Features in the Cosmic Ray Energy Spectrum Observed with Telescope Array Surface Detectors

TL;DR

This work presents a comprehensive analysis of the ultra-high-energy cosmic ray energy spectrum measured by the Telescope Array surface detectors over 16 years, focusing on spectral features and a declination-dependent flux. The spectrum is described with a thrice-broken power law, locating the ankle, shoulder, and cutoff at $E_{ankle}=10^{18.70 \pm 0.01}$ eV, $E_{shoulder}=10^{19.15 \pm 0.08}$ eV, and $E_{cutoff}=10^{19.83 \pm 0.03}$ eV, with high significances for the shoulder ($5.2\sigma$) and cutoff ($6.3\sigma$). Energy reconstructions are cross-validated through MC linearly, SD–FD cross-calibration, and a data-driven CIC method, establishing a robust energy scale. A joint TA–Auger analysis reveals an $8\sigma$ declination-dependent difference in the full sky, which reduces to $1.8\sigma$ in the common sky and remains significant after energy-scale uncertainties, suggesting real hemispheric variations in the UHECR flux. The results emphasize the need to account for exposure biases in cross-experiment comparisons and demonstrate the value of multi-method calibration for interpreting spectral features and anisotropies in UHECRs.

Abstract

Ultra-high energy cosmic rays (UHECRs) are extremely energetic charged particles that originate from outer space. The Telescope Array (TA) experiment, the largest UHECR observatory in the Northern Hemisphere, has provided high-precision measurements of the cosmic ray energy spectrum due to its stable operation and efficient data collection. These measurements have revealed three significant spectral features: the ankle, shoulder, and cutoff. Analyzing these features is crucial for understanding the origin and propagation of UHECRs. In this talk, we will present the latest energy spectrum measured by the TA surface detectors and discuss the observed differences in the UHECR energy spectrum between the northern and southern skies.

Figures (4)

• Figure 1: Linearity in energy reconstruction. The ratios of reconstructed to thrown energy in the MC simulation (left), reconstructed energy measured by the SD and FD (middle), and the TA standard energy reconstruction to the CIC method (right), all as functions of energy, consistently demonstrate the linearity of the energy reconstruction.
• Figure 2: Energy spectrum from 16 years of TA SD observations. Black markers with error bars indicate the measured data, while the red line represents a fit using a thrice-broken power law model. This model incorporates three energy breakpoints ($E_{\mathrm{ankle}}$, $E_{\mathrm{shoulder}}$, and $E_{\mathrm{cutoff}}$) and four spectral slopes ($p_1$, $p_2$, $p_3$, and $p_4$). The resulting fit parameters are superimposed on the graph.
• Figure 3: Energy spectra measured by Auger and TA across their full apertures (top) and in the common sky with cuts applied to TA data (bottom). The blue open squares represent Auger data with a $+4.5\%$ energy shift, and the black solid squares represent TA data with a $-4.5\%$ shift. The red lines in the top panels show the same broken power-law model obtained from a simultaneous fit to both spectra, yielding a significance of $8\sigma$. The bottom-left and bottom-right panels show Auger and TA data, respectively, in the common sky region with cuts applied to TA. The red lines in the bottom panels represent the result of the simultaneous fit, which yields a significance of $1.8\sigma$.
• Figure 4: Comparison of Auger and TA exposures and spectra (a) Exposure distributions for the Auger vertical, Auger inclined, and TA spectra, highlighting the complementary coverage of the declination band. (b) Exposure ratio of TA to Auger as a function of declination, illustrating the mismatch in coverage. (c) Comparison of the Auger inclined spectrum and a weighted mix of the Auger vertical spectrum (up to $24.8^\circ$) and the TA spectrum ($24.8^\circ < \delta < 44.8^\circ$), showing agreement. (d) Comparison of the Auger inclined spectrum and the TA spectrum in the same band weighted by the exposure ratio, showing consistency between the two experiments in $24.8^\circ < \delta < 44.8^\circ$.