On the origin of ultra high energy cosmic rays: Subluminal and superluminal relativistic shocks

Abstract

The flux of Ultra High Energy Cosmic Rays (UHECRs) at $E>10^{18.5}$ eV is believed to arise in plasma shock environments in extragalactic sources. In this paper, we present a systematic study of particle acceleration by relativistic shocks, in particular concerning the dependence on bulk Lorentz factor and the angle between the magnetic field and the shockflow. For the first time, simulation results of super- and subluminal shocks with boost factors up to $\Gamma=1000$ are investigated and compared systematically. While superluminal shocks are shown to be inefficient at the highest energies ($E>10^{18.5}$ eV), subluminal shocks may provide particles up to $10^{21}$ eV, limited only by the Hillas-criterion. For the subluminal case, we find that mildly relativistic shocks, thought to occur in jets of Active Galactic Nuclei (AGN, $\Gamma\sim 10-30$) yield energy spectra of $dN/dE\sim E^{-2}$. Highly relativistic shocks expected in Gamma Ray Bursts (GRBs, $100<\Gamma<1000$), on the other hand, have spectra as flat as $E^{-1.5}$. The model results are compared to the measured flux of Cosmic Rays at the highest energies and it is shown that, while AGN spectra are well-suited, GRB spectra are too flat to explain the observed flux. The first evidence of a correlation between the Cosmic Ray flux above $5.7\cdot 10^{10}$ GeV and the distribution of AGN by Auger are explained by the model. Neutrino production is expected in GRBs, either in mildly or highly relativistic shocks and although these sources are excluded as the principle origin of UHECRs, superluminal shocks in particular may be observable via neutrino and photon fluxes, rather than as protons.