Accretion onto SMBH is believed to occur mostly in obscured AGN. Such objects are proving rather elusive in surveys of distant galaxies, including those at X-ray energies. Our main goal is to determine whether the revised IRAC criteria of Donley et al. (2012) (objects with an IR power-law spectral shape), are effective at selecting X-ray type-2 AGN. We present the results from the X-ray spectral analysis of 147 AGN selected by cross-correlating the highest spectral quality ultra-deep XMM-Newton and the Spitzer/IRAC catalogues in the CDF-S. Consequently it is biased towards sources with high S/N X-ray spectra. In order to measure the amount of intrinsic absorption in these sources, we adopt a simple X-ray spectral model that includes a power-law modified by intrinsic absorption and a possible soft X-ray component. We find 21/147 sources to be heavily absorbed but the uncertainties in their obscuring column densities do not allow us to confirm their Compton-Thick nature without resorting to additional criteria. Although IR power-law galaxies are less numerous in our sample than IR non-power-law galaxies (60 versus 87 respectively), we find that the fraction of absorbed (N_{H} > 10^{22} cm^{-2}) AGN is significantly higher (at about 3 sigma level) for IR-power-law sources ($sim$2/3) than for those sources that do not meet this IR selection criteria ($sim$1/2). This behaviour is particularly notable at low luminosities, but it appears to be present, although with a marginal significance, at all luminosities. We therefore conclude that the IR power-law method is efficient in finding X-ray-absorbed sources. We would then expect that the long-sought dominant population of absorbed AGN is abundant among IR power-law spectral shape sources not detected in X-rays.
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