We analyze the size evolution of HII regions around 27 quasars between z=5.7
to 6.4 ('quasar near-zones' or NZ). We include more sources than previous
studies, and we use more accurate redshifts for the host galaxies, with 8 CO
molecular line redshifts and 9 MgII redshifts. We confirm the trend for an
increase in NZ size with decreasing redshift, with the luminosity normalized
proper size evolving as: R_{NZ,corrected} = (7.4 \pm 0.3) - (8.0 \pm 1.1)
\times (z-6) Mpc. While derivation of the absolute neutral fraction remains
difficult with this technique, the evolution of the NZ sizes suggests a
decrease in the neutral fraction of intergalactic hydrogen by a factor ~ 9.4
from z=6.4 to 5.7, in its simplest interpretation. Alternatively, recent
numerical simulations suggest that this rapid increase in near-zone size from
z=6.4 to 5.7 is due to the rapid increase in the background photo-ionization
rate at the end of the percolation or overlap phase, when the average mean free
path of ionizing photons increases dramatically. In either case, the results
are consistent with the idea that z ~ 6 to 7 corresponds to the tail end of
cosmic reionization. The scatter in the normalized NZ sizes is larger than
expected simply from measurement errors, and likely reflects intrinsic
differences in the quasars or their environments. We find that the near-zone
sizes increase with quasar UV luminosity, as expected for photo-ionization
dominated by quasar radiation.Comment: 16 pages, aas format, 4 figures, to appear in the ApJ letter