Very Strong TeV Emission as $\gamma$-Ray Burst Afterglows

Gamma-ray bursts (GRBs) and following afterglows are considered to be produced by dissipation of kinetic energy of a relativistic fireball and radiation process is widely believed as synchrotron radiation or inverse Compton scattering of electrons. We argue that the transfer of kinetic energy of ejecta into electrons may be inefficient process and hence the total energy released by a GRB event is much larger than that emitted in soft gamma-rays, by a factor of \sim (m_p/m_e). We show that, in this case, very strong emission of TeV gamma-rays is possible due to synchrotron radiation of protons accelerated up to \sim 10^{21} eV, which are trapped in the magnetic field of afterglow shock and radiate their energy on an observational time scale of \sim day. This suggests a possibility that GRBs are most energetic in TeV range and such TeV gamma-rays may be detectable from GRBs even at cosmological distances, i.e., z gives a quantitative explanation for the famous long-duration GeV photons detected from GRB940217. If TeV gamma-ray emission which is much more energetic than GRB photons is detected, it provides a strong evidence for acceleration of protons up to \sim 10^{21} eV.