The spatial distribution of X-ray selected AGN in the Chandra deep fields: a theoretical perspective

We study the spatial distribution of X-ray selected active galactic nuclei (AGN) in the framework of hierarchical coevolution of supermassive black holes and their host galaxies and dark matter haloes. To this end, we have applied the theoretical model developed by Croton et al., De Lucia & Blaizot and Marulli et al. to the output of the Millennium Run and obtained hundreds of realizations of past light cones from which we have extracted realistic mock AGN catalogues that mimic the Chandra deep fields. We find that the model AGN number counts are in fair agreement with observations both in the soft and in the hard X-ray bands, except at fluxes <= 10(-15) erg cm(-2) s(-1), where the model systematically overestimates the observations. However, a large fraction of these faint objects are typically excluded from the spectroscopic AGN samples of the Chandra fields. We find that the spatial two-point correlation function predicted by the model is well described by a power-law relation out to 20 h(-1) Mpc, in close agreement with observations. Our model matches the correlation length r(0) of AGN in the Chandra Deep Field-North but underestimates it in the Chandra Deep Field-South. When fixing the slope to gamma = 1.4, as in Gilli et al., the statistical significance of the mismatch is 2 sigma-2.5 sigma, suggesting that the predicted cosmic variance, which dominates the error budget, may not account for the different correlation length of the AGN in the two fields. However, the overall mismatch between the model and the observed correlation function decreases when both r(0) and gamma are allowed to vary, suggesting that more realistic AGN models and a full account of all observational errors may significantly reduce the tension between AGN clustering in the two fields. While our results are robust to changes in the model prescriptions for the AGN light curves, the luminosity dependence of the clustering is sensitive to the different light-curve models adopted. However, irrespective of the model considered, the luminosity dependence of the AGN clustering in our mock fields seems to be weaker than in the real Chandra fields. The significance of this mismatch needs to be confirmed using larger data sets.