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Astron. Astrophys. Suppl. Ser. 138, 549-550

Particle acceleration at ultra-relativistic shocks

Gamma-ray burst afterglow spectra and UHECRs

Y.A. Gallant1 - A. Achterberg1 - J.G. Kirk2

Send offprint request: Y.A. Gallant

1 - Astronomical Institute, Utrecht University, P.O. Box 80000, 3508 TA Utrecht, Netherlands
2 - Max-Planck-Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany

Received December 18, 1998; accepted January 26, 1999


We consider particle acceleration of the Fermi type at the ultra-relativistic shock bounding an expanding relativistic fireball. We distinguish between the initial shock crossing cycle, in which particles can gain a large factor in energy, and subsequent crossing cycles, where the energy typically only doubles. We show that repeated shock crossings yield a power-law spectrum of accelerated particles with index $p \sim 2.2-2.3$, compatible with afterglow observations. We suggest that ultra-high-energy cosmic rays (UHECRs) might be produced by the initial boost in a relativistic fireball expanding into a pulsar wind bubble created by the progenitor system.

Key words: acceleration of particles -- relativity -- shock waves -- gamma-rays: bursts -- cosmic rays

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