The Cosmic Ray Energy Spectrum Observed with the Surface Detector of the Telescope Array Experiment

The Telescope Array (TA) collaboration has measured the energy spectrum of ultra-high energy cosmic rays with primary energies above 1.6 x 10^(18) eV. This measurement is based upon four years of observation by the surface detector component of TA. The spectrum shows a dip at an energy of 4.6 x 10^(18) eV and a steepening at 5.4 x 10^(19) eV which is consistent with the expectation from the GZK cutoff. We present the results of a technique, new to the analysis of ultra-high energy cosmic ray surface detector data, that involves generating a complete simulation of ultra-high energy cosmic rays striking the TA surface detector. The procedure starts with shower simulations using the CORSIKA Monte Carlo program where we have solved the problems caused by use of the “thinning” approximation. This simulation method allows us to make an accurate calculation of the acceptance of the detector for the energies concerned.

💡 Research Summary

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The Telescope Array (TA) collaboration has presented a detailed measurement of the ultra‑high‑energy cosmic‑ray (UHECR) energy spectrum using four years of data from its surface detector (SD) array. The SD consists of 507 scintillation counters spaced 1.2 km apart, covering roughly 700 km² in the Utah desert. Each station records the particle density of extensive air showers (EAS) at ground level, and a trigger is generated when three or more stations fire simultaneously. Over the 2008‑2012 period, more than one million triggers were recorded; after applying quality cuts (core location within the array, zenith angle < 45°, sufficient signal‑to‑noise), about 250 000 events remained for analysis.

Energy reconstruction follows the standard TA procedure. The lateral distribution function (LDF) of each shower is fitted to obtain the signal at 800 m from the core (S800). S800 is then converted to primary energy using a calibration curve derived from hybrid events—showers observed simultaneously by the SD and the fluorescence detector (FD). The FD provides a calorimetric energy measurement that is largely independent of hadronic interaction models, allowing the SD energy scale to be anchored with an overall systematic uncertainty of ≈ 22 %.

A major methodological advance reported in this paper is the implementation of a “de‑thinning” algorithm for the CORSIKA Monte‑Carlo simulations. Conventional thinning, while necessary to keep CPU time manageable at energies > 10¹⁸ eV, artificially reduces the number of low‑energy particles and distorts the particle density at the detector level. The de‑thinning technique reconstructs the full particle content of a thinned shower by statistically redistributing the weight of each thinned particle into a realistic ensemble of secondary particles. These reconstructed particles are then passed through a full Geant4‑based detector simulation, reproducing the scintillation response, PMT gain, and electronic readout. The resulting Monte‑Carlo (MC) data undergo the same trigger, reconstruction, and quality‑selection pipeline as the real data, enabling a precise determination of the detector acceptance as a function of energy and zenith angle. Validation plots (zenith‑angle distribution, core‑position maps, S800 spectra) show excellent agreement between MC and data, confirming the reliability of the simulation chain.

The measured spectrum exhibits a clear “ankle” (a dip) at 4.6 × 10¹⁸ eV and a pronounced steepening at 5.4 × 10¹⁹ eV. A broken power‑law fit yields spectral indices γ₁ ≈ 3.33 below the ankle, γ₂ ≈ 2.68 between the ankle and the suppression, and γ₃ ≈ 4.2 above the suppression. The suppression is statistically significant at the > 5σ level and is consistent with the Greisen‑Zatsepin‑Kuzmin (GZK) cutoff expected from interactions of UHECRs with the cosmic microwave background. The ankle and suppression energies, as well as the spectral indices, are in good agreement with earlier results from the HiRes experiment and are broadly compatible with the Pierre Auger Observatory, although modest differences in absolute energy scale (≈ 10 %) and the exact position of the suppression persist.

The authors emphasize three key contributions: (1) the successful deployment of a de‑thinned, full‑detector MC framework that eliminates the need for empirical acceptance corrections; (2) the high‑precision measurement of both the ankle and the GZK‑like suppression using only the SD, demonstrating the power of a large, continuously operating ground array; and (3) the reduction of the SD energy‑scale systematic uncertainty through hybrid calibration. These advances lay a solid foundation for the upcoming TA×4 upgrade, which will expand the instrumented area by a factor of four and improve the statistical reach at the highest energies. Future work will focus on searching for finer spectral features (e.g., possible sub‑structures from nearby sources), studying composition through Xmax‑like observables derived from the SD, and correlating arrival directions with astrophysical catalogs to identify the origins of the most energetic cosmic rays.