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 Ly alpha, Ly beta, and Ly gamma 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 tau(eff)(GP) similar to (1 + z)(4.3) to (1 + z) greater than or similar to 11, and the average length of dark gaps with tau > 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 greater than or similar to 4 in the UV background at z > 6, when the mean free path of UV photons is comparable to the correlation length of the starforming galaxies that are thought to have caused reionization. The mean length of dark gaps shows the most dramatic increase at z similar to 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 greater than or similar to 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 similar to 6.2 based on the GP optical depth and H (II) region size measurements. The observations suggest that z similar to 6 is the end of the overlapping stage of reionization and are inconsistent with a mostly neutral IGM at z similar to 6, as indicated by the finite length of the dark absorption gaps.