Particle acceleration at ultra-relativistic shocks

Gamma-ray burst afterglow spectra and UHECRs

¹ Astronomical Institute, Utrecht University, P.O. Box 80 000, 3508 TA Utrecht, Netherlands
² Max–Planck–Institut für Kernphysik, Postfach 10 39 80, 69029 Heidelberg, Germany

Send offprint request to: Y.A. Gallant

Received: 18 December 1998
Accepted: 26 January 1999

Abstract

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 , 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.