Proton Synchrotron Origin of the Very-high-energy Emission of GRB 190114C

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 similar to 1054.5 erg, ambient density similar to 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 approximate to 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.