Background of radio photons from primordial black holes

We compute the isotropic radiation background due to Hawking emission from primordial black holes (PBHs), and examine if this background is a viable option in explaining the excess radiowave background observed by the ARCADE2 and LWA1 experiments at $\lesssim 1\,$GHz. We find that even under the extreme assumption that all of the dark matter is in the form of PBHs, the radio brightness temperature induced by Hawking evaporation of PBHs is $\mathcal{O}(10^{-46})\,$K, highly subdominant compared to the cosmic microwave background. The main reason for this is that for PBHs in the mass range $\sim10^{12}$-$10^{14}\,$kg, which can be constrained by Hawking emission, the spectrum peaks at $10^7$ to $10^5\,$eV. As the Hawking spectrum is power law suppressed towards lower energies, negligible flux of $\mu$eV photons is obtained. The peak of the Hawking spectrum shifts to lower energies for higher masses, but the number density is low and so is the specific intensity. Because Hawking emission from PBHs is thus unable to explain the observed excess radio background, we also consider the alternative possibility of radio emission from gas accretion onto supermassive PBHs. These PBHs can readily produce strong radio emission that could easily explain the ARCADE2/LWA1 excess.