Disentangling the anisotropic radio sky: Fisher forecasts for 21cm arrays

The existence of a radio synchrotron background (RSB) is implied by a number of measurements, including excess emission seen by the ARCADE2 and LWA experiments. Highly sensitive wideband radio arrays, of the kind used to measure the cosmic 21-cm signal, provide a promising way to further constrain the RSB through its anisotropy, providing additional insight into its origin. We present a framework for evaluating the potential of 21-cm arrays to disentangle different components of the diffuse radio sky based on the combination of their frequency spectrum and angular power spectrum (APS). The formalism is designed to calculate uncertainties due to the intrinsic cosmic variance alone or together with instrumental noise. In particular, we predict the potential for measuring the anisotropy of a broad generalised class of excess radio background models using the low-frequency HERA array as an example. We find that a HERA-like array can distinguish an RSB from other sky components based on its angular clustering and spectral dependence, even if these are quite similar to one or more of the other components -- but only in the case that the RSB is relatively bright.