Constraints on the Accretion History of Massive Black Holes from Faint X-ray Counts

We investigate how hierarchical models for the co-evolution of the massive black hole (MBH) and AGN population can reproduce the observed faint X-ray counts. We find that the main variable influencing the theoretical predictions is the Eddington ratio of accreting sources. We compare three different models proposed for the evolution of AGN Eddington ratio, f_Edd: constant f_Edd=1, f_Edd decreasing with redshift, and f_Edd depending on the AGN luminosity, as suggested by simulations of galactic mergers including BHs and AGN feedback. We follow the full assembly of MBHs and host halos from early times to the present in a LambdaCDM cosmology. AGN activity is triggered by halo major mergers and MBHs accrete mass until they satisfy the observed correlation with velocity dispersion. We find that all three models can reproduce fairly well the total faint X-ray counts. The redshift distribution is however poorly matched in the first two models. The Eddington ratios suggested by merger simulations predicts no turn-off of the faint end of the AGN optical luminosity function at redshifts z>=1 down to very low luminosity.