Ensuring the Robustness of SVD Analysis for Global 21-cm Signal Extraction

The highly redshifted 21-cm transition of neutral hydrogen offers the chance to directly observe both the Dark Ages and Cosmic Dawn. The Dark Ages Polarimeter PathfindER (DAPPER) is a NASA-funded mission concept to measure the 21-cm global signal from the radio quiet lunar farside. Pylinex is a publicly available code designed for extracting the 21-cm global signal from observations in the presence of systematic effects for experiments such as DAPPER. The signal extraction method relies on Singular Value Decomposition (SVD) of “training sets” built from measurements, theory, and simulations. SVD then produces eigenmodes specifically suited for a given observation with which to fit the data. Pylinex has been heavily tested with simulated data in which the true 21-cm signal is known. However, in the case of real observations, the true form of the signal will not be known. In this instance, an independent test that does not rely on the true signal must be able to detect whether the signal extraction is reliable. Commonly used goodness-of-fit metrics such as chi-squared may indicate a good fit to the full data set even when the 21-cm signal has not been extracted properly. However, the number of SVD eigenmodes chosen for each component (e.g. foreground and 21-cm signal) by minimizing an information criterion can provide more information about the quality of the 21-cm signal reconstruction in terms of its separation from the other components. A reference distribution created by fitting simulated data realizations taken from the training set curves directly serves as the baseline against which the fit to the observed data is compared. Fits performed with data realizations that differ in key ways from the training sets show that if a given realization falls outside the reference distribution, the signal extraction is likely unreliable. Based on where the fit falls in the number of SVD eigenmodes space relative to the reference distribution, this test might also be able to identify aspects in which the training sets need to be altered to better represent the data.