Linking black hole growth with host galaxies: The accretion-stellar mass relation and its cosmic evolution

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 [BHAR(M_*, z)] over ranges of log (M_*/M_⊙) = 9.5-12 and z = 0.4-4. Our BHAR(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_*, BHAR is higher at high redshift. This redshift dependence is stronger in more massive systems [for log (M_*/M_⊙) ≈ 11.5, BHAR is three decades higher at z = 4 than at z = 0.5], possibly due to AGN feedback. Our results indicate that the ratio between BHAR and average star formation rate (SFR) rises towards high M_* at a given redshift. This BHAR/SFR dependence on M_* does not support the scenario that SMBH and galaxy growth are in lockstep. We calculate SMBH mass history [MBH(z)] based on our BHAR(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 logM_* ≲ 10.5 to ≈1/500 at logM_* ≳ 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.