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_HII, of the quasar HII region, or to the distance, R^{max}_w, at which the transmitted flux drops to =0.1 and a Gunn-Peterson (GP) trough appears. In the first case (HR regime), one can determine the IGM mean HI fraction, x_HI; in the second (PR regime), the value of R_w allows 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+SPH numerical simulations, and applied to 15 high-z (z>5.8) quasars sample from Fan et al. (2006). 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_HI. Four sample quasars show evidence for a local enhancement (up to 50%) in the local photoionization rate possibly produced by a galaxy overdensity. We discuss the possible interpretations and uncertainties of this result.