The Reionization History in the Lognormal Model

We study the evolution of baryonic gas before reionization in the lognormal (LN) model of cosmic clustering. We show that the thermal history of the universe around reionization can roughly be divided into three epochs: (1) a cold dark age z > zr, in which the baryon gas is neutral and opaque to Lyα photons; (2) a hot dark age zr > z > zGP, in which a predominant part of the baryon gas is ionized and hot but is still opaque to Lyα photons; and (3) a bright age z < zGP, in which the universe is ionized enough to be transparent to Lyα photons. In the flat cold dark matter cosmological models given by WMAP and COBE, the difference of the two redshifts zr - zGP is found to be as large as ~10, with zr ~ 17 and zGP ~ 7. This reionization history naturally yields a high optical depth of the CMB τe ≃ 0.12-0.19, which is observed in the TE polarization in the WMAP data, and a low redshift zGP for the appearance of the Lyα Gunn-Peterson trough, zGP ≃ 6-8, in QSO absorption spectra. The universe stays so long in an ionized, yet Lyα opaque, stage because the first photoionization heats the intergalactic gas effectively and balances the gravitational clustering for a long period of time. Therefore, a high τe and low zGP is a result of all the considered models. Besides the cosmological parameters, the only free parameter we used in the calculation is Nion, the mean number of ionization photons produced by each baryon in collapsed objects. We take it to be 40-80 in the calculations.