Electron Acceleration in Relativistic Gamma-Ray Burst Shocks

The shock model of gamma-ray bursts (GRBs) contains two equipartitionparameters: the magnetic energy density and the kinetic energy density of theelectrons relative to the total energy density of the shock, "epsilon_B" and"epsilon_e", respectively. These are free parameters within the model. Whereasthe Weibel shock theory and numerical simulations fix "epsilon_B" at the levelof ~few times(10^{-3}...10^{-4}), no understanding of "epsilon_e" exists sofar. Here we demonstrate that it inevitably follows from the theory that"epsilon_e"~(epsilon_B)^(1/2). The GRB afteglow data fully agree with thistheoretical prediction. Our result explains why the electrons are close toequipartition in GRBs. The "epsilon_e"-"epsilon_B" relation can potentially beused to reduce the number of free parameters in afterglow models.Comment: 4 pages, 2 figs; ApJL accepte