Linking X-ray AGN with dark matter halos: a model compatible with AGN
  luminosity function and large-scale clustering properties
  Our goal is to find a minimalistic model that describes the luminosity
function and large-scale clustering bias of the X-ray-selected AGN in the
general framework of the concordance LCDM model. We assume that a simple
population-averaged scaling relation between the AGN X-ray luminosity L_X and
the host dark matter halo mass M_h exists. With such a relation, the AGN X-ray
luminosity function can be computed from the halo mass function. Using the
concordance LCDM halo mass function for the latter, we obtain the M_h-L_X
relation required to match the redshift-dependent AGN X-ray luminosity function
known from X-ray observations. We find that with a simple power-law-scaling M_h
\propto L_X^\Gamma(z), our model can successfully reproduce the observed X-ray
luminosity function. Furthermore, we automatically obtain predictions for the
large-scale AGN clustering amplitudes and their dependence on the luminosity
and redshift, which seem to be compatible with AGN clustering measurements. Our
model also includes the redshift-dependent AGN duty cycle which peaks at the
redshift z ~ 1, and its peak value is consistent with unity, suggesting that on
average there is no more than one AGN per dark matter halo. For a typical
X-ray-selected AGN at z ~ 1, our best-fit M_h-L_X scaling implies low Eddington
ratio L_X/L_Edd ~ 10^{-4}-10^{-3} (2-10 keV band, no bolometric correction
applied) and correspondingly large mass growth e-folding times, suggesting that
the typical X-ray AGN are dominantly fueled via relatively inefficient
'hot-halo' accretion mode.
