A new estimate of the extragalactic radio background and implications for ultra-high-energy gamma-ray propagation

We make a new estimate of the extragalactic radio background down to kHz frequencies based on the observed luminosity functions and radio spectra of normal galaxies and radio galaxies. We have constructed models for the spectra of these two classes of objects down to low frequencies based on observations of our Galaxy, other normal galaxies and radio galaxies. We check that the models and evolution of the luminosity functions give source counts consistent with data and calculate the radio background expected from kHz to GHz frequencies. The motivation for this calculation is that the propagation of ultra-high energy gamma-rays in the universe is limited by photon-photon pair production on the radio background. Electromagnetic cascades involving photon-photon pair production and subsequent synchrotron radiation in the intergalactic magnetic field may develop. Such gamma-rays may be produced in acceleration sites of ultra-high energy cosmic rays, as a result of interactions with the microwave background, or emitted as a result of decay or annihilation of topological defects. We find that photon-photon pair production on the radio background remains the dominant attenuation process for gamma-rays from $3 \times 10^{10}$ GeV up to GUT scale energies.