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Self-Regulated Star Formation and the Black Hole-Galaxy Bulge Relation

We show that star formation in galaxy bulges is self-regulating through momentum feedback, limiting the stellar bulge mass to M_b ~ sigma^4. Together with a black hole mass M_BH ~ sigma^4 set by AGN momentum feedback, this produces a linear M_BH - M_b relation. At low redshift this gives M_BH/M_b ~ 0.001, close to the observed ratio. We show that AGN feedback can remove any remaining gas from the bulge and terminate star formation once the central black hole reaches the M_BH - sigma value, contrary to earlier claims. We find a mild upward deviation from the sigma^4 law at higher redshift and at higher sigma.