TITLE:
Astrophysical Sources of Ultra-High-Energy Cosmic Rays
AUTHORS:
Anaya Vachhani, Sananjay Biswas
KEYWORDS:
Ultra-High-Energy Cosmic Rays (UHECRs), Particle Acceleration, Astrophysical Sources, Cosmic-Ray Propagation, Multi-Messenger Astronomy
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
15,
2026
ABSTRACT: Ultra-high-energy cosmic rays (UHECRs) with energies greater than (1018) eV are the highest energy particles ever measured in nature; however, their astrophysical sources have not yet been identified. This work reviews existing data on UHECR sources based on the analysis of the energy spectrum, mass composition, and anisotropy of the arrival direction. Different acceleration mechanisms (diffusive shock acceleration, magnetic reconnection, unipolar induction) are compared with the Hillas condition and physical properties of the possible candidates (active galactic nuclei, gamma-ray bursts, starburst galaxies, compact objects). Special focus is paid to propagation effects, such as energy losses, the Greisen-Zatsepin-Kuzmin suppression, and deflections by magnetic fields. The review points out open issues regarding the composition, correlation between sources and arrival directions, modeling of the extragalactic magnetic field and how multi-messenger measurements of neutrinos and gamma rays are helping us reduce the number of viable UHECR sources. Finally, new generation facilities and their possibilities are discussed.