A general Bayesian framework to account for foreground map errors in global 21-cm experiments

Measurement of the global 21-cm signal during Cosmic Dawn and the Epoch of Reionization is made difficult by bright foreground emission which is 2-5 orders of magnitude larger than the expected signal. Fitting for a physics-motivated parametric forward model of the data within a Bayesian framework provides a robust means to separate the signal from the foregrounds, given sufficient information about the instrument and sky. It has previously been demonstrated that, within such a modelling framework, a foreground model of sufficient fidelity can be generated by dividing the sky into N regions and scaling a base map assuming a distinct uniform spectral index in each region. Using the Radio Experiment for the Analysis of Cosmic Hydrogen as our fiducial instrument, we show that, if unaccounted-for, amplitude errors in low-frequency radio maps used for our base map model will prevent recovery of the 21-cm signal within this framework, and that the level of bias in the recovered 21-cm signal is proportional to the amplitude and the correlation length of the base-map errors in the region. We introduce an updated foreground model that is capable of accounting for these measurement errors by fitting for a monopole offset and a set of spatially dependent scale factors describing the ratio of the true and model sky temperatures, with the size of the set determined by Bayesian evidence-based model comparison. We show that our model is flexible enough to account for multiple foreground error scenarios allowing the 21-cm sky-averaged signal to be detected without bias from simulated observations with a smooth conical log spiral antenna.