Modeling active galactic nuclei: ongoing problems for the faint-end of   the luminosity function
  We consider simple semi-analytic models that relate the active galactic nuclei (AGN) evolution to the merging history of their host dark matter haloes and quantify their ability of matching the AGN luminosity function and its spatial clustering at low and intermediate redshifts. In particular, we focus on the recent determinations of the AGN luminosity function in the hard X-ray band at z~0 which constitutes the most stringent observational test for our models. Indeed, while we find an acceptable agreement between the model bolometric luminosity function and the data at 1<z<2 and for luminosities larger than 1e10 solar bolometric luminosities, no semi-analytic model is capable of reproducing the number density of faint X-ray sources in the local universe. Some improvement can be obtained by advocating energy feedback that we model through a time-dependent Eddington ratio. Even in this case, however, the number density of faint AGNs is significantly below observations. This failure indicates that major mergers cannot constitute the only trigger to accretion episodes in the local AGN population. 
F. Marulli, E. Branchini, L. Moscardini and M. Volonteri