Bottom-up Acceleration of Ultra-High-Energy Cosmic Rays in the Jets of Active Galactic Nuclei

Abstract: It has been proposed that Ultra-High-Energy Cosmic Rays (UHECRs) up to $10^{20}$eV could be produced in the relativistic jets of powerful Active Galactic Nuclei (AGNs) via a one-shot reacceleration of lower-energy CRs produced in supernova remnants (the $\textit{espresso}$ mechanism). We test this theory by propagating particles in realistic 3D magneto-hydrodynamic simulations of ultra-relativistic jets and find that about $10\%$ of the CRs entering the jet are boosted by at least a factor of $\sim\Gamma^2$ in energy, where $\Gamma$ is the jet's effective Lorentz factor, in agreement with the analytical expectations. Furthermore, about $0.1\%$ of the CRs undergo two or more shots and achieve boosts well in excess of $\Gamma^2$. Particles are typically accelerated up to the Hillas limit, suggesting that the $\textit{espresso}$ mechanism may promote galactic-like CRs to UHECRs even in AGN jets with moderate Lorentz factors, and not in powerful blazars only. Finally, we find that the sign of the toroidal magnetic field in the jet and in the cocoon controls the angular distribution of the reaccelerated particles, leading to a UHECR emission that may be either quasi-isotropic or beamed along the jet axis. These findings strongly support the idea that $\textit{espresso}$ acceleration in AGN jets can account for the UHECR spectra, chemical composition, and arrival directions measured by Auger and Telescope Array.