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The HI 21cm absorption line is masked by bright foregrounds and systematicdistortions that arise due to the chromaticity of the antenna used to make theobservation coupling to the spectral inhomogeneity of these foregrounds. Wedemonstrate that these distortions are sufficient to conceal the 21cm signalwhen the antenna is not perfectly achromatic and that simple correctionsassuming a constant spatial distribution of foreground power are insufficientto overcome them. We then propose a new physics-motivated method of modellingthe foregrounds of 21cm experiments in order to fit the chromatic distortionsas part of the foregrounds. This is done by generating a simulated sky modelacross the observing band by dividing the sky into $N$ regions and scaling abase map assuming a distinct uniform spectral index in each region. Theresulting sky map can then be convolved with a model of the antenna beam togive a model of foregrounds and chromaticity parameterised by the spectralindices of the $N$ regions. We demonstrate that fitting this model for varying$N$ using a Bayesian nested sampling algorithm and comparing the results usingthe evidence allows the 21cm signal to be reliably detected in data of arelatively smooth conical log spiral antenna. We also test a much morechromatic conical sinuous antenna and find this model will not produce areliable signal detection, but in a manner that is easily distinguishable froma true detection.

A General Bayesian Framework for Foreground Modelling and Chromaticity Correction for Global 21cm Experiments