Implications for the Cosmic Reionization from the Optical Afterglow Spectrum of the Gamma-Ray Burst 050904 at z = 6.3

The gamma-ray burst (GRB) 050904 at z = 6.3 provides the first opportunity of probing the intergalactic medium (IGM) by GRBs at the epoch of the reionization. Here we present a spectral modeling analysis of the optical afterglow spectrum taken by the Subaru Telescope, aiming to constrain the reionization history. The spectrum shows a clear damping wing at wavelengths redward of the Lyman break, and the wing shape can be fit either by a damped Ly alpha system with a column density of log (N_HI/cm^{-2}) ~ 21.6 at a redshift close to the detected metal absorption lines (z_metal = 6.295), or by almost neutral IGM extending to a slightly higher redshift of z_{IGM,u} ~ 6.36. In the latter case, the difference from z_metal may be explained by acceleration of metal absorbing shells by the activities of the GRB or its progenitor. However, we exclude this possibility by using the light transmission feature around the Ly beta resonance, leading to a firm upper limit of z_{IGM,u} < 6.314. We then show an evidence that the IGM was largely ionized already at z=6.3, with the best-fit neutral fraction of IGM, x_HI = N_HI/N_H = 0.00, and upper limits of x_HI < 0.17 and 0.60 at 68 and 95% C.L., respectively. This is the first direct and quantitative upper limit on x_HI at z > 6. Various systematic uncertainties are examined, but none of them appears large enough to change this conclusion. To get further information on the reionization, it is important to increase the sample size of z >~ 6 GRBs, in order to find GRBs with low column densities (log N_HI