History of hydrogen reionization in the cold dark matter model

We calculate the reionization history in CDM (cold dark matter) models. The epoch of the end of reionization and the Thomson scattering optical depth to the cosmic microwave background depend on the power spectrum amplitude on small scales and on the ionizing photon emissivity per unit mass in collapsed halos. We calibrate the emissivity to reproduce the measured ionizing background intensity at z = 4. Models in which all CDM halos have either a constant emissivity or a constant energy emitted per Hubble time per unit mass predict that reionization ends near z ∼ 6 and that the optical depth is in the range 0.05 < τ_e < 0.09, consistent with Wilkinson Microwave Anisotropy Probe (WMAP) results at the 1-2 σ level. If the optical depth is as high as 0.17 (as suggested by WMAP), halos of velocity dispersion ∼3-35 km s^-1 at z > 15 must have ionizing emissivities per unit mass larger by a factor ≳50 compared with the more massive halos that produce the ionizing emissivity at z = 4. This factor increases to 100 if the CDM power spectrum amplitude is required to agree with the recent Croft et al. measurement from the Lyα forest. If τ_e τ 0.17 is confirmed, a higher ionizing emissivity at z > 15 compared with z = 4 might arise from an enhanced star formation rate or quasar abundance per unit mass and an increased escape fraction for ionizing photons; the end of reionization could have been delayed to z ∼ 6 because of the suppression of gas accretion and star formation in low-mass halos as the medium was reionized.