Link between star formation and the properties of supermassive black holes

It is well known that supermassive black holes (SMBHs) and their host galaxies undergo a process of co-evolution. Feedback from active galactic nuclei (AGNs) plays an important role in this symbiosis. To study the effect of AGN feedback on the host galaxy, one popular method is to study the star formation rate (SFR) as a function of the X-ray luminosity (L_X). However, hydrodynamical simulations suggest that the cumulative impact of AGN feedback on a galaxy is encapsulated in the mass of the SMBH, M_BH, rather than the L_X. In this study, we compare the SFRs of AGN and non-AGN galaxies as a function of L_X, M_BH, the Eddington ratio (n_Edd), and the specific black hole accretion rate (λ_sBHAR). For that purpose, we used 122 X-ray AGN in the XMM-XXL field and 3371 galaxies from the VIPERS survey to calculate the SFR_norm parameter, defined as the ratio of the SFR of AGN to the SFR of non-AGN galaxies with similar stellar mass, M_*, and redshift. Our datasets span a redshift range of 0.5 ≤ z ≤ 1.2. The results show that the correlation between SFR_norm and M_BH is stronger compared to that between SFR_norm and L_X. A weaker correlation is found between SFR_norm and λ_sBHAR. No correlation is detected between SFR_norm and n_Edd. These results corroborate the notion that the M_BH is a more robust tracer of the cumulative impact of the AGN feedback, compared to the instantaneous accretion rate (L_X). Thus, it may serve as a better predictive parameter of changes in the SFR of the host galaxy.