The Lyman-alpha Forest Flux Distribution at z\sim 5.2 and the Evolution of the Ionizing Background

We use the redshift evolution of the lyman-alpha forest mean transmitted flux at z>2.5 to infer the evolution of the intensity of the ionizing background, using theoretical predictions for the density distribution of the intergalactic gas giving rise to the lyman-alpha forest. The proper background intensity declines gradually with redshift, decreasing by a factor \sim 3 between z=3 and z=5. The gravitational structure formation theory of the lyman-alpha forest implies that, given the observed mean transmitted flux of \bar{F}=0.1 in the highest redshift quasar (with a mean lyman-alpha forest redshift z=5.2), only about 3% of the lyman-alpha spectrum should have a flux higher than 50% of the continuum, and less than 0.5% of pixels should have flux above 75% of the continuum, assuming a uniform ionizing background intensity. We show that this is consistent with the spectrum shown in Fan et al