Cosmic Ray Protons Illuminate Dark Matter Axions

Cosmic ray protons propagating in a spatially-homogeneous but time-dependent field of axions or axion-like particles (ALPs) emit photons in a way that is reminiscent of Cherenkov radiation by charged particles in a preferred background. We compute the emission rate and energy spectrum of the photons, and discuss the possibility of their detection using the Square Kilometre Array which is currently under construction. In the case of a non-detection, constraints can be placed on the parameter space of ALPs whose mass lie between ${10}^{-7}$eV and ${10}^{-5}$ eV under the assumption that they are the primary constituent of dark matter.