A general Bayesian framework for foreground modelling and chromaticity correction for global 21 cm experiments

The Hi 21 cm absorption line is masked by bright foregrounds and systematic distortions that arise due to the chromaticity of the antenna used to make the observation coupling to the spectral inhomogeneity of these foregrounds. We demonstrate that these distortions are sufficient to conceal the 21 cm signal when the antenna is not perfectly achromatic and that simple corrections assuming a constant spatial distribution of foreground power are insufficient to overcome them. We then propose a new physics-motivated method of modelling the foregrounds of 21 cm experiments in order to fit the chromatic distortions as part of the foregrounds. This is done by generating a simulated sky model across the observing band by dividing the sky into N regions and scaling a base map assuming a distinct uniform spectral index in each region. The resulting sky map can then be convolved with a model of the antenna beam to give a model of foregrounds and chromaticity parametrized by the spectral indices of the N regions. We demonstrate that fitting this model for varying N using a Bayesian nested sampling algorithm and comparing the results using the evidence allows the 21 cm signal to be reliably detected in data of a relatively smooth conical log spiral antenna. We also test a much more chromatic conical sinuous antenna and find this model will not produce a reliable signal detection, but in a manner that is easily distinguishable from a true detection.