2000ApJ...530....1M

A model of the density distribution in the intergalactic medium (IGM), motivated by that found in numerical simulations, is used to demonstrate the effect of a clumpy IGM and discrete sources on the reionization of the universe. In an inhomogeneous universe reionization occurs outside-in, starting in voids and gradually penetrating into overdense regions. Reionization should not be sudden but gradual, with a continuous rise of the photon mean free path over a fair fraction of the Hubble time as the emissivity increases. We show that a hydrogen Gunn-Peterson trough should be present at z≃6 unless the emissivity increases with redshift at z>4. However, the epoch of overlap of cosmological H II regions could have occurred at a higher redshift if sources of low luminosity reionized the IGM; the Gunn-Peterson trough at z∼6 would then appear because even the most underdense voids have a large enough neutral fraction in ionization equilibrium to be optically thick to Lyα photons. Cosmological H II regions near the epoch of overlap can produce gaps of transmitted flux only if luminous quasars contributed to the reionization, producing large H II regions. Despite the clumpiness of the matter distribution, recombinations do not increase the required emissivity of ionizing photons by a large factor during the reionization of hydrogen because the high-density gas is not ionized until a late time. We show that the He II reionization was most likely delayed relative to the hydrogen reionization but was probably complete by z∼3 (the redshift where observations are available). The reported large optical depth fluctuations of He II are not necessarily due to an incomplete He II reionization but can arise from a combination of IGM density fluctuations and variations in the intensity of the He II ionizing background due to luminous QSOs.