A Simulation Study of Ultra-relativistic Jets -- III. Particle Acceleration at FR-II Jets

We study the acceleration of ultra-high-energy cosmic rays (UHECRs) at FR-II radio galaxies by performing Monte Carlo simulations for the transport, scattering, and energy change of the CR particles injected into the time-evolving jet flows that are realized through relativistic hydrodynamic (RHD) simulations. Toward that end, we adopt physically motivated models for the magnetic field and particle scattering. By identifying the primary acceleration process among diffusive shock acceleration (DSA), turbulent shear acceleration (TSA), and relativistic shear acceleration (RSA), we find that CRs of $E\lesssim1$ EeV gain energy mainly through DSA in the jet-spine flow and the backflow containing many shocks and turbulence. After they attain $E\gtrsim$ a few EeV, CRs are energized mostly via RSA at the jet-backflow interface, reaching energies well above $10^{20}$ eV. TSA makes a relatively minor contribution. The time-asymptotic energy spectrum of escaping particles is primarily governed by the jet power, shifting to higher energies at more powerful jets. The UHECR spectrum fits well to the double-power-law form, whose break energy, $E_{\rm break}$, corresponds to the size-limited maximum energy. It is close to $d\mathcal{N}/dE\propto E^{-0.5}$ below $E_{\rm break}$, while it follows $d\mathcal{N}/dE\propto E^{-2.6}$ above $E_{\rm break}$, decreasing more gradually than the exponential. The power-law slope of the high-energy end is determined by the energy boosts via non-gradual shear acceleration across the jet-backflow interface and the confinement by the elongated cocoon. We conclude that giant radio galaxies could be major contributors to the observed UHECRs.