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.

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