Measurements of the z ~ 6 Intergalactic Medium Optical Depth and
  Transmission Spikes Using a New z > 6.3 Quasar Sample
  We report new measurements of the intergalactic medium (IGM) Ly$\alpha$ and
Ly$\beta$ effective optical depth at $5.3<z<6.5$, using a new sample of quasar
sightlines including 32 quasars at $6.308\le z\le7.00$. These quasars provide a
large statistical sample to measure the IGM evolution during the transition
phase of the reionization epoch. We construct a data set of deep optical
spectra of these quasars using VLT, Keck, Gemini, LBT, and MMT. We measure the
Ly$\alpha$ effective optical depth at $5.36<z<6.57$ using the Ly$\alpha$
forests of both individual spectra and the stacked spectrum. The large scatter
of individual measurements is consistent with previous work, suggesting an
inhomogeneous reionization process. Combining our new measurements and previous
results, we obtain a best-fit for the Ly$\alpha$ effective optical depth
evolution at $z>5.3$, $\tau\propto(1+z)^{8.6\pm1.0}$. We then estimate the
observed Ly$\beta$ effective optical depth using Ly$\beta$ forests and convert
them to Ly$\alpha$ optical depth for comparison, which provides additional
constraints on the evolution of the IGM optical depth. The Ly$\beta$-based
measurements are generally in agreement with the best-fit evolution obtained
from Ly$\alpha$ forests. Using this new sample, we identify 389 Ly$\alpha$ and
50 Ly$\beta$ transmission spikes at $5.5<z<6.3$. The upper limits of Ly$\alpha$
optical depth estimated using transmission spikes are well consistent with our
best-fit evolution. The evolution in number density of these high-redshift
transmission spikes suggests a rapid transition phase at the end of the
reionization. Comparison of our optical depth measurements with hydrodynamical
simulations indicates a IGM neutral hydrogen fraction $\langle f_{\rm
HI}\rangle\gtrsim10^{-4}$ at $z=6$.
