The efficiency of electron acceleration in collisionless shocks and GRB energetics

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Abstract
Afterglow observations are commonly used to determine the parameters of GRB explosions, the energy E, surrounding density n, post-shock magnetic field equipartition fraction \epsilon_B and electron equipartition fraction \epsilon_e, under the frequently made assumption that the efficiency of electron "injection" into relativistic shock acceleration is high, i.e. that the fraction f of electrons which undergo acceleration is f~1. We show that the value of f can not be determined by current observations, since currently testable model predictions for a parameter choice {E'=E/f,n'=n/f,\epsilon'_B=f\epsilon_B,\epsilon'_e=f\epsilon_e} are independent of the value of f for m_e/m_p< f< 1. Current observations imply that the efficiency f is similar for highly relativistic and for sub relativistic shocks, and plausibly suggest that f~1, quite unlike the situation in the Crab Nebula. However, values m_e/m_p< f<< 1 can not be ruled out, implying a factor m_e/m_p uncertainty in determination of model parameters. We show that early, <10 hr, radio afterglow observations, which will be far more accessible in the SWIFT era, may provide constraints on f. Such observations will therefore provide a powerful diagnostic of GRB explosions and of the physics of particle acceleration in collisionless shocks.

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