Luminosity-dependent unification of active galactic nuclei and the X-ray Baldwin effect

The existence of an anti-correlation between the equivalent width (EW) of the narrow core of the iron Kα line and the luminosity of the continuum (i.e., the X-ray Baldwin effect) in type I active galactic nuclei has been confirmed in recent years by several studies carried out with XMM-Newton, Chandra and Suzaku. However, no general consensus on the origin of this trend has been reached so far. Several works have proposed the decrease of the covering factor of the molecular torus with the luminosity (in the framework of the luminosity-dependent unification models) as a possible explanation for the X-ray Baldwin effect. Using the fraction of obscured sources measured by recent X-ray and infrared (IR) surveys as a proxy of the half-opening angle of the torus and recent Monte Carlo simulations of the X-ray radiation reprocessed by a structure with a spherical-toroidal geometry, we test the hypothesis that the X-ray Baldwin effect is related to the decrease of the half-opening angle of the torus with the luminosity. Simulating the spectra of an unabsorbed population with a luminosity-dependent covering factor of the torus as predicted by recent X-ray surveys, we find that this mechanism is able to explain the observed X-ray Baldwin effect. Fitting the simulated data with a log-linear L_{2-10 keV} - EW relation, we found that in the Seyfert regime (L_{2-10 keV} ≤ 10^44.2 erg s^-1) luminosity-dependent unification produces a slope consistent with the observations for average values of the equatorial column densities of the torus of log N_H^T ≳ 23.2, and can reproduce both the slope and the intercept for log N_H^T ≃ 23.2. Lower values of N_H^T are obtained assuming the decrease of the covering factor of the torus with the luminosity extrapolated from IR observations (22.9 ≲ log N_H^T ≲ 23). In the quasar regime (L _{2-10 keV} > 10^44.2 erg s^-1), a decrease of the covering factor of the torus with the luminosity slower than that observed in the Seyfert regime (as found by recent hard X-ray surveys) is able to reproduce the observations for 23.2 ≲ log N_H^T ≲ 24.2.