The Implications of TeV-detected GRB Afterglows for Acceleration at Relativistic Shocks

Motivated by the detection of very-high-energy (VHE) gamma rays deep in the afterglow emission of a gamma-ray burst (GRB), we revisit predictions of the maximum energy to which electrons can be accelerated at a relativistic blast wave. Acceleration at the weakly magnetized forward shock of a blast wave can be limited by either the rapid damping of turbulence generated behind the shock, the effect of a large-scale ambient magnetic field, or radiation losses. Within the confines of a standard, single-zone, synchrotron self-Compton (SSC) model, we show that observations of GRB 190829A rule out a rapid damping of the downstream turbulence. Furthermore, simultaneous fits to the X-ray and TeV gamma-ray emission of this object are not possible unless the limit on acceleration imposed by the ambient magnetic field is comparable to or weaker than that imposed by radiation losses. This requires the dominant length scale of the turbulence behind the shock to be larger than that implied by particle-in-cell simulations. However, even then, Klein-Nishina effects prevent production of the hard VHE gamma-ray spectrum suggested by observations. Thus, TeV observations of GRB afterglows, though still very sparse, are already in tension with the SSC emission scenario.