Cosmic Variance in the Transparency of the Intergalactic Medium after Reionization

Following the completion of cosmic reionization, the mean-free-path of ionizing photons was set by a population of Ly-limit absorbers. As the mean-free-path steadily grew, the intensity of the ionizing background also grew, thus lowering the residual neutral fraction of hydrogen in ionization equilibrium throughout the diffuse intergalactic medium (IGM). Lyα photons provide a sensitive probe for tracing the distribution of this residual hydrogen at the end of reionization. Here we calculate the cosmic variance among different lines-of-sight in the distribution of the mean Lyα optical depths. We find fractional variations in the effective post-reionization optical depth that are of order unity on a scale of ∼ 100 co-moving Mpc, in agreement with observations towards high-redshift quasars. The variations are dominated by the cosmic variance in the density contrast on the scale of the mean-free-path for ionizing photons, and by fluctuations in the ionizing background induced by delayed or enhanced structure formation. Cosmic variance results in a highly asymmetric distribution of transmission through the IGM, with fractional fluctuations in Lyα transmission that are larger than in Lyβ transmission. Subject headings: cosmology: theory galaxies: formation