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 active galactic nucleus (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 an 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 MBHs and AGN feedback. We follow the full assembly of MBHs and host haloes from early times to the present in a Lambda cold dark matter (Lambda CDM) cosmology. An AGN activity is triggered by halo major mergers and MBH accrete mass until they satisfy the observed correlation with velocity dispersion. We find that all the 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 predict no turn-off of the faint end of the AGN optical luminosity function at redshifts z greater than or similar to 1, down to very low luminosity.