Muon content of extensive air showers: comparison of the energy spectra obtained by the Sydney University Giant Air-shower Recorder and by the Pierre Auger Observatory

The Sydney University Giant Air-shower Recorder (SUGAR) measured the energy spectrum of ultra-high-energy cosmic rays reconstructed from muon-detector readings, while the Pierre Auger Observatory, looking at the same Southern sky, uses the calorimetric fluorescence method for the same purpose. Comparison of their two spectra allows us to reconstruct the empirical dependence of the number of muons in the shower on the primary energy for energies between $10^{17}$ and $10^{18.5}$ eV. We compare this dependence with the predictions of hadronic interaction models \mbox{QGSJET-II-04} and \mbox{EPOS-LHC}. The empirically determined number of muons with energies above 0.75 GeV exceeds the simulated one by the factors $\sim$1.67 and $\sim$1.28 for $10^{17}$ eV proton and iron primaries, respectively. The muon excess grows moderately with the primary energy, increasing by an additional factor of $\sim 1.2$ for $10^{18.5}$ eV primaries.