A polarimetric approach for constraining the dynamic foreground spectrum for cosmological global 21-cm measurements

The cosmological global (sky-averaged) 21-cm signal is a powerful tool to probe the evolution of the intergalactic medium (IGM) in high-redshift Universe ($z \leq 6$). One of the biggest observational challenges is to remove the foreground spectrum which is at least four orders of magnitude brighter than the cosmological 21-cm emission. Conventional global 21-cm experiments rely on the spectral smoothness of the foreground synchrotron emission to separate it from the unique 21-cm spectral structures in a single total-power spectrum. However, frequency-dependent instrumental and observational effects are known to corrupt such smoothness and complicates the foreground subtraction. We introduce a polarimetric approach to measure the projection-induced polarization of the anisotropic foreground onto a stationary dual-polarized antenna. Due to Earth rotation, when pointing the antenna at a celestial pole, the revolving foreground will modulate this polarization with a unique frequency-dependent sinusoidal signature as a function of time. In our simulations, by harmonic decomposing this dynamic polarization, our technique produces two separate spectra in parallel from the same observation: (i) a total sky power consisting both the foreground and the 21-cm background, (ii) a model-independent measurement of the foreground spectrum at a harmonic consistent to twice the sky rotation rate. In the absence of any instrumental effects, by scaling and subtracting the latter from the former, we recover the injected global 21-cm model within assumed uncertainty. We further discuss several limiting factors and potential remedies for future implementation.