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 (∼ 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 (∼ 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.

All 21 cm signal experiments rely on electronic receivers that affect the data via both multiplicative and additive biases through the receiver’s gain and noise temperature. While experiments attempt to remove these biases, the residuals of their imperfect calibration techniques can still confuse signal extraction algorithms. In this paper, the fourth and final installment of our pipeline series, we present a technique for fitting out receiver effects as efficiently as possible. The fact that the gain and global signal, which are multiplied in the observation equation, must both be modeled implies that the model of the data is nonlinear in its parameters, making numerical sampling the only way to explore the parameter distribution rigorously. However, multi-spectra fits, which are necessary to extract the signal confidently as demonstrated in the third paper of the series, often require large numbers of foreground parameters, increasing the dimension of the posterior distribution that must be explored and therefore causing numerical sampling inefficiencies. Building upon techniques in the second paper of the series, we outline a method to explore the full parameter distribution by numerically sampling a small subset of the parameters and analytically marginalizing over the others. We test this method in simulation using a type I Chebyshev bandpass filter gain model and a fast signal model based on a spline between local extrema. The method works efficiently, converging quickly to the posterior signal parameter distribution. The final signal uncertainties are of the same order as the noise in the data.

We present an investigation of the horizon and its effect on global 21 cm observations and analysis. We find that the horizon cannot be ignored when modeling low-frequency observations. Even if the sky and antenna beam are known exactly, forward models cannot fully describe the beam-weighted foreground component without accurate knowledge of the horizon. When fitting data to extract the 21 cm signal, a single time-averaged spectrum or independent multi-spectrum fits may be able to compensate for the bias imposed by the horizon. However, these types of fits lack constraining power on the 21 cm signal, leading to large uncertainties on the signal extraction, in some cases larger in magnitude than the 21 cm signal itself. A significant decrease in uncertainty can be achieved by performing multi-spectrum fits in which the spectra are modeled simultaneously with common parameters. The cost of this greatly increased constraining power, however, is that the time dependence of the horizon’s effect, which is more complex than its spectral dependence, must be precisely modeled to achieve a good fit. To aid in modeling the horizon, we present an algorithm and Python package for calculating the horizon profile from a given observation site using elevation data. We also address several practical concerns such as pixelization error, uncertainty in the horizon profile, and foreground obstructions such as surrounding buildings and vegetation. We demonstrate that our training-set-based analysis pipeline can account for all of these factors to model the horizon well enough to precisely extract the 21 cm signal from simulated observations.