X-ray absorption in Compton-thin AGN: the predictions of a model revisited

Context. The evidence of a decrease with increasing luminosity in the fraction f(abs) of absorbed and Compton-thin among X-ray-selected (2-10 keV) AGN is observationally well supported, while that of an increase in f(abs) with redshift is fairly controversial. In a previous paper, 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 the black-hole mass M(BH). Aims. 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. Methods. The findings for lambda(M(BH), z) are properly treated 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 first adopted a distribution of gas surface density Sigma, observed in a sample of local spiral galaxies, irrespective of the galaxy morphological type and z. Results. Assuming the Eddington limit, lambda = 1, in the lambda(M(BH), z) distribution as a "natural" cut-off, the predictions are consistent with the existence of an anti-correlation between f(abs) and L(X), but they fail to reproduce an increase in f(abs) with z. Because the early type galaxies are on average 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 in typical values of Sigma with z, correlated with the activity, might explain an increase in f(abs) with z. However, f(abs) could hardly exceed about 0.3 at the highest luminosities.