Measurement of the Fluctuations in the Number of Muons in Extensive Air Showers with the Pierre Auger Observatory

We present the first measurement of the fluctuations in the number of muons in extensive air showers produced by ultrahigh energy cosmic rays. We find that the measured fluctuations are in good agreement with predictions from air shower simulations. This observation provides new insights into the origin of the previously reported deficit of muons in air shower simulations and constrains models of hadronic interactions at ultrahigh energies. Our measurement is compatible with the muon deficit originating from small deviations in the predictions from hadronic interaction models of particle production that accumulate as the showers develop.

Figure 1

Number of muons as a function of the measured energy. The black line is the fitted $⟨R_{\mu }⟩=a[E/({10}^{19}\mathrm{eV}){]}^b$. Markers on the top of the frame define the bins in which the fluctuations are evaluated. The numbers give the events in each bin. The effect of the uncertainty of the absolute energy scale is indicated by ${\sigma }_{\mathrm{sys}}(E)$. The best-fit values for parameters $a,b$ and the deviance per degree of freedom (n.d.f.) in the fit are shown on the lower right.

Figure 2

Measured relative fluctuations in the number of muons as a function of the energy and the predictions from three interaction models for proton (red) and iron (blue) showers. The gray band represents the expectations from the measured mass composition interpreted with the interaction models. The statistical uncertainty in the measurement is represented by the error bars. The total systematic uncertainty is indicated by the square brackets.

Figure 3

Data (black, with error bars) compared to models for the fluctuations and the average number of muons for showers with a primary energy of ${10}^{19}\mathrm{eV}$. Fluctuations are evaluated in the energy range from ${10}^{18.97}$ to ${10}^{19.15}\mathrm{eV}$. The statistical uncertainty is represented by the error bars. The total systematic uncertainty is indicated by the square brackets. The expectation from the interaction models for any mixture of the four components $p$, He, N, Fe is illustrated by the colored contours. The values preferred by the mixture derived from the $X_{\max }$ measurements are indicated by the star symbols. The shaded areas show the regions allowed by the statistical and systematic uncertainties of the $X_{\max }$ measurement [39].