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 nineteen quasars at 5.74 < z _ { em } < 6.42 discovered in the Sloan Digital Sky Survey .
Three methods are used to trace IGM properties : ( a ) the evolution of the Gunn-Peterson ( GP ) optical depth in the Ly \alpha , \beta , and \gamma transitions ; ( b ) the distribution of lengths of dark absorption gaps , and ( c ) the size of HII 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 } \sim ( 1 + z ) ^ { 4.3 } to ( 1 + z ) ^ { \gtrsim 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 \gtrsim 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 \sim 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 HII regions around luminous quasars decrease rapidly towards higher redshift , suggesting that the neutral fraction of the IGM has increased by a factor of \gtrsim 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 \sim 6.2 based on the GP optical depth and HII region size measurements .
The observations suggest that z \sim 6 is the end of the overlapping stage of reionization , and are inconsistent with a mostly neutral IGM at z \sim 6 , as indicated by the finite length of dark absorption gaps .