THE COSMIC EVOLUTION OF MASSIVE BLACK HOLES AND GALAXY SPHEROIDS: GLOBAL CONSTRAINTS AT REDSHIFT z ≲ 1.2

We study observational constraints on the cosmic evolution of the relationships between massive black hole (MBH) mass (M-center dot) and stellar mass (M-*,M-sph; or velocity dispersion sigma) of a host galaxy/spheroid. Assuming that the M-center dot-M-*,M-sph (or M-center dot-sigma) relation evolves with redshift as proportional to (1 + z)(Gamma), the MBH mass density can be obtained from either the observationally determined galaxy stellar mass functions or velocity dispersion distribution functions over redshift z similar to 0-1.2 for any given Gamma. The MBH mass density at different redshifts can also be inferred from the luminosity function of QSOs/active galactic nuclei (AGNs) provided the radiative efficiency epsilon is known. By matching the MBH density inferred from galaxies to that obtained from QSOs/AGNs, we find that Gamma = 0.6(-0.29)(+0.27) for the M-center dot-M-*,M-sph relation and Gamma = -0.21(-0.33)(+0.28) for the M-center dot-sigma relation, and epsilon = 0.1(-0.03)(+0.04). Our results suggest that MBH mass growth precedes bulge mass growth but that the galaxy velocity dispersion does not increase with the mass growth of the bulge after nuclear activity is quenched, which is roughly consistent with the two-phase galaxy formation scenario proposed by Oser et al. in which a galaxy roughly doubles its mass after z = 1 due to accretion and minor mergers while its velocity dispersion drops slightly.