Two-phase model for Black Hole feeding and feedback

We study effects of AGN feedback outflows on multi-phase inter stellar medium (ISM) of the host galaxy. We argue that SMBH growth is dominated by accretion of dense cold clumps and filaments. AGN feedback outflows overtake the cold medium, compress it, and trigger a powerful starburst -- a positive AGN feedback. This predicts a statistical correlation between AGN luminosity and star formation rate at high luminosities. Most of the outflow's kinetic energy escapes from the bulge via low density voids. The cold phase is pushed outward only by the ram pressure (momentum) of the outflow. The combination of the negative and positive forms of AGN feedback leads to an $M-\sigma$ relation similar to the result of King (2003). Due to porosity of cold ISM in the bulge, SMBH influence on the low density medium of the host galaxy is significant even for SMBH well below the $M-\sigma$ mass. The role of SMBH feedback in our model evolves in space and time with the ISM structure. In the early gas rich phase, SMBH accelerates star formation in the bulge. During later gas poor (red-and-dead) phases, SMBH feedback is mostly negative everywhere due to scarcity of the cold ISM.