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

Abstract

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 MBH-M* relation has weak redshift evolution since z ≈ 2. The MBH/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 MBH/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.