High-energy emission from the prompt gamma-ray burst

We study the synchrotron and synchrotron self-Compton (SSC) emission from internal shocks that are responsible for the prompt gamma-ray emission in gamma-ray bursts (GRBs) and consider the relation between these two components, taking into account the high-energy cutoff due to pair production and Thomson scattering. We find that in order for the peak energy of the synchrotron to be E_p ∼ 300 keV with a variability time t_v ≳ 1 ms, a Lorentz factor of Γ ≲ 200 is needed, implying no high-energy emission above ∼30 MeV and the synchrotron component dominating at all energies. If we want both E_p ∼ 300 keV and prompt high-energy emission up to ∼2 GeV, as detected by EGRET for GRB 940217, we need Γ ∼ 600 and t_v ∼ 0.1 ms, which might be resolved by Super Agile. If such prompt high-energy emission is common in GRBs, as may be tested by the Gamma-Ray Large Area Space Telescope (GLAST), then for t_v ≳ 1 ms, we need Γ ≳ 350, which implies E_p ≲ 100 keV. Therefore, if X-ray flashes are GRBs with high values of t_v and Γ, they should produce ≳ 1 GeV emission. For an electron power-law index p > 2, the SSC component dominates the emission above ∼100 MeV. Future observations by GLAST may help determine the value of p and whether the high-energy emission is consistent with a single power law (implying that one component, the synchrotron, is dominant) or has a break where the νF _ν slope turns from negative to positive, which implies that the SSC component becomes dominant above ∼100 MeV. The high-energy emission is expected to show similar variability and time structure to that of the soft gamma-ray emission. Finally, we find that in order to see delayed high-energy emission from the prompt GRB due to pair production with the cosmic IR background, extremely small intergalactic magnetic fields (≲ 10 ^-22 G) are required.