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 Lyα line from a single gamma-ray burst (GRB) afterglow cannot be used to constrain the global neutral fraction of the intergalactic medium (IGM),     , at the GRB's redshift to better than     . Some GRB sightlines will encounter more neutral hydrogen than others at fixed     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     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 ratio similar to the Subaru FOCAS spectrum of GRB050904 and that the column density distribution of damped Lyα absorbers is the same as measured at lower redshifts, a GRB from an epoch when     can be used to detect a partly neutral IGM at 97 per cent confidence level ≈10 per cent of the time (and, for an observation with three times the sensitivity, ≈30 per cent of the time).