The Lyα forest flux distribution at z ∼ 5.2 and the evolution of the ionizing background

We use the redshift evolution of the Ly alpha forest mean transmitted flux at z greater than or similar to 2.5 to infer the evolution of the intensity of the ionizing background, based on theoretical predictions for the density distribution of the intergalactic gas giving rise to the Ly alpha forest. The proper background intensity declines gradually with redshift, decreasing by a factor of similar to3 between z = 3 and z = 5. Detailed predictions of the flux distribution at high redshift are presented. If the Ly alpha forest is due to the gravitational evolution of structure originating from Gaussian primordial fluctuations, the highest values of the transmitted flux should reflect the lowest gas densities of voids, except near the epoch of reionization, when large fluctuations in the ionizing background can alter the distribution of transmitted flux. For the highest redshift quasar known (with a mean Ly alpha forest redshift z = 5.2), and given the observed mean transmitted flux of (F) over bar = 0.09, we predict that only about 3% of the Ly 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 background intensity. We show that this is consistent with the spectrum shown in Fan et al. The result found here for the evolution of the ionizing background implies that the comoving ionizing emissivity decreases from z = 3 to z = 5 by a factor of similar to2, which is much less than the reduction in the number of quasars, suggesting that a different population of sources dominates the background at z = 5.