X-ray absorption in Compton-thin AGN: the predictions of a model   revisited
  The evidence of a decrease with increasing luminosity of the fraction f_{abs} of absorbed and Compton-thin among X-ray (2-10 keV) selected AGN is observationally rather well supported, while that of an increase of f_{abs} with redshift is rather controversial. In Lamastra, Perola & Matt (2006) the gravitational effect of the SMBH on the molecular interstellar gas, in the central region of the host galaxy, was shown to predict an anti-correlation between f_{abs} and M_{BH}. The most recent findings on the distribution of the Eddington ratio \lambda=L_b/L_E as a function of M_{BH} and z are used to convert that relationship into one between f_{abs} and both bolometric (L_b) and X-ray (L_X) luminosities at various values of z. The findings on \lambda(M_{BH},z) are properly treated in order to ensure completeness in the prediction of f_{abs} above a certain luminosity, at values of z=0.1, 0.35, 0.7 and >1. To verify the consequence of these findings alone, we adopted in a first istance a distribution of gas surface density \Sigma, observed in a sample of local spiral galaxies, irrespective of the galaxy morphological type and z. Assuming in the \lambda(M_{BH},z) distribution the Eddington limit, \lambda=1, as a ``natural'' cut-off, the predictions are consistent with the existence of an anti-correlation between f_{abs} and L_X, but fail to reproduce an increase of f_{abs} with z. Because the early type galaxies on average are much poorer in molecular gas than late type ones, a quantitative agreement with the local value of f_{abs} requires the existence of a correlation between \Sigma and the central activity. An increase of typical values of \Sigma with z, correlated with the activity, might explain an increase of f_{abs} with z. However, at the highest luminosities f_{abs} could hardly exceed about 0.3. 
A. Lamastra, G. C. Perola, G. Matt