Constraining the fraction of primary gamma rays at ultra-high energies from the muon data of the Yakutsk extensive-air-shower array

By making use of the data on the total signal and on the muon component of the air showers detected by the Yakutsk array, we analyze, in the frameworks of the recently suggested event-by-event approach, how large the fraction of primary gamma-rays at ultra-high energies can be. We derive upper limits on the photon fraction in the integral flux of primary cosmic rays. At the 95% confidence level (CL), these limits are 22% for primary energies $E_0>4\cdot10^{19}$ eV and 12% for $E_0>2\cdot10^{19}$ eV. Despite the presence of muonless events, the data are consistent with complete absence of photons at least at 95% CL. The sensitivity of the results to systematic uncertainties, in particular to those of the energy determination for non-photon primaries, is discussed.