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Using X-ray stacking analyses we estimate the average amounts of supermassive black hole (SMBH) growth taking place in star-forming galaxies at z ∼ 1 and z ∼ 2 as a function of galaxy stellar mass ( M * ). We find that the average SMBH growth rate follows remarkably similar trends with M * and redshift as the average star formation rates (SFRs) of their host galaxies (i.e., ∝ M * 0.86 ± 0.39 for the z ∼ 1 sample and ∝ M * 1.05 ± 0.36 for the z ∼ 2 sample). It follows that the ratio of SMBH growth rate to SFR is (1) flat with respect to M * , (2) not evolving with redshift, and (3) close to the ratio required to maintain/establish an SMBH to stellar mass ratio of ≈10 −3 as also inferred from today's M BH – M Bulge relationship. We interpret this as evidence that SMBHs have, on average, grown in step with their host galaxies since at least z ∼ 2, irrespective of host galaxy mass and active galactic nucleus triggering mechanism. As such, we suggest that the same secular processes that drive the bulk of star formation are also responsible for the majority of SMBH growth. From this, we speculate that it is the availability of gas reservoirs that regulate both cosmological SMBH growth and star formation.
A 2012 study studied this question.