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Electron Acceleration in Relativistic Gamma-Ray Burst Shocks

The shock model of gamma-ray bursts (GRBs) contains two equipartition parameters: the magnetic energy density and the kinetic energy density of the electrons relative to the total energy density of the shock, ϵB and ϵe, respectively. These are free parameters within the model. Whereas the Weibel shock theory and numerical simulations fix ϵB at the level of a few times 10-3 to 10-4, no understanding of ϵe exists so far. Here we demonstrate that it inevitably follows from the theory that ϵe ≃ 1/2. The GRB afterglow data fully agree with this theoretical prediction. Our result explains why the electrons are close to equipartition in GRBs. The ϵe-ϵB relation can potentially be used to reduce the number of free parameters in afterglow models.