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How the central black hole may shape its host galaxy through AGN feedback

Active galactic nucleus (AGN) feedback provides the link between the central black hole and its host galaxy. We assume AGN feedback driven by radiation pressure on dust, which sweeps up the ambient dusty gas into an outflowing shell, and consider feedback-triggered star formation in the outflow. An upper limit to the characteristic size of galaxies may be defined by the critical radius beyond which radiation pressure on dust is no longer able to drive the shell. The corresponding enclosed mass may be compared with the host galaxy bulge mass. We show that the resulting relation between characteristic radius and mass, of the form $R \propto \sqrt M$, corresponds to the observed mass-radius relation of early-type galaxies. We suggest that such simple physical scalings may account for a number of observed galaxy scaling relations. In this picture, both the size and structural evolution of galaxies can be interpreted as a consequence of AGN feedback-driven star formation, mainly associated with the spheroidal component. The accreting black hole is responsible for triggering star formation in the host galaxy, while ultimately clearing the dusty gas out of the host, thus also contributing to the chemical evolution of galaxies. We discuss the importance of radiation pressure on dust in determining the galaxies large-scale properties, and consider the possibility of the central black hole directly shaping its host galaxy through AGN feedback.