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

Abstract

The gamma-ray burst (GRB) 050904 at $z = 6.3$ provides the first opportunity to probe the intergalactic medium (IGM) by GRBs at the epoch of 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 fitted either by a damped Ly$\alpha$ system with a column density of $\log [N_{\mathrm{H {I}}} \,(\mathrm{cm}^{-2})] \sim 21.6$ at a redshift close to the detected metal absorption lines ($z_{\mathrm{metal}} = 6.295$), or by almost neutral IGM extending to a slightly higher redshift of $z_{\mathrm{IGM,u}} \sim 6.36$. In the latter case, the difference between the two redshifts may be explained by the acceleration of metal absorbing shells in 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 $z_{\mathrm{IGM,u}} \leq 6.314$. We then show evidence that the IGM was already largely ionized at $z = 6.3$ with the best-fit neutral fraction of IGM, $x_{\mathrm{H {I}}} \; (\equiv n_{\mathrm{H {I}}} / n_{\mathrm{H}}) = 0.00$, and upper limits of $x_{\mathrm{H {I}}} < 0.17$ and 0.60 at 68% and 95% confidence levels, respectively. This is the first direct and quantitative upper limit on $x_{\mathrm{H {I}}}$ at $z \gt 6$. Various systematic uncertainties are examined, but none of them appears large enough to change our conclusion. To get further information on the reionization, it is important to increase the sample size of $z \gtrsim 6$ GRBs, in order to find GRBs with low column densities ($\log N_{\mathrm{H {I}}} \lesssim 20$) within their host galaxies and to make statistical studies of Ly$\alpha$ line emission from host galaxies.