GZK Photons as Ultra High Energy Cosmic Rays

We calculate the flux of "GZK-photons", namely the flux of Ultra High Energy Cosmic Rays (UHECR) consisting of photons produced by extragalactic protons through the resonant photoproduction of pions, the so called Greisen-Zatsepin-Kuzmin (GZK) effect. We show that if the UHECR are mostly protons, depending on the UHECR spectrum, the slope of the proton flux at the source, distribution of sources and intervening backgrounds, between $10^{-4}$ and $10^{-2}$ of the UHECR above $10^{19}$ eV and between $10^{-5}$ and 0.6 of the UHECR above $10^{20}$ eV are photons (the range being much higher for the AGASA than for the HiRes spectrum). Detection of these photons would open the way for UHECR gamma-ray astronomy. Detection of a larger photon flux would imply the emission of photons at the source or new physics. In fact, we find that at energiesclose to $10^{20}$ eV the maximum expected GZK photon fraction is comparable to (for the AGASA spectrum) or much smaller than (for the HiRes spectrum) the minimum photon ratio predicted by Top-Down models which fit the AGASA or the HiRes data, thus, the photon fraction at $10^{20}$ eV is a crucial test for Top-Down models.