The efficiency of electron acceleration in collisionless shocks and gamma-ray burst energetics

Afterglow observations are commonly used to determine the parameters of GRB explosions, the energy E, surrounding density n, postshock magnetic field equipartition fraction ε_B, and electron equipartition fraction ε_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 that undergo acceleration is f ≈ 1. We show that the value of f cannot be determined by current observations, since currently testable model predictions for a parameter choice {E′ = E/f, n′ = n/f, ε′_B =f ε_B, ε′_e =f ε_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 subrelativistic shocks and plausibly suggest that f ∼ 1, quite unlike the situation in the Crab Nebula. However, values m_e/m_p ≤ f ≪ 1 cannot 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.