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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 accretionof dense cold clumps and filaments. AGN feedback outflows overtake the coldmedium, compress it, and trigger a powerful starburst -- a positive AGNfeedback. This predicts a statistical correlation between AGN luminosity andstar formation rate at high luminosities. Most of the outflow's kinetic energyescapes from the bulge via low density voids. The cold phase is pushed outwardonly by the ram pressure (momentum) of the outflow. The combination of thenegative and positive forms of AGN feedback leads to an $M-\sigma$ relationsimilar 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 evenfor SMBH well below the $M-\sigma$ mass. The role of SMBH feedback in our modelevolves 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 toscarcity of the cold ISM.

Two-phase model for Black Hole feeding and feedback