The evolution of the M_BH-σ relation

We examine the evolution of the black hole mass-stellar velocity dispersion (M_BH-σ) relation over cosmic time, using simulations of galaxy mergers that include feedback from supermassive black hole growth. For a range in redshifts z = 0-6, we modify the virial mass, gas fraction, interstellar medium equation of state, surface mass density, and concentration of dark matter halos of the merger progenitors to match those expected at various cosmic times. We find that the slope of the M_BH-σ relation is insensitive to the redshift-dependent properties of merger progenitors and should be roughly constant at redshifts z = 0-6. For the same feedback efficiency that reproduces the observed amplitude of the M_BH-σ relation at z = 0, there is a weak redshift dependence to the normalization, corresponding to an evolution in the Faber-Jackson relation, which results from an increasing velocity dispersion for a given galactic stellar mass. We develop a formalism to connect redshift evolution in the M_BH-σ relation to the scatter in the local relation at z = 0. For an assumed model for the accumulation of black holes with different masses over cosmic time, we show that the scatter in the local relation places severe constraints on the redshift evolution of both the normalization and slope of the M_BH-σ relation. Furthermore, we demonstrate that the cosmic downsizing of the black hole population introduces a black hole mass-dependent dispersion in the M _BH-σ relation and that the skewness of the distribution about the locally observed M_BH-σ relation is sensitive to redshift evolution in the normalization and slope. In agreement with existing constraints, our simulations imply that hierarchical structure formation should produce the relation with small intrinsic scatter, as the physical origin of the M_BH-σ enjoys a remarkable resiliency to the redshift-dependent properties of merger progenitors.