Muon deficit in air shower simulations estimated from AGASA muon measurements

In this work, direct measurements of the muon density at 1000 m from the shower axis obtained by the Akeno Giant Air Shower Array (AGASA) are analyzed. The selected events have zenith angles $\theta \le 36°$ and reconstructed energies in the range $18.83\le {\log }_{10}(E_R/\mathrm{eV})\le 19.46$. These are compared to the predictions corresponding to proton, iron, and mixed composition scenarios obtained by using the high-energy hadronic interaction models EPOS-LHC, QGSJetII-04, and Sibyll2.3c. The mass fractions of the mixed composition scenarios are taken from the fits to the depth of the shower maximum distributions performed by the Pierre Auger Collaboration. The cross-calibrated energy scale from the Spectrum Working Group [D. Ivanov, for the Pierre Auger Collaboration and the Telescope Array Collaboration, PoS(ICRC2017) 498 (2017)] is used to combine results from different experiments. The analysis shows that the AGASA data are compatible with a heavier composition with respect to the one predicted by the mixed composition scenarios. Interpreting this as a muon deficit in air shower simulations, the incompatibility is quantified. The muon density obtained from AGASA data is greater than that of the mixed composition scenarios by a factor of $1.49\pm 0.11(\mathrm{stat})\pm 0.18(\mathrm{syst})$, $1.54\pm 0.12(\mathrm{stat})\pm 0.18(\mathrm{syst})$, and $1.66\pm 0.13(\mathrm{stat})\pm 0.20(\mathrm{syst})$ for EPOS-LHC, Sibyll2.3c, and QGSJetII-04, respectively.

Figure 1

Average muon density at 1000 m divided by the energy (reconstructed energy), as a function of the logarithm of the input energy of the simulations (the logarithm of the reconstructed energy in the center of the $i$th bin) in dashed lines (solid lines). The bin width considered is $\mathrm{\Delta }{\log }_{10}(E/\mathrm{eV})=0.2$. The model used is EPOS-LHC, and the primaries are proton (red) and iron (blue).

Figure 2

Logarithm of the muon density as a function of the logarithm of the reconstructed energy (in the reference scale). For the events below the dashed line, no muons were measured in any muon detector. The data points are extracted from Fig. 7 of Ref. [26].

Figure 3

Average muon density divided by the reconstructed energy, as a function of the logarithm of the reconstructed energy in the center of the $i$th bin. Superimposed to AGASA data points [26] are the predictions for proton (red) and iron (blue) primaries, and for the mixed composition scenario corresponding to the models Sibyll2.3c (top panel), EPOS-LHC (middle panel), and QGSJetII-04 (lower panel). The systematic uncertainties are enclosed by square brackets. The latter account for systematic uncertainties in the energy scale (consequently, they are diagonal), and also in the mass fractions in the case of the mixed composition scenarios. The vertical dashed lines correspond to the limits of the reconstructed energy bins considered.

Figure 4

Average muon density divided by the reconstructed energy for AGASA data and for proton, iron, and mixed composition scenarios. The obtained values are reported in the table (left) and are also plotted (right) on the same line. The energy range under consideration is $18.83\le {\log }_{10}(E_R/\mathrm{eV})\le 19.46$. The analyzed models are QGSJetII-04, EPOS-LHC, and Sibyll2.3c. The square brackets correspond to the systematic uncertainties.

Figure 5

Muon density correction factor $F$ corresponding to the single nuclei and mixed composition scenarios. The obtained values are reported in the table (left) and are also plotted (right) on the same line. The analyzed models are QGSJetII-04, EPOS-LHC, and Sibyll2.3c. The energy range under consideration is $18.83\le {\log }_{10}(E_R/\mathrm{eV})\le 19.46$. The square brackets correspond to the systematic uncertainties.

Figure 6

Logarithm of the UHECR flux multiplied by the energy to the power of 3 as a function of the logarithm of the energy. The data points correspond to the measurements done by Telescope Array [19], and the solid line corresponds to the fit of the data (see text for details). The energy scale of Telescope Array is shifted to the reference energy scale.

Figure 7

Relative reconstructed energy uncertainty as a function of the logarithm of the energy. The data points are obtained from simulations [21]. The zenith angles of the showers are in the range $33°\le \theta \le 44°$. The solid line corresponds to an approximating function (see the text for details).