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We present a multi-wavelength study of seven AGN at spectroscopic redshift>2.5 in the 7 Ms Chandra Deep Field South, selected to have good FIR/sub-mmdetections. Our aim is to investigate the possibility that the obscurationobserved in the X-rays can be produced by the interstellar medium (ISM) of thehost galaxy. Based on the 7 Ms Chandra spectra, we measured obscuring columndensities N$_{H, X}$ in excess of 7x10$^{22}$ cm$^{-2}$ and intrinsic X-rayluminosities L$_{X}$>10$^{44}$ erg s$^{-1}$ for our targets, as well asequivalent widths for the Fe K$\alpha$ emission line EW>0.5-1 keV. We built theUV-to-FIR spectral energy distributions by using broad-band photometry fromCANDELS and Herschel catalogs. By means of an SED decomposition technique, wederived stellar masses (M$_{*}$~10$^{11}$ Msun), IR luminosities(L$_{IR}$>10$^{12}$ Lsun), star formation rates (SFR~190-1680 Msun yr$^{-1}$)and AGN bolometric luminosities (L$_{bol}$~10$^{46}$ erg s$^{-1}$) for oursample. We used an empirically-calibrated relation between gas masses andFIR/sub-mm luminosities and derived M$_{gas}$~0.8-5.4x10$^{10}$ Msun.High-resolution (0.3-0.7'') ALMA data (when available, CANDELS data otherwise)were used to estimate the galaxy size and hence the volume enclosing most ofthe ISM under simple geometrical assumptions. These measurements were thencombined to derive the column density associated with the ISM of the host, onthe order of N$_{H, ISM}$~10$^{23-24}$ cm$^{-2}$. The comparison between theISM column densities and those measured from the X-ray spectral analysis showsthat they are similar. This suggests that, at least at high redshift,significant absorption on kpc scales by the dense ISM in the host likely addsto or substitutes that produced by circumnuclear gas on pc scales (i.e., thetorus of unified models). The lack of unobscured AGN among our ISM-rich targetssupports this scenario.

The X-ray emission of z>2.5 active galactic nuclei can be obscured by their host galaxies