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 _•) and stellar mass (M _{*, sph}; or velocity dispersion σ) of a host galaxy/spheroid. Assuming that the M _•-M _{*, sph} (or M _•-σ) relation evolves with redshift as vprop(1 + z)^Γ, the MBH mass density can be obtained from either the observationally determined galaxy stellar mass functions or velocity dispersion distribution functions over redshift z ~ 0-1.2 for any given Γ. 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 Γ = 0.64^+0.27 _{- 0.29} for the M _•-M _{*, sph} relation and Γ = -0.21^+0.28 _{- 0.33} for the M _•-σ relation, and epsilon = 0.11^+0.04 _{- 0.03}. 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.