COSMOLOGICAL EVOLUTION OF SUPERMASSIVE BLACK HOLES. I. MASS FUNCTION AT 0 < z ≲ 2

We present the mass function of supermassive black holes (SMBHs) over the redshift range z = 0-2, using the latest deep luminosity and mass functions of field galaxies to constrain the masses of their spheroids, which we relate to SMBH mass through the empirical correlation between SMBH and spheroid mass (the M-center dot-M-sph relation). In addition to luminosity fading of the stellar content of the spheroids, we carefully consider the variation of the bulge-to-total luminosity ratio of the galaxy populations and the M-center dot/M-sph ratio, which, according to numerous recent studies, evolves rapidly with redshift. The SMBH mass functions derived from the galaxy luminosity and mass functions show very good agreement, both in shape and in normalization. The resultant SMBH mass function and integrated mass density for the local epoch (z approximate to 0) match well those derived independently by other studies. Consistent with other evidence for cosmic downsizing, the upper end of the mass function remains roughly constant since z approximate to 2, while the space density of lower mass black holes undergoes strong evolution. We carefully assess the impact of various sources of uncertainties on our calculations. A companion paper uses the mass function derived in this work to determine the radiative efficiency of black hole accretion and constraints that can be imposed on the cosmological evolution of black hole spin.