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, used 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 a vertical shower on the primary energy for energies between $10^{17}$ and $10^{18.5}\mathrm{eV}$. We compare this dependence with the predictions of hadronic interaction models QGSJET-II-04, EPOS-LHC and SIBYLL-2.3c. The empirically determined number of muons with energies above 0.75 GeV in a vertical shower exceeds the simulated one by the factors $\sim 1.7$ and $\sim 1.3$ for $10^{17}\mathrm{eV}$ proton and iron primaries, respectively. The muon excess grows moderately with the primary energy, increasing by an additional factor of $\sim 1.2$ for $10^{18.5}\mathrm{eV}$ primaries.

Figure 1

SUGAR differential vertical-equivalent muon-number ($N_{\mathrm{v}}$) spectrum [18]. The line presents the power-law fit for $N_{\mathrm{v}}<{10}^{7.5}$.

Figure 2

The SUGAR differential energy spectrum [18] estimated using the Hillas model [21] in Eqs. (4) and (5) (red empty triangles); the Auger differential combined energy spectrum [22] (blue filled circles); the SUGAR differential energy spectrum estimated using the empirical $E(N_{\mathrm{v}})$ relation in Eqs. (4) and (6) (red empty circles; this work). The inclined bar represents the systematic uncertainty in terms of $E$, summed in quadratures.

Figure 3

Mean effective number of vertical muons $N_{\mathrm{v}}$ as a function of the primary energy. Points indicate the results of Monte Carlo simulations with QGSJET-II-04 (protons—red open circles, iron—blue open circles), EPOS-LHC (protons—red open triangles, iron—blue open triangles) and SIBYLL-2.3c (protons—red open squares, iron—blue open squares). The dashed blue line corresponds to our empirical model Eqs. (4) and (6); the shaded blue area indicates the total uncertainly (statistical and systematic errors summed in quadrature). Statistical error bars for the Monte Carlo points are shown where they are larger than symbols.

Figure 4

Best-fit muon excess, $N_{\mathrm{v}}/N_{\mathrm{v}}^{\mathrm{MC}}$, as a function of the primary energy $E$. QGSJET-II-04—full lines, EPOS-LHC—dashed lines; SIBYLL-2.3c—dotted lines (protons—red, iron—blue). The vertical bar indicates the estimated systematic error.