Comparison of the spatial and the angular clustering of X-ray AGN
  The angular correlation function is a powerful tool for deriving the
clustering properties of AGN and hence the mass of the corresponding dark
matter halos in which they reside. However, studies based on the application of
the angular correlation function on X-ray samples, yield results apparently
inconsistent with those based on the direct estimation of the spatial
correlation function. The goal of the present paper is to attempt to
investigate this issue by analysing a well defined sample. To this end we use
the hard-band (2-10 keV) X-ray selected sources of the Chandra AEGIS fields,
chosen because of the availability of accurately derived flux sensitivity maps.
In particular we use the 186 hard-band sources with spectroscopic redshifts in
the range z=0.3-1.3, a range selected in order to contain the bulk of the AGN
while minimizing the contribution of unknown clustering and luminosity
evolution from very high redshifts. Using the projected spatial
auto-correlation function, we derive a clustering comoving length of 5.4+-1.0
Mpc (for gamma=1.8), consistent with results in the literature. We further
derive the angular correlation function and the corresponding spatial
clustering length using the Limber's inversion equation and a novel
parametrization of the clustering evolution model that also takes into account
the bias evolution of the host dark matter halo. The Limber's inverted spatial
comoving clustering length of 5.5+-1.2 Mpc at a median redshift of z~0.75,
matches the directly measured one, from the spatial correlation function
analysis, but for a significant non-linear contribution to the growing mode of
perturbations, estimated independently from literature results of x_0 at
different redshifts. Therefore, using this sample of X-ray AGN and our
clustering evolution parametrization we have found an excellent consistency
between the angular and spatial clustering analysis.
