Reionization of the inhomogeneous universe

A model of the density distribution in the intergalactic medium (IGM), moti vated by that found in numerical simulations, is used to demonstrate the ef fect of a clumpy IGM and discrete sources on the reionization of the univer se. In an inhomogeneous universe reionization occurs outside-in, starting i n voids and gradually penetrating into overdense regions. Reionization shou ld not be sudden but gradual, with a continuous rise of the photon mean fre e 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 simila r or equal to 6 unless the emissivity increases with redshift at z > 4. How ever, 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 G unn-Peterson trough at z similar to 6 would then appear because even the mo st underdense voids have a large enough neutral fraction in ionization equi librium to be optically thick to Ly alpha photons. Cosmological H II region s near the epoch of overlap can produce gaps of transmitted flux only if lu minous quasars contributed to the reionization, producing large H II region s. Despite the clumpiness of the matter distribution, recombinations do not increase the required emissivity of ionizing photons by a large factor dur ing the reionization of hydrogen because the high-density gas is not ionize d until a late time. We show that the He II reionization was most likely de layed relative to the hydrogen reionization but was probably complete by z similar to 3 (the redshift where observations are available). The reported large optical depth fluctuations of He II are not necessarily due to an inc omplete He II reionization but can arise from a combination of IGM density fluctuations and variations in the intensity of the He II ionizing backgrou nd due to luminous QSOs.