Measurement of the ultra-high-energy cosmic-ray energy spectrum with the Telescope Array surface detector using a Bayesian forward-folding approach

Kozo Fujisue^1*, Anatoli Fedynitch¹, Anton Prosekin¹

¹Institute of Physics, Academia Sinica, Taipei, Taiwan

* Presenter:Kozo Fujisue, email:kkfujisue@gmail.com

The measurement of the ultra-high-energy cosmic-ray (UHECR) energy spectrum provides key insights into the acceleration mechanisms and propagation of the most energetic particles in the Universe. However, discrepancies have been reported between the spectra measured by the Telescope Array (TA) experiment and the Pierre Auger Observatory (Auger) at the highest energies. These differences may reflect genuine variations in the distribution of cosmic-ray sources due to different sky exposures, or they may arise from systematic uncertainties in the respective experiments. In particular, while TA has reported indications of anisotropy in the energy spectrum, Auger has not observed significant anisotropic features. A detailed comparison that accounts for systematic effects is therefore essential for a unified understanding of UHECRs across the full sky.
In this study, we develop a new analysis framework for the TA surface detector (SD) array that combines a forward-folding approach with Bayesian inference using Markov Chain Monte Carlo (MCMC) techniques. This method enables statistically consistent estimation of the UHECR flux and its uncertainties. We discuss the impact of systematic factors—including spectral shape and mass composition models—on the inferred energy spectrum, and outline prospects for further extensions of this approach.

Keywords: Ultra-high-energy cosmic ray, Telescope Array, Cosmic ray, Energy spectrum