Interpreting the transmission windows of distant quasars

We propose the apparent shrinking criterion (ASC) to interpret the spatial extent, R-w, of transmitted flux windows in the absorption spectra of high-z quasars. The ASC can discriminate between the two regimes in which R-w corresponds either to the physical size, R-H (II), of the quasar H II region or to the distance, R-w(max) , at which the transmitted flux drops to = 0.1 and a Gunn-Peterson (GP) trough appears. In the first case [H II region (HR) regime], one can determine the intergalactic medium mean H I fraction, x(H) (I); in the second [proximity region (PR) regime], the value of R-w allows one to measure the local photoionization rate and the local enhancement of the photoionization rate, Gamma(G), due to nearby/intervening galaxies. The ASC has been tested against radiative transfer+smoothed particle hydrodynamics numerical simulations, and applied to a sample of 15 high-z (z > 5.8) quasar spectra. All sample quasars are found to be in the PR regime; hence, their observed spectral properties (inner flux profile, extent of transmission window) cannot reliably constrain the value of x(H) (I). Four sample quasars show evidence for a local enhancement (up to 50 per cent) in the local photoionization rate possibly produced by a galaxy overdensity. We discuss the possible interpretations and uncertainties of this result.