Constraining the Evolution of the Ionizing Background and the Epoch of Reionization with z ∼ 6 Quasars. II. A Sample of 19 Quasars^{* **}

We study the evolution of the ionization state of the intergalactic medium (IGM) at the end of the reionization epoch using moderate-resolution spectra of a sample of 19 quasars at 5.74 < z_em < 6.42 discovered in the Sloan Digital Sky Survey. Three methods are used to trace IGM properties: (1) the evolution of the Gunn-Peterson (GP) optical depth in the Lyα, Lyβ, and Lyγ transitions; (2) the distribution of lengths of dark absorption gaps; and (3) the size of H II regions around luminous quasars. Using this large sample, we find that the evolution of the ionization state of the IGM accelerated at z > 5.7: the GP optical depth evolution changes from τ ∼ (1 + z)^4.3 to (1 + z)^≳11, and the average length of dark gaps with τ > 3.5 increases from <10 to >80 comoving Mpc. The dispersion of IGM properties along different lines of sight also increases rapidly, implying fluctuations by a factor of ≳4 in the UV background at z > 6, when the mean free path of UV photons is comparable to the correlation length of the star-forming galaxies that are thought to have caused reionization. The mean length of dark gaps shows the most dramatic increase at z ∼ 6, as well as the largest line-of-sight variations. We suggest using dark gap statistics as a powerful probe of the ionization state of the IGM at yet higher redshift. The sizes of H II regions around luminous quasars decrease rapidly toward higher redshift, suggesting that the neutral fraction of the IGM has increased by a factor of ≳10 from z = 5.7 to 6.4, consistent with the value derived from the GP optical depth. The mass-averaged neutral fraction is 1%-4% at z ∼ 6.2 based on the GP optical depth and H II region size measurements. The observations suggest that z ∼ 6 is the end of the overlapping stage of reionization and are inconsistent with a mostly neutral IGM at z ∼ 6, as indicated by the finite length of the dark absorption gaps.