  By means of a one-zone evolutionary model, we study the co-evolution of
supermassive black holes and their host galaxies, as a function of the
accretion radiative efficiency, dark matter content, and cosmological infall of
gas. In particular, the radiation feedback is computed by using the
self-regulated Bondi accretion. The models are characterized by strong
oscillations when the galaxy is in the AGN state with a high accretion
luminosity. We found that these one-zone models are able to reproduce two
important phases of galaxy evolution, namely an obscured-cold phase when the
bulk of star formation and black hole accretion occur, and the following
quiescent hot phase in which accretion remains highly sub-Eddington. A
Compton-thick phase is also found in almost all models, associated with the
cold phase. An exploration of the parameter space reveals that the closest
agreement with the present-day Magorrian relation is obtained, independently of
the dark matter halo mass, for galaxies with a low-mass seed black hole, and
the accretion radiative efficiency ~0.1.
