A remarkably flat relationship between the average star formation rate and AGN luminosity for distant X-ray AGN

In this study we investigate the relationship between the star formation rate, SFR, and AGN luminosity, L(AGN), for ~2000 X-ray detected AGN. The AGN span over three orders of magnitude in X-ray luminosity (10^(42) < L(2-8keV) < 10^(45.5) erg/s) and are in the redshift range z = 0.2 - 2.5. Using infrared (IR) photometry (8 - 500um), including deblended Spitzer and Herschel images and taking into account photometric upper limits, we decompose the IR spectral energy distributions into AGN and star formation components. Using the IR luminosities due to star formation, we investigate the average SFRs as a function of redshift and AGN luminosity. In agreement with previous studies, we find a strong evolution of the average SFR with redshift, tracking the observed evolution of the overall star forming galaxy population. However, we find that the relationship between the average SFR and AGN luminosity is flat at all redshifts and across all the AGN luminosities investigated; in comparison to previous studies, we find less scatter amongst the average SFRs across the wide range of AGN luminosities investigated. By comparing to empirical models, we argue that the observed flat relationship is due to short timescale variations in AGN luminosity, driven by changes in the mass accretion rate, which wash out any underlying correlations between SFR and L(AGN). Furthermore, we show that the exact form of the predicted relationship between SFR and AGN luminosity (and it's normalisation) is highly sensitive to the assumed intrinsic Eddington ratio distribution.