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 (ν/1 GHz)⁻² ( DM/10⁵ 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 ~ 10³(ν/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 ~ 10⁵ 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.