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

¹ Department of Physics, National University of Athens, Panepistimiopolis Zografos 15783, Greece
² Institut für Physik, Universität Dortmund, 44221 Dortmund, Germany
³ Erlangen Center for Astroparticle Physics, Universität Erlangen-Nürnberg, Germany e-mail: athina.meli@physik.uni-erlangen.de
⁴ Institutionen för Fysik, Göteborgs Universitet, 41296 Göteborg, Sweden e-mail: julia.becker@physics.gu.se
⁵ High Energy Physics Group, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BZ, UK e-mail: j.quenby@imperial.ac.uk

Received: 15 September 2007
Accepted: 1 October 2008

Abstract

Aims. 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 cosmic ray (CR) particle acceleration by relativistic shocks, in particular concerning the dependence on bulk Lorentz factor and the angle between the magnetic field and the shock flow. The contribution to the observed diffuse CR spectrum provided by the accelerated particles is discussed.

Methods. For the first time, Monte Carlo simulations for super- and subluminal shocks are extended to boost factors up to Γ = 1000 and systematically compared. The source spectra derived are translated into the expected diffuse proton flux from astrophysical sources by folding the spectra with the spatial distribution of active galactic nuclei (AGN) and gamma ray bursts (GRBs). Results of these predictions are compared with UHECR data.

Results. While superluminal shocks are shown to be inefficient at providing acceleration to the highest energies (E > 10^18.5 eV), subluminal shocks may provide particles up to 10²¹ eV, limited only by the Hillas-criterion. In the subluminal case, we find that mildly-relativistic shocks, thought to occur in jets of AGN (Γ ~ 10-30), yield energy spectra of dN/dE ~ E^-2. Highly relativistic shocks expected in GRBs (100 < Γ < 1000), on the other hand, produce spectra as flat as ~ E^-1.0 above 10^9.5 GeV. The model results are compared with the measured flux of CRs at the highest energies and it is shown that, while AGN spectra provide an excellent fit, GRB spectra are too flat to explain the observed flux. The first evidence of a correlation between the CR flux above 5.7 10¹⁰ GeV and the distribution of AGN provided by Auger are explained by our model. Although GRBs are excluded as the principle origin of UHECRs, neutrino production is expected in these sources either in mildly or highly relativistic shocks. In particular, superluminal shocks in GRBs may be observable via neutrino and photon fluxes, rather than as protons.