Late-time X-ray afterglows of GRBs: Implications for particle acceleration at relativistic shocks

Particle-in-cell (PIC) numerical simulations are currently among the most advanced tools to investigate particle acceleration at relativistic shocks. Still, they come with limitations imposed by finite computing power, whose impact is not straightforward to evaluate a priori. Observational features are hence required as verification. energy electrons accelerated at external shocks, provides a testbed for such predictions. Current numerical studies suggest that in GRB afterglows the maximum synchrotron photon energy, which corresponds to the limit of electron acceleration, may fall within the $\sim$ 0.1--10 keV X-ray energy band at late times, $t\gtrsim 10^6 - 10^7$ s. To test this prediction, we analyzed the X-ray spectra of six GRBs with \emph{Swift}/XRT detections beyond $10^7$ s: our analysis reveals no clear evidence of a spectral cutoff. Using a model that accounts for the effect of the finite opening angle of the shock on the observed maximum synchrotron photon energy, we show that these observations are incompatible with PIC simulation predictions, unless one or more physical afterglow parameters attain values at odds with those typically inferred from afterglow modeling (small radiative efficiency, low ambient density, large equipartition fraction $ε_{\rm B}$ of the magnetic field). These findings challenge existing numerical simulation results and imply a more efficient acceleration of electrons to high-energies than seen in PIC simulations, with important implications for our understanding of particle acceleration in relativistic shocks.