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) over bar (H), at the GRB's redshift to better than delta(x) over bar (H) similar to 0.3. Some GRB sightlines will encounter more neutral hydrogen than others at fixed, H owing to the patchiness of reionization. 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) over bar (H) from the z = 6.3 burst, GR13050904, 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 ratio similar to the Subaru FOCAS spectrum of GRB050904 and that the column density distribution of damped Lya. absorbers is the same as measured at lower redshifts, a GRB from an epoch when (x) over bar (H) = 0.5 can be used to detect a partly neutral IGM at 97 per cent confidence level approximate to 10 per cent of the time (and, for an observation with three times the sensitivity, approximate to 30 per cent of the time).