Mass-dependent evolution of the relation between supermassive black hole
  mass and host spheroid mass since z ~ 1
  We investigate the evolution of supermassive black hole mass (M_BH) and the
host spheroid mass (M_sph) in order to track the history of the M_BH-M_sph
relationship. The typical mass increase of M_BH is calculated by a continuity
equation and accretion history, which is estimated from the active galactic
nucleus (AGN) luminosity function. The increase in M_sph is also calculated by
using a continuity equation and a star formation model, which uses
observational data for the formation rate and stellar mass function. We find
that the black hole to spheroid mass ratio is expected to be substantially
unchanged since z~1.2 for high mass objects (M_BH>10^8.5M_SUN and
M_sph>10^11.3M_SUN). In the same redshift range, the spheroid mass is found to
increase more rapidly than the black hole mass if M_sph>10^11M_SUN. The
proposed mass-dependent model is consistent with the current available
observational data in the M_BH-M_sph diagram.
