Fraction of the X-ray optical depth at the observed energy E = 0.5 keV as a function of the cell over-density, temperature, and redshift (from top to bottom). The left panels refer to the mean of the five LOS with the minimal absorption, while the right panels refer to the mean of 68% of the LOS around the median. Solid, short-dashed, and long-dashed lines refer to the VZW, SW, and CW models, respectively. Note that the CW model slightly overpredicts the minimum envelope of the N_H − z distribution, as noted in the text.