Reconstructing the Thomson Optical Depth due to Patchy Reionization with 21 cm Fluctuation Maps

Large fluctuations in the electron column density can occur during thereionization process. We investigate the possibility of deriving the electrondensity fluctuations through detailed mapping of the redshifted 21-cm emissionfrom the neutral medium during reionization. We find that theelectron-scattering optical depth and 21-cm differential brightness temperatureare strongly anti-correlated, allowing optical depth estimates based entirelyon redshifted 21-cm measurements. This should help isolate the CMB polarizationfluctuations that are due to reionization, allowing both cleaning of the patchyreionization polarization signal as a contaminating source of confusion toother signals and a measurement of the primordial quadrupole that would bemeasured at various locations in the universe at the epoch of reionization.This latter application in principle allows mapping of the primordial densityfield at z~1100 over a large fraction of the Hubble volume.Comment: 4 pages, submitted to ApJ