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The gamma-ray burst (GRB) 050904 at z = 6.3 provides the first opportunity ofprobing the intergalactic medium (IGM) by GRBs at the epoch of thereionization. Here we present a spectral modeling analysis of the opticalafterglow spectrum taken by the Subaru Telescope, aiming to constrain thereionization history. The spectrum shows a clear damping wing at wavelengthsredward of the Lyman break, and the wing shape can be fit either by a damped Lyalpha system with a column density of log (N_HI/cm^{-2}) ~ 21.6 at a redshiftclose to the detected metal absorption lines (z_metal = 6.295), or by almostneutral IGM extending to a slightly higher redshift of z_{IGM,u} ~ 6.36. In thelatter case, the difference from z_metal may be explained by acceleration ofmetal absorbing shells by the activities of the GRB or its progenitor. However,we exclude this possibility by using the light transmission feature around theLy beta resonance, leading to a firm upper limit of z_{IGM,u} < 6.314. We thenshow an evidence that the IGM was largely ionized already at z=6.3, with thebest-fit neutral fraction of IGM, x_HI = N_HI/N_H = 0.00, and upper limits ofx_HI < 0.17 and 0.60 at 68 and 95% C.L., respectively. This is the first directand quantitative upper limit on x_HI at z > 6. Various systematic uncertaintiesare examined, but none of them appears large enough to change this conclusion.To get further information on the reionization, it is important to increase thesample size of z >~ 6 GRBs, in order to find GRBs with low column densities(log N_HI <~ 20) within their host galaxies, and for statistical studies of Lyalpha line emission from host galaxies.

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