  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.
