Demonstrating Agreement between Radio and Fluorescence Measurements of the Depth of Maximum of Extensive Air Showers at the Pierre Auger Observatory

Abstract

We show, for the first time, radio measurements of the depth of shower maximum ($X_\text{max}$) of air showers induced by cosmic rays that are compared to measurements of the established fluorescence method at the same location. Using measurements at the Pierre Auger Observatory we show full compatibility between our radio and the previously published fluorescence data set, and between a subset of air showers observed simultaneously with both radio and fluorescence techniques, a measurement setup unique to the Pierre Auger Observatory. Furthermore, we show radio $X_\text{max}$ resolution as a function of energy and demonstrate the ability to make competitive high-resolution $X_\text{max}$ measurements with even a sparse radio array. With this, we show that the radio technique is capable of cosmic-ray mass composition studies, both at Auger and at other experiments.

Figures (4)

• Figure 1: Mean (left) and standard deviation (right) of the $X_\textup{max}$ distribution as measured by AERA in this work (black). The results are compared to predictions from CORSIKA air-shower simulations for three hadronic interaction models (lines) for proton (red) and iron (blue) mass compositions ref:hadr_eposref:hadr_sibyllref:hadr_qgsref:POA_Composition_ICRC2019 and compared to measurements by the Auger FD ref:POA_Composition_ICRC2019. The statistical uncertainties on the mean and width of the measurements are plotted as error bars and the systematic uncertainties with capped markers.
• Figure 2: Comparison of $X_\text{max}$ for showers measured simultaneously by both AERA and the FD. A diagonal line is shown to guide the eye. Shown at the top is the Pearson correlation coefficient $r$ with corresponding $p$ value (the probability to obtain an $r$ of at least that value from uncorrelated data). Shown at the bottom is the distribution (kernel density estimation) of the differences with mean $\mu$ and spread $\sigma$.
• Figure 3: Resolution of the $X_\textup{max}$ reconstruction method, $\delta_{X_\text{max}}$, as a function of energy in units of column density. The median values of the uncertainties on $X_\text{max}$ (circles with uncertainties $\sigma_b$ from bootstrap resampling) for our set of showers are shown per energy bin along with the parametrized fit [Eq. (\ref{['eq:EnergyResolution']})] of the resolution of $X_\text{max}$ (solid line with $1\sigma$-confidence bands). Also shown are the resolutions achieved by the Auger fluorescence telescopes ref:FDXmaxSyst. The black hatched region at low energy indicates the cut on energy for this AERA analysis. The size of the energy bins with the number of showers per bin is inset at the bottom of the figure.
• Figure 4: Mean of the $X_\textup{max}$ distribution as measured by AERA in this work (black). The results are compared to predictions from air-shower simulations for multiple hadronic interaction models (lines) for proton (red) and iron (blue) mass compositions ref:hadr_eposref:hadr_sibyllref:hadr_qgsref:POA_Composition_ICRC2019 and compared to measurements by LOFAR ref:LOFAR2021, Tunka-Rex ref:Xmax_TunkaREX, Yakutsk-Radio ref:YakutskXmax2019, and Auger FD ref:POA_Composition_ICRC2019. Note that the Yakutsk-Radio results do not account for aperture effects on the same level as the other experiments. Colors have been used to highlight the measurements with the radio technique. The statistical uncertainties on the measurements are shown as vertical bars and for radio the systematic uncertainties, if available, are shown with caps.