Updated comparison of the UHECR energy spectra measured by the Pierre Auger Observatory and the Telescope Array

TL;DR

This study re-evaluates the energy-scale agreement between the Pierre Auger Observatory and Telescope Array using expanded data sets and a joint calibration framework, comparing spectra in both full and common sky regions. It demonstrates that most of the low-energy difference arises from calibration choices, with a residual ~4% offset when harmonized calibrations are used, but reveals a significant energy-dependent discrepancy above $10^{19}$ eV that points to instrumental or analysis-related origins. By examining systematic uncertainties, composition effects, and hadronic-model dependencies, the work highlights the need for coordinated cross-checks and future projects (e.g., AugerPrime, Auger@TA, EarthCARE) to reconcile the spectra and enable robust astrophysical interpretation.

Abstract

The Pierre Auger and Telescope Array joint Working Group on the UHECR energy spectrum was established in 2012 to analyze energy scale uncertainties in both experiments and to in vestigate their systematic differences, particularly in the spectral shape of the flux measurements. Previous studies have indeed shown that, within systematic uncertainties, the energy s pectra measured by the two observatories are consistent below~$10\,\mathrm{EeV}$. However, at higher energies, a significant difference remains. In this work, we re-examine this discrepan cy in greater detail and explore its possible origins. We consider systematic and statistical uncertainties, including the conversion from directly measured observables to energy and the calculation of exposures. We present an updated energy scale comparison between the two experiments and updated flux measurements in the common declination band.

Figures (5)

• Figure 1: Comparison of the spectra measured in the full declination band. The offset between the two measurements below $10^{19}\,\mathrm{eV}$ is well described by an overall energy shift of 11.2% fully compatible within the systematic uncertainties. A better agreement between the spectra is obtained when using the same model for the fluorescence yield and the invisible energy ($E_\text{inv}$) as shown in the right panel. In this configuration, a residual 4% energy shift remains. This illustrates how calibration choices can account for a substantial part of the observed difference. The interpretation of the comparison at lower energies should be considered with care.
• Figure 2: Comparison between the Auger and TA spectra measured in the two common declination bands, the one used in previous reports (upper-left panel) and the enlarged one attainable including the Auger events inclined at large zenith angles (lower-left panel). The spectra are obtained using the same model for the fluorescence yield and the invisible energy ($E_\text{inv}$). The figures in the right panels show the ratio of the spectra shown on the left.
• Figure 3: Auger and TA spectra in the common declination bands after the application of a hypothetical energy-dependent energy shift needed to bring the spectra in agreement. The energy shift is defined as $\Delta E/E = \left[\pm 2.0 \pm \frac{F}{2}(\log_{10}E-19)\right]\%$ where the constant factor ($\pm 2.0\%$) is the shift determined in the full band and $F$ is 16% and 20% for the left and right figure, respectively.
• Figure 4: Left panel: ratio $E_\mathrm{TBL}/E_\mathrm{FD}$ for Auger hybrid events using lookup tables built using Sibyll 2.3c under different primary assumptions. A clear energy-dependent drift is observed when using fixed composition assumptions such as pure proton or pure iron. In contrast, adopting the AugerMix composition, which reflects the mass evolution with energy, results in a stable ratio consistent with the standard Auger calibration. Right panel: TA's energy ratio plots as a function of energy that represents the SD/FD energy ratio using hybrid events with the standard MC-based SD reconstruction. No energy-dependent non-linearity is observed.
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