UHECR acceleration at GRB internal shocks

Recent results from the Pierre Auger Observatory suggest that nuclei heavier than protons might be present in significant amounts among ultrahigh-energy cosmic rays (UHECRs). It is therefore interesting to investigate the acceleration both protons and nuclei in relativistic jets. We calculate the acceleration of a mixed composition of cosmic rays at Gamma-ray burst (GRB) internal shocks, taking into account the relevant energy loss processes. 3D trajectories during the relativistic Fermi cycles are simulated following previous works by Niemiec & Ostrowski. We use the internal shock model of Daigne & Mochkovitch to derive the evolution of the relevant physical quantities (magnetic fields, baryon and photon densities, shock velocity). We consider different phenomenological hypotheses about the sharing of the dissipated energy between accelerated cosmic rays, electrons and the magnetic field. For various choices of the parameters, we calculate the spectrum of cosmic rays escaping from the GRB environment as well as secondary particles produced either during the acceleration or extragalactic propagation of UHECRs. Only models where (i) the prompt emission represents only a small fraction of the energy dissipated at internal shocks and (ii) most of this dissipated energy is communicated to cosmic rays, are able to reproduce the magnitude of the UHECR flux observed on Earth. For these models, however, the observed shape of the UHECR spectrum can be well reproduced above the ankle, with an evolution of the composition compatible with the trend suggested by Auger, and associated diffuse fluxes of secondary particles which do not violate current observational limits.