Black hole growth and activity in a LambdaCDM Universe

The observed properties of supermassive black holes suggest a fundamental link between their assembly and the formation of their host spheroids. We model the growth and activity of black holes in galaxies using LambdaCDM cosmological hydrodynamic simulations by following the evolution of the baryonic mass component in galaxy potential wells. We find that the observed steep relation between black hole mass and spheroid velocity dispersion, M_BH propto sigma^4, is reproduced by a linear relation between the total gas mass in bulges and the black hole mass. We show that star formation and supernova feedback can be the fundamental regulating factors limiting the growth of the central black hole and of its gas supply. Black hole growth saturates because of the competition with star-formation and in particular feedback, both of which determine the gas fraction available for accretion. Unless other processes also operate, we predict that the steep dependence of black hole mass on velocity dispersion is not set in primordial structures but is fully established at low redshifts, z < 2, and is shallower at earlier times. Assuming that the lifetime of quasars is t ~ 10^7 yr, we show that the star-formation regulated depletion of gas in spheroids is sufficient to explain, for the most part, the decrease of the quasar population at redshift z < 3. In this model, we predict that the number density of quasars in the redshift range 4 < z < 7 should exceed the observed value by up to a factor ~5, implying that current observations may be significantly affected by dust extinction. Our model predicts that the majority of black hole mass is assembled in galaxies by z ~ 3 and that the black hole accretion rate density peaks in rough correspondence to the star formation rate density at z ~ 4-5