Origin likelihood functions for extreme-energy cosmic rays

Abstract

Unlike neutrinos and photons arriving from extra-galactic sources, ultra-high energy cosmic rays (UHECRs) do not trace back to their origins due to propagation effects such as magnetic deflections and energy losses. For ankle energies, UHECRs can propagate for hundreds of megaparsecs with negligible energy losses but the directional information is lost after a few megaparsecs. On the other hand, at the highest energies the directions are kept for larger distances due to the increased rigidity but the interaction rates with the cosmic microwave background strongly suppress the cosmic rays within a few to tens of megaparsecs. Therefore, UHECRs with energies $E > 10^{20}$ eV (extreme-energy cosmic rays (ExECRs)) such as the Amaterasu event recently reported by Telescope Array, are of particular interest to identify the sources within our galactic neighborhood. However, photonuclear interactions are stochastic in nature and produce changes in the nuclear species emitted, which makes it difficult the task of estimating the likelihood distribution of its origin. This work discusses a novel procedure to estimate the likelihood of the origin for extreme-energy cosmic rays based on probability distributions for UHECR stochastic interactions. The method is applied to the Amaterasu event and compared to recently published works which employ Monte Carlo codes (e.g. CRPropa) in their analysis. The advantages of the method presented here are demonstrated by the increased resolution and the ease of computation unlike other approaches employed so far. The results presented indicate that the localization of the origin of extreme energy cosmic rays could be possible in some cases without knowledge of the original composition.