Assessment of the Projection-induced Polarimetry Technique for Constraining the Foreground Spectrum in Global 21 cm Cosmology

Detecting the cosmological sky-averaged (global) 21 cm signal as a function of observed frequency will provide a powerful tool to study the ionization and thermal history of the intergalactic medium (IGM) in the early Universe ($\sim$ 400 million years after the Big Bang). The greatest challenge in conventional total-power global 21 cm experiments is the removal of the foreground synchrotron emission ($\sim 10^3$-$10^4$ K) to uncover the weak cosmological signal (tens to hundreds of mK), especially since the intrinsic smoothness of the foreground spectrum is corrupted by instrumental effects. Although the EDGES team has recently reported an absorption profile at 78 MHz in the sky-averaged spectrum, it is necessary to confirm this detection with an independent approach. The projection effect from observing anisotropic foreground source emission with a wide-view antenna pointing at the North Celestial Pole (NCP) can induce a net polarization, referred as the Projection-Induced Polarization Effect (PIPE). Due to Earth's rotation, observation centered at the circumpolar region will impose a dynamic sky modulation on the net polarization's waveforms which is unique to the foreground component. In this study, we review the implementation practicality and underlying instrumental effects of this new polarimetry-based technique with detailed numerical simulation and a testbed instrument, the Cosmic Twilight Polarimeter (CTP). In addition, we explore an SVD-based analysis approach for separating the foreground and instrumental effects from the background global 21 cm signal using the sky-modulated PIPE.