The Acceleration of Ultra--High-Energy Cosmic Rays in Gamma-Ray Bursts

Ultra-high-energy cosmic rays (UHECRs) are roughly isotropic and attain very large energies, E ≳ 3 × 10²⁰ eV. Conventional models fail to explain both facts. I show here that acceleration of UHECRs in gamma-ray bursts (GRBs) satisfies both observational constraints. Using the Mészáros & Rees model (see their recent work) of GRBs as due to hyperrelativistic shocks, I show that the highest energies that can be attained thusly are E ≌ 10²⁰ θ^-5/3/ ^{n₁5/6 eV, explaining the energy of the Bird et al. event (described in their recent work) even without beaming. The traditional photopion catastrophe affecting UHECR acceleration in active galactic nuclei is circumvented. An order of magnitude estimate shows that the total energy flux of UHECRs at Earth is also correctly reproduced. A test of the model based upon the UHECRs' distribution upon the plane of the sky is briefly discussed.}