Mass-dependent evolution of the relation between the supermassive black hole mass and host spheroid mass since z ∼ 1

We investigate the evolutions of supermassive black hole mass (M-BH) and host spheroid mass (M-sph) in order to track the history of the M-BH-M-sph relationship. The typical mass increase in M-BH is calculated by a continuity equation and accretion history, which is estimated from the active galactic nucleus 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 similar to 1.2 for high mass objects (M-BH > 108.5 M-circle dot and M-sph > 1011.3 M-circle dot). In the same redshift range, the spheroid mass is found to increase more rapidly than the black hole mass if M-sph > 1011 M-circle dot. The proposed mass-dependent model is consistent with the current available observational data in the M-BH-M-sph diagram.