Espresso Acceleration of Ultra-High-Energy Cosmic Rays up to the Hillas Limit in Relativistic MHD Jets

Espresso is a novel acceleration model for Ultra-High-Energy Cosmic Rays (UHECRs), where lower-energy CRs produced in supernova remnants experience a one-shot reacceleration in the relativistic jets of powerful Active Galactic Nuclei (AGNs) to reach energies up to ${10}^{20}$ eV. To test the espresso framework, we follow UHECR acceleration bottom-up from injection to the highest energies by propagating 100,000 particles in realistic 3D magneto-hydrodynamic (MHD) simulations of ultra-relativistic jets. We find that simulations agree well with analytical expectations in terms of trajectories of individual particles. We also quantify that $\sim 10\mathrm{\%}$ of CR seeds gain a factor of $\sim {\mathrm{\Gamma }}^2$ in energy, where $\mathrm{\Gamma }$ is the jet’s effective Lorentz factor; moreover, about $0.1\mathrm{\%}$ of the particles undergo two or more shots to achieve gains in excess of ${\mathrm{\Gamma }}^2$. Particles are generally accelerated up to the jet’s Hillas limit, indicating that the espresso mechanism should boost galactic CRs to UHECRs in typical AGN jets. Finally, we discuss how espresso acceleration in AGN jets is consistent with UHECR spectra and chemical composition, and also with the UHECR arrival directions measured by Auger and Telescope Array.