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 Mb∝σ4. Together with a black hole mass MBH∝σ4 set by active galactic nucleus (AGN) momentum feedback, this produces a linear MBH–Mb relation. At low redshift this gives MBH/Mb∼ 10−3, 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 MBH–σ value, contrary to earlier claims. We find a mild upward deviation from the σ4 law at higher redshift and at higher σ.