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 [\overlineBHAR(M_{\star }, z)] over ranges of log (M_⋆/M_⊙) = 9.5-12 and z = 0.4-4. Our \overlineBHAR(M_{\star }, 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_⋆, \overlineBHAR is higher at high redshift. This redshift dependence is stronger in more massive systems [for log (M_⋆/M_⊙) ≈ 11.5, \overlineBHAR is three decades higher at z = 4 than at z = 0.5], possibly due to AGN feedback. Our results indicate that the ratio between \overlineBHAR and average star formation rate (\overlineSFR) rises towards high M_⋆ at a given redshift. This \overlineBHAR/\overlineSFR 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 \overlineBHAR(M_{\star }, 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.