Intensity correlation of ionizing background at high redshifts

We derive the joint probability distribution of intensities of ionizing field at two different places. The intensity correlation function ξJ is calculated for randomly distributed QSOS as the main ionizing sources, taking into account the absorption produced by QSO absorption-line systems. We show that the Lyα forest line clouds can be used as intensity indicators to reveal ξJ at high z. We measure the equivalent width correlation ξ1/W for eight selected QSOS and find, in some cases, significant 1/W correlations produced mainly by the lines near the QSO emission redshifts. Such correlation may be generated by the non-uniform spectral signal-to-noise ratio, or it may be caused by the enhanced ionizing field near the QSOS. If the latter explanation is correct, then from the affected wavelength range in Q0000 – 263 we conclude that |J₋₂₁ 0.1 z 4|⁠. We point out some difficulties involved in comparing the observed ξ1/W with the calculated ξJ. We need superb observational data and simulated spectra to examine the non-uniform signal-to-noise ratio effect. When better data eventually become available, the method we describe here can be used to set important constraints on the dominating ionizing sources at early epochs.