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

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 (FR) in the detection of polarization of 21 cm radiation. Since the effect of FR is strong due to the large wavelength nature of redshifted 21 cm signal, the initial E-mode signal carried by 21 cm photons is modified in its entirety. We show that a 99 % accuracy on rotation measure (RM) data is necessary to recover the initial E-mode signal. We conclude that, given the current status of RM observations, it is not possible to retrieve the initial polarization signal of 21 cm from the EoR. However, we are optimistic that it may be possible from the next generation radio surveys.