2018MNRAS.475.1887Y

Previous studies suggest that the growth of supermassive black holes (SMBHs) may be fundamentally related to host-galaxy stellar mass (M_*). To investigate this SMBH growth-M_* relation in detail, we calculate long-term SMBH accretion rate as a function of M_* and redshift [(M_*, z)] over ranges of log (M_*/M_☉) = 9.5-12 and z = 0.4-4. Our (M_*, z) is constrained by high-quality survey data (GOODS-South, GOODS-North and COSMOS), and by the stellar mass function and the X-ray luminosity function. At a given M_*,  is higher at high redshift. This redshift dependence is stronger in more massive systems [for log (M_*/M_☉) ≃ 11.5,  is three decades higher at z = 4 than at z = 0.5], possibly due to AGN feedback. Our results indicate that the ratio between  and average star formation rate () rises towards high M_* at a given redshift. This / dependence on M_* does not support the scenario that SMBH and galaxy growth are in lockstep. We calculate SMBH mass history [M_BH(z)] based on our (M_*, z) and the M_*(z) from the literature, and find that the M_BH-M_* relation has weak redshift evolution since z ≃ 2. The M_BH/M_* ratio is higher towards massive galaxies: it rises from ≃1/5000 at log M_* <= 10.5 to ≃1/500 at log M_* >= 11.2. Our predicted M_BH/M_* ratio at high M_* is similar to that observed in local giant ellipticals, suggesting that SMBH growth from mergers is unlikely to dominate over growth from accretion.