2004MNRAS.354L..37M

We examine possible phenomenological constraints for the joint evolution of supermassive black holes (SMBHs) and their host spheroids. We compare all the available observational data on the redshift evolution of the total stellar mass and star formation rate density in the Universe with the mass and accretion rate density evolution of SMBHs, estimated from the hard X-ray selected luminosity function of quasars and active galactic nuclei for a given radiative efficiency, ε. We assume that the ratio of the stellar mass in spheroids to the black hole mass density evolves as (1 +z)^–α, while the ratio of the stellar mass in discs + irregulars to that in spheroids evolves as (1 +z)^–β, and we derive constraints on α, β and ε. We find that α > 0 at more than the 4σ level, implying a larger black hole mass at higher redshift for a given spheroid stellar mass. The favoured values for β are typically negative, suggesting that the fraction of stellar mass in spheroids decreases with increasing redshift. This is consistent with recent determinations that show that the mass density at high redshift is dominated by galaxies with irregular morphology. In agreement with earlier work, we constrain ε to be between 0.04 and 0.11, depending on the exact value of the local SMBH mass density, but almost independently of α and β.