Detecting Cosmic 21 cm Global Signal Using an Improved Polynomial Fitting Algorithm

Abstract: Detecting the cosmic 21 cm signal from Epoch of Reionization (EoR) has always been a difficult task. Although the Galactic foreground can be regarded as a smooth power-law spectrum, due to the chromaticity of the antenna, additional structure will be introduced into the global spectrum, making the polynomial fitting algorithm perform poorly. In this paper, we introduce an improved polynomial fitting algorithm - the Vari-Zeroth-Order Polynomial (VZOP) fitting and use it to fit the simulation data. This algorithm is developed for the upcoming Low-frequency Anechoic Chamber Experiment (LACE), yet it is a general method suitable for application in any single antenna-based global 21 cm signal experiment. VZOP defines a 24-hour averaged beam model that brings information about the antenna beam into the polynomial model. Assuming that the beam can be measured, VZOP can successfully recover the 21 cm absorption feature, even if the beam is extremely frequency-dependent. In real observations, due to various systematics, the corrected measured beam contains residual errors that are not completely random. Assuming the errors are frequency-dependent, VZOP is capable of recovering the 21 cm absorption feature even when the error reaches 10%. Even in the most extreme scenario where the errors are completely random, VZOP can at least give a fitting result that is not worse than the common polynomial fitting. In conclusion, the fitting effect of VZOP depends on the structure of the error and the accuracy of the beam measurement.