Semi-analytic modelling of AGNs: auto-correlation function and halo
  occupation
  The spatial clustering of active galactic nuclei (AGNs) is considered to be
one of the important diagnostics for the understanding of the underlying
processes behind their activities complementary to measurements of the
luminosity function (LF). We analyse the AGN clustering from a recent
semi-analytic model performed on a large cosmological $N$-body simulation
covering a cubic gigaparsec comoving volume. We have introduced a new
time-scale of gas accretion on to the supermassive black holes to account for
the loss of the angular momentum on small scales, which is required to match
the faint end of the observed X-ray LF. The large simulation box allows us
accurate determination of the auto-correlation function of the AGNs. The model
prediction indicates that this time-scale plays a significant role in allowing
massive haloes to host relatively faint population of AGNs, leading to a higher
bias factor for those AGNs. The model predictions are in agreement with
observations of X-ray selected AGNs in the luminosity range
$10^{41.5}~\mathrm{erg} \ \mathrm{s}^{-1} \leq L_{2-10\mathrm{keV}} \leq
10^{44.5}~\mathrm{erg} \ \mathrm{s}^{-1}$, with the typical host halo mass of
$10^{12.5-13.5} h^{-1}\,{\rm M}_{\odot}$ at $z \lesssim 1$. This result shows
that the observational clustering measurements impose an independent constraint
on the accretion time-scale complementary to the LF measurements. Moreover, we
find that not only the effective halo mass corresponding to the overall bias
factor, but the extended shape of the predicted AGN correlation function shows
remarkable agreement with those from observations. Further observational
efforts towards the low luminosity end at $z \sim 1$ would give us stronger
constraints on the triggering mechanisms of AGN activities through their
clustering.
