar mass ratio of the host galaxy, 2) the lifetime of the luminous quasar phase, 3) the mass of stars formed in the host galaxy within the last Gyr, and 4) the X-ray luminosity of the hot diffuse gas. As a result, we try to pin down the most successful range of mechanical feedback efficiencies. We find that while low feedback efficiencies result in too much growth of the SMBH, high efficiencies totally blow out the hot interstellar gas, and the models are characterized by very low thermal X-ray luminosity well below the observed range. The net lifetime of the quasar phase is strongly coupled to the mass ratio between SMBH and its host galaxy, while the X-ray luminosity is generally correlated to the recent star formation within the last Gyr. When considering the popularly adopted model of the constant feedback efficiency, the feedback energy deposited into the ambient medium should be more than 0.01% of the SMBH accretion energy to be consistent with the SMBH mass to stellar mass ratio in the local universe. Yet, the X-ray luminosity of the hot gas favors about 0.005% of the accretion energy as the mechanical AGN feedback energy. We conclude that the purely mechanical feedback mode is unlikely to be simultaneously compatible with all four observable tests, even allowing a broad range of feedback efficiencies, and that including both radiative and mechanical feedback together may be a solution to comply the observational constraints. [abridged]
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