Can photo-ionization explain the decreasing fraction of X-ray obscured AGN with luminosity?

Chandra and XMM surveys show that the fraction of obscured AGN decreases rapidly with increasing luminosity. Although this is usually explained by assuming that the covering factor of the central engine is much smaller at luminous QSOs, the exact origin of this effect remains unknown. We perform toy simulations to test whether photo-ionisation of the obscuring screen in the presence of a strong radiation field can reproduce this effect. In particular, we create X-ray spectral simulations using a warm absorber model assuming a range of input column densities and ionization parameters. We fit instead the simulated spectra with a simple cold absorption power-law model that is the standard practice in X-ray surveys. We find that the fraction of absorbed AGN should fall with luminosity as $L^{-0.16\pm0.03}$ in rough agreement with the observations. Furthermore, this apparent decrease in the obscuring material is consistent with the dependence of the FeK$\alpha$ narrow-line equivalent width on luminosity, ie. the X-ray Baldwin effect.