The link between star-formation and supermassive black hole properties

It is well known that supermassive black holes (SMBHs) and their host galaxies co-evolve. AGN feedback plays an important role on this symbiosis. To study the effect of the AGN feedback on the host galaxy, a 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 SFR of AGN and non-AGN galaxies as a function of L$_X$, M$_{BH}$, Eddington ratio (n$_{Edd}$) and specific black hole accretion rate ($\lambda _{sBHAR}$). For that purpose, we use 122 X-ray AGN in the XMM-XXL field and 3371 galaxies from the VIPERS survey and 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 $\rm 0.5\leq z\leq 1.2$. 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 $\lambda _{sBHAR}$. No correlation is detected between SFR$_{norm}$ and n$_{Edd}$. These results corroborate the idea that the M$_{BH}$ is a more robust tracer of the cumulative impact of the AGN feedback compared to the instantaneous accretion rate (L$_X$) and, thus, a better predictive parameter of the changes of the SFR of the host galaxy.