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We study the growth of massive black holes (BHs) in galaxies using smoothed particle hydrodynamic simulations of major galaxy mergers with new implementations of BH accretion and feedback. The effect of BH accretion on gas in its host galaxy is modelled by depositing momentum at the rate of  ∼τ L / c   into the ambient gas, where   L   is the luminosity produced by accretion on to the BH and  τ  is the wavelength‐averaged optical depth of the galactic nucleus to the AGN’s radiation (a free parameter of our model). The accretion rate on to the BH is relatively independent of our subgrid accretion model and is instead determined by the BH’s dynamical impact on its host galaxy: BH accretion is thus self‐regulated rather than ‘supply limited’. We show that the final BH mass and total stellar mass formed during a merger are more robust predictions of the simulations than the time dependence of the star formation rate or BH accretion rate. In particular, the latter depend on the assumed interstellar medium physics, which determines when and where the gas fragments to form star clusters; this in turn affects the fuel available for further star formation and BH growth. Simulations over a factor of  ∼30  in galaxy mass are consistent with the observed   M  BH –σ  relation for a mean optical depth of  τ∼ 25 . This requires that most BH growth occur when the galactic nucleus is optically thick to far‐infrared radiation, consistent with the hypothesized connection between ultraluminous infrared galaxies and quasars. We find tentative evidence for a shallower   M  BH –σ  relation in the lowest‐mass galaxies,  σ≲ 100 km s −1  . Our results demonstrate that feedback‐regulated BH growth and consistency with the observed   M  BH –σ  relation do not require that BH feedback terminate star formation in massive galaxies or unbind large quantities of cold gas.

The growth of massive black holes in galaxy merger simulations with feedback by radiation pressure