A closer look at dark photon explanations of the excess radio background

The observed excess radio background has remained a puzzle for over a decade. A recent new physics solution involves dark matter that decays into dark photons in the presence of a thermal dark photon background. The produced non-thermal dark photon spectrum then converts into standard photons around the reionization era, yielding an approximate power-law radio excess with brightness temperature $T(\nu)\simeq \nu^{-2.5}$ over a wide range of frequencies, $\nu$. This simple power-law model comes intriguingly close to the current data, even if several ingredients are required to make it work. In this paper, we investigate some of the details of this model, showcasing the importance of individual effects. In particular, significant deviation from a power law are present at $\nu\lesssim 100\,{\rm MHz}$ and $\nu\gtrsim 1\,{\rm GHz}$. These effects result in improving the fit to data compared to a power-law spectrum, and may become testable in future observations. We also highlight independent signatures that can be tested with future CMB spectral distortion experiments such as {\it PIXIE}.