Asking Fast Radio Bursts for More than Reionization History

We propose different estimators to probe the intergalactic medium (IGM) during the epoch of reionization (EoR) using the dispersion measure (DM) of the fast radio bursts. We consider three different reionization histories, which we can distinguish with a total of ≲1000 DM measurements during EoR if their redshifts are known. We note that the redshift derivatives of DM are also directly sensitive to the reionization history. The major point of this work is to explore the variance in the DM measurements and the information encoded in them. We find that the all-sky average DM ¯ ( z ) gets biased from the line-of-sight fluctuations in the DM measurements introduced by the ionization of the IGM during EoR. We find that the ratio σ DM / DM ¯ depends directly on the ionization bubble sizes as well as the reionization history. On the other hand, we also find that angular variance (coined as structure function) of DM encodes the information about the duration of reionization and the typical bubble sizes as well. We establish the usefulness of variances in DM using toy models of reionization and later verify it with the realistic reionization simulations.