  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]
