Upper limit on gamma-ray flux above 1019 eV estimated by the akeno giant air shower array experiment

The origin of the highest energy cosmic rays (≥ 1020 eV) is not well understood. Interesting models called "top-down" scenarios have been proposed to explain the origin. The γ-ray flux in ultra-high-energy cosmic rays is a key parameter for giving constraints on such models. To study the properties of γ-ray showers, we carry out simulation studies that take into account both the Landau-Pomeranchuk-Migdal effect and electromagnetic interactions in the geomagnetic field. Based on an analysis of muons in air showers observed by the Akeno Giant Air Shower Array, the upper limits on the γ-ray flux are estimated to be 28% above 1019 eV and 67% above 1019.5 eV in the observed air showers at a confidence level of 95%. Above 1020 eV, the primary composition is in agreement with an extrapolation from lower energies, and there is no indication that the observed events are mostly γ-ray showers. These results provide observational constraints for origin models up to the highest energies.