The Cosmic Dispersion Measure from Gamma-Ray Burst Afterglows: Probing the Reionization History and the Burst Environment

We show a possible way to measure the column density of free electrons along the light path, the so-called Dispersion Measure (DM), from the early 415 (/1 GHz) ^-2 (DM/10^5 pc cm^-3) s radio afterglows of the gamma-ray bursts. We find that the proposed Square Kilometer Array can detect bright radio afterglows around the time 10^3 (/160 MHz) ^-2 s to measure the intergalactic DM (6000 pc cm^-3 at redshift z>6) up to z 30, from which we can determine the reionization history of the universe and identify the missing warm-hot baryons. At low z, DM in the host galaxy may reach 10^5 pc cm^-3 depending on the burst environment, which may be probed by the current detectors. Free-free absorption and diffractive scattering may also affect the radio emission in a high density.