Correlation of black hole-bulge masses by AGN jets

I propose a feedback model to explain the correlation between the supermassive black hole (SMBH) mass and the host galaxy bulge mass. The feedback is based on narrow jets that are launched by the central SMBH, and expel large amounts of mass to large distances. The condition is that the jets do not penetrate through the inflowing gas, such that they can deposit their energy in the inner region where the bulge is formed. For that to occur, the SMBH must move relative to the inflowing gas, such that the jets continuously encounter fresh gas. Taking into account the relative motion of the SMBH and the inflowing gas I derive a relation between the mass accreted by the SMBH and the mass that is not expelled, and is assumed to form the bulge. This relation is not linear, but rather the SMBH to bulge mass ratio increases slowly with mass. The same mechanism was applied to suppress star formation in cooling flow clusters, making a tighter connection between the feedback in galaxy formation and cooling flows.