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By means of a one-zone evolutionary model, we study the co-evolution ofsupermassive black holes and their host galaxies, as a function of theaccretion radiative efficiency, dark matter content, and cosmological infall ofgas. In particular, the radiation feedback is computed by using theself-regulated Bondi accretion. The models are characterized by strongoscillations when the galaxy is in the AGN state with a high accretionluminosity. We found that these one-zone models are able to reproduce twoimportant phases of galaxy evolution, namely an obscured-cold phase when thebulk of star formation and black hole accretion occur, and the followingquiescent hot phase in which accretion remains highly sub-Eddington. ACompton-thick phase is also found in almost all models, associated with thecold phase. An exploration of the parameter space reveals that the closestagreement with the present-day Magorrian relation is obtained, independently ofthe dark matter halo mass, for galaxies with a low-mass seed black hole, andthe accretion radiative efficiency ~0.1.

One-zone models for spheroidal galaxies with a central supermassive black-hole. Self-regulated Bondi accretion