2023ApJ...955...70I

We consider here a proton-synchrotron model to explain the MAGIC observation of GRB 190114C afterglow in the energy band of 0.2-1 TeV, while the X-ray spectra are explained by electron-synchrotron emission. Given the uncertainty of the particle acceleration process, we consider several variations of the model, and show that they all match the data very well. We find that the values of the uncertain model parameters are reasonable: isotropic explosion energy ∼10^54.5 erg, ambient density ∼10-100 cm^–3, and the fraction of electrons/protons accelerated to a high-energy power law is of a few percent. All these values are directly derived from the observed teraelectronvolt and X-ray fluxes. The model also requires that protons be accelerated to observed energies as high as a few 10²⁰ eV. Further, assuming that the jet break takes place after 10⁶ s gives the beaming-corrected energy of the burst to be ≈10⁵³ erg, which is one to two orders of magnitude higher than usually inferred, because of the small fraction of electrons accelerated. Our modeling is consistent with both late time data at all bands, from optical to X-rays, and with numerical models of particle acceleration. Our results thus demonstrate the relevance of proton-synchrotron emission to the high-energy observations of gamma-ray bursts during their afterglow phase.