Evidence for a mass-dependent AGN Eddington ratio distribution via the
  flat relationship between SFR and AGN luminosity
  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.
