Galactic Faraday rotation effect on polarization of 21 cm lines from the epoch of reionization

A redshifted 21 cm signal from neutral hydrogen is one of the most competitive probes of the epoch of reionization (EoR). Unpolarized 21 cm radiation acquires a certain level of linear polarization during the EoR due to Thompson scattering. This linear polarization, if measured, could probe important information about the EoR. We study the effect of Galactic Faraday rotation in the detection of polarization of 21 cm radiation. The effect of Faraday rotation is strong due to the large wavelength nature of the redshifted 21 cm signal. Thus, an initial E-mode signal carried by 21 cm photons is modified in its entirety. We show that a 99% accuracy on rotation measure data is necessary to recover the initial E-mode signal. We conclude that, given the current status of rotation measure observations, it is not possible to retrieve the initial polarization signal of 21 cm from the EoR. However, future radio observations of pulsar sources may improve the accuracy of the Galactic rotation measure to a high degree, making the reconstruction of the initial 21 cm polarization possible.