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 Lyman 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 postreionization optical depth that are of order unity on a scale of ∼100 comoving Mpc, in agreement with observations toward high-redshift quasars. Significant contributions to these variations are provided 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.