Testing reionization with gamma-ray burst absorption spectra

We propose to study cosmic reionization using absorption-line spectra of high-redshift gamma-ray burst (GRB) afterglows. We show that the statistics of the dark portions (gaps) in GRB absorption spectra represent exquisite tools to discriminate among different reionization models. We then compute the probability to find the largest gap in a given width range [W_max, W_max+ dW] at a flux threshold F_th for burst afterglows at redshifts 6.3 ≤z≤ 6.7. We show that different reionization scenarios populate the (W_max, F_th) plane in a very different way, allowing to distinguish among different reionization histories. We provide here useful plots that allow a very simple and direct comparison between observations and model results. Finally, we apply our methods to GRB 050904 detected at z= 6.29. We show that the observation of this burst strongly favours reionization models which predict a highly ionized intergalactic medium at z∼ 6, with an estimated mean neutral hydrogen fraction x_H i= 6.4 ± 0.3 × 10⁻⁵ along the line of sight towards GRB 050904.