Probing the Neutral Fraction of the IGM with GRBs during the Epoch of Reionization

We show that near-infrared observations of the red side of the Ly-alpha line from a single gamma ray burst (GRB) afterglow cannot be used to constrain the global neutral fraction of the intergalactic medium (IGM), x_H, at the GRB's redshift to better than ~0.3. Some GRB sight-lines will encounter more neutral hydrogen than others at fixed x_H owing to the patchiness of reionisation. GRBs during the epoch of reionization will often bear no discernible signature of a neutral IGM in their afterglow spectra. We discuss the constraints on x_H from the z = 6.3 burst, GRB050904, and quantify the probability of detecting a neutral IGM using future spectroscopic observations of high-redshift, near-infrared GRB afterglows. Assuming an observation with signal-to-noise similar to the Subaru FOCAS spectrum of GRB050904 and that the column density distribution of damped Ly-alpha absorbers is the same as measured at lower redshifts, a GRB from an epoch when x_H = 0.5 can be used to detect a partly neutral IGM at 98% confidence level 10% of the time (and, for an observation with three times the sensitivity, 30% of the time).