On the acceleration of Ultra High Energy Cosmic Rays in Gamma Ray Bursts

Abstract

UHECRs are roughly isotropic and attain very large energies, $E \gtrsim 3\times 10^{20} \; eV$. Conventional models fail to explain both facts. I show here that acceleration of UHECRs in GRBs satisfies both observational constraints. Using M\'esz\'aros and Rees' (1994) model of GRBs as due to hyperrelativistic shocks, I show that the highest energies that can be attained thusly are $E\simeq 10^{20}\;\theta^{-5/3} n_1^{-5/6}\; eV$, explaining the energy of the Bird \etal\/ (1995) event even without beaming. The traditional photopion catastrophe affecting UHECR acceleration in AGNs is circumvented. An order of magnitude estimate shows that the total energy flux of UHECRs at the Earth is also correctly reproduced. A test of the model based upon the UHECRs' distribution upon the plane of the sky is briefly discussed.