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.