Comparison of spatial and angular clustering of X-ray AGN

The angular correlation function is a powerful tool for deriving the clustering properties of active galactic nuclei (AGN) and hence the mass of the corresponding dark matter halos in which they reside. However, recent studies based on the application of the angular correlation function on X-ray samples, yield results that are 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 comoving clustering length of x 0 = 5.4 ± 1.0 h -1  Mpc (for γ = 1.8), which is consistent with results in the literature. We further derive the angular correlation function and corresponding spatial clustering length using the Limber’s inversion equation and a novel parametrization of the clustering evolution model that also takes the bias evolution of the host dark matter halo into account. The Limber’s inverted spatial comoving clustering length of x 0 = 5.5 ± 1.2 h -1  Mpc at a median redshift of z ≃ 0.75 matches the clustering length that is directly measured from the spatial correlation function analysis, but after introducing a significant non-linear contribution to the growing mode of perturbations; this contribution is estimated independently from literature results of x 0 at different redshifts. Therefore, using this sample of hard X-ray AGN and our clustering evolution parametrization, we find an excellent consistency between the angular and spatial clustering analysis.