The Evolution of the Mbh-σ Relation

We examine the evolution of the black hole mass stellar velocity dispersion (MBH−σ) relation over cosmic time using simulations of galaxy mergers that include feedback from supermassive black hole growth. Our calculations have been shown to reproduce the power-law scaling of the local, redshift zero MBH−σ relation and yield the observed normalization for an appropriate choice of the feedback efficiency. In the present paper, we consider mergers of galaxies varying the properties of the progenitors to match those expected at various cosmic times. In particular, we examine a range in redshifts z = 0-6, where we modify the virial mass, gas fraction, interstellar medium equation of state, surface mass density, and concentration of the dark matter halos. We find that the slope of the resulting MBH−σ relation is the same at all redshifts. For the same feedback efficiency that reproduces the observed amplitude of the MBH−σ relation at z = 0, there is a weak redshiftdependence 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 MBH−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 MBH−σ relation. Furthermore, we demonstrate that the cosmic downsizing of the black hole population introduces a black hole mass-dependent dispersion in the MBH−σ relation and that the skewness of the distribution about the locally observed MBH−σ relation is sensitive to redshift evolution in the normalization and slope. Improving the statistics of the local relation to measure the moments of its distribution will therefore make it possible to constrain the evolution of the MBH−σ relation and black hole population at redshifts that are currently not observationally accessible. In principle, these various diagnostics provide a method for differentiating between theories for producing the MBH−σ relation. 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 MBH−σ enjoys a remarkable resiliency to the redshift-dependent properties of merger progenitors. Subject headings: galaxies: formation – galaxies: evolution