We study the incidence of nuclear obscuration on a complete sample of 1310 AGN selected on the basis of their rest-frame 2-10 keV X-ray flux from the XMM-COSMOS survey, in the redshift range 0.3<z<3.5. We classify the AGN as obscured or un-obscured on the basis of either the optical spectral properties and the overall SED or the shape of the X-ray spectrum. The two classifications agree in about 70% of the objects, and the remaining 30% can be further subdivided into two distinct classes: at low luminosities X-ray un-obscured AGN do not always show signs of broad lines or blue/UV continuum emission in their optical spectra, most likely due to galaxy dilution effects; at high luminosities broad line AGN may have absorbed X-ray spectra, which hints at an increased incidence of small-scale (sub-parsec) dust-free obscuration. We confirm that the fraction of obscured AGN is a decreasing function of the intrinsic X-ray luminosity, while the incidence of absorption shows significant evolution only for the most luminous AGN, which appear to be more commonly obscured at higher redshift. We find no significant difference between the mean stellar masses and star formation rates of obscured and un-obscured AGN hosts. We conclude that the physical state of the medium responsible for obscuration in AGN is complex, and mainly determined by the radiation environment (nuclear luminosity) in a small region enclosed within the gravitational sphere of influence of the central black hole, but is largely insensitive to the wider scale galactic conditions.
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