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 [similar to415(nu/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 similar to 10(3) (nu/160 MHz)(-2) s to measure the intergalactic DM (greater than or similar to 6000 pc cm(-3) at redshift z > 6) up to z similar to 30, from which we can determine the reionization history of the universe and identify the missing warm-hot baryons if many DMs can be measured. At low z, the DM in the host galaxy may reach similar to10(5) pc cm 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 at a high density.