The presence of a cold, neutral medium along the line of sight introduces a sharp photoelectric absorption cutoff in the power-law spectrum emitted by the nuclear source. It is possible to accurately determine the column of absorbing material by measuring the energy of the photoelectric absorption. At NH > 1024 cm-2 the gas is thick to Compton scattering (dubbed as "Compton thick"). In this case the primary X-ray radiation is completely absorbed at energies < 10 keV. However, as long as the column of gas does not exceed 1025 cm-2 the primary radiation is still transmitted and observable at energies in the range 10 - 100 keV. In Compton thick sources with NH > 1025 cm-2 the direct, primary X-ray radiation is totally absorbed at any energy [Matt et al. (1997)].
Although, the primary radiation is totally absorbed (at least at E < 10 keV), Compton thick sources are still observable through radiation that is scattered into our line of sight either by a cold, Compton thick medium ("cold reflection") or, less frequently, by a warm medium ("warm reflection"), either of such scattering media must extend on scales larger than the absorber. The reflected component is about two orders of magnitude fainter than the primary radiation; therefore Compton thick sources are much more difficult to detect, especially at high redshift. Compton thick, reflection-dominated sources are generally characterized also by the presence of a prominent FeK line at 6.4 keV. This line is partly produced in the accretion disk and is partly excited in the circumnuclear medium on larger scales. In Compton thin sources this iron line is heavily diluted by the direct, primary radiation, and its observed equivalent width is of a few hundred eV. In Compton thick sources the primary continuum is suppressed, and therefore the iron line emitted by the circumnuclear medium is observed with an equivalent width which easily exceeds 1 keV.
Note however that an X-ray spectrum which appear reflection-dominated, and with a prominent iron K line, does not necessarily imply that the source is Compton thick along our line of sight. Indeed, if the active nucleus fades, its light echo keeps the circumnuclear medium reflecting the radiation for several years, producing a reflection-dominated spectrum, even if the nucleus is totally unobscured. Compton thin to Compton thick transitions have been sometimes interpreted in terms of this "fossil" scenario [Guainazzi et al. (2002), Matt et al. (2003)]. However, in most of these cases it is difficult to distinguish whether the spectral change is really due to an intrinsic fading of the source or to an increase of the absorbing column density (see Sect.5). Yet, in a few cases the systemic decline of the luminosity, monitored through various epochs, unambiguously identifies the Compton thick - like appearance of the final spectrum as due to the fossil nature of the source [Gilli et al. (2000)].
Finally, it should be noted that absorption in the hard X-rays is due to metals, therefore what we actually is the column of metals. To infer the equivalent column of hydrogen people generally assume (explicitly or, more often, implicitly) solar abundances. However, nearly all AGNs display super-solar abundances [Hamann et al. (2002), Nagao et al. (2006a), Nagao et al. (2006b)]. As a consequence, hydrogen column densities inferred from X-ray spectra are generally overestimated.