The lack of a strong correlation between AGN X-ray luminosity ($L_X$; a proxy for AGN power) and the star formation rate (SFR) of their host galaxies has recently been attributed to stochastic AGN variability. Studies using population synthesis models have incorporated this by assuming a broad, universal (i.e. does not depend on the host galaxy properties) probability distribution for AGN specific X-ray luminosities (i.e. the ratio of $L_X$ to host stellar mass; a common proxy for Eddington ratio). However, recent studies have demonstrated that this universal Eddington ratio distribution fails to reproduce the observed X-ray luminosity functions beyond z$sim$1.2. Furthermore, empirical studies have recently shown that the Eddington ratio distribution may instead depend upon host galaxy properties, such as SFR and/or stellar mass. To investigate this further we develop a population synthesis model in which the Eddington ratio distribution is different for star-forming and quiescent host galaxies. We show that, although this model is able to reproduce the observed X-ray luminosity functions out to z$sim$2, it fails to simultaneously reproduce the observed flat relationship between SFR and X-ray luminosity. We can solve this, however, by incorporating a mass dependency in the AGN Eddington ratio distribution for star-forming host galaxies. Overall, our models indicate that a relative suppression of low Eddington ratios ($lambda_{rm Edd}lesssim$0.1) in lower mass galaxies (M<$10^{10-11}$Msun) is required to reproduce both the observed X-ray luminosity functions and the observed flat SFR/X-ray relationship.
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