The cosmic evolution of massive black holes and galaxy spheroids: global
  constraints at redshift z<~1.2
  We study the observational constraints on the cosmic evolution of the
relationships between the massive black hole (MBH) mass (M_bh) and the stellar
mass (M^*_sph; or velocity dispersion \sigma) of the host galaxy/spheroid.
Assuming that the M_bh-M^*_sph (or M_bh-\sigma) relation evolves with redshift
as \propto (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~0-1.2 for any given \Gamma. The MBH mass
density at different redshifts can also be inferred from the luminosity
function of QSOs/AGNs provided known radiative efficiency \epsilon. By matching
the MBH density inferred from galaxies to that obtained from QSOs/AGNs, we find
that \Gamma=0.64^{+0.27}_{-0.29} for the M_bh-M^*_sph relation and
\Gamma=-0.21^{+0.28}_{-0.33} for the M_bh-\sigma relation, and
\epsilon=0.11^{+0.04}_{-0.03}. Our results suggest that the MBH mass growth
precedes the bulge mass growth but the galaxy velocity dispersion does not
increase with the mass growth of the bulge after the quench of nuclear
activity, which is roughly consistent with the two-phase galaxy formation
scenario proposed by Oser et al. (2012) in which a galaxy roughly double its
masses after z=1 due to accretion and minor mergers while its velocity
dispersion drops slightly.
