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 IGM at the end of the reionization epoch using spectra of a sample of nineteen quasars at 5.74<z<6.42 discovered in the SDSS. Three methods are used to trace IGM properties: (a) the evolution of the Gunn-Peterson optical depth in the Ly alpha,beta, and gamma; (b) the distribution of dark absorption gaps, and (c) the size of HII regions around quasars. We find that the evolution of the IGM accelerated at z>5.7: the optical depth evolution changes from tau ~ (1+z)^{4.3} to (1+z)^{>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 >4 in the UV background at z>6, when the mean free path of UV photons is comparable to the correlation length of galaxies. The mean length of dark gaps shows the most dramatic increase at z~6, as well as the largest varianace. We suggest using dark gap statistics as a powerful probe of the ionization state of the IGM at yet higher redshift. The sizes of HII regions around quasars decrease rapidly towards higher redshift, suggesting that the neutral fraction of the IGM has increased by a factor of >10 from z=5.7 to 6.4. The mass-averaged neutral fraction is 1-4% at z~6.2 based on the GP optical depth and HII region sizes. The observations suggest that z~6 is the the end of the overlapping stage of reionization, and are inconsistent with a neutral IGM at z~6, as indicated by the finite length of dark absorption gaps. 
Xiaohui Fan, Michael A. Strauss, Robert H. Becker, Richard L. White,   James E. Gunn, Gillian R. Knapp, Gordon T. Richards, ...