The efficiency of electron acceleration in collisionless shocks and GRB energetics

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.