Spectral energy distributions of gamma-ray bursts energized by external shocks

Sari, Piran, & Narayan have derived analytic formulae to model the spectra from gamma-ray burst blast waves that are energized by sweeping up material from the surrounding medium. We extend these expressions to apply to gener al radiative regimes and to include the effects of synchrotron self-absorpt ion. Electron energy losses due to the synchrotron self-Compton process are also treated in a very approximate way. The calculated spectra are compare d with detailed numerical simulation results. We find that the spectral and temporal breaks from the detailed numerical simulation are much smoother t han the analytic formulae imply and that the discrepancies between the anal ytic and numerical results are greatest near the breaks and endpoints of th e synchrotron spectra. The expressions are most accurate (within a factor o f similar to 3) in the optical/X-ray regime during the afterglow phase and are more accurate when epsilon(e), the fraction of swept-up particle energy that is transferred to the electrons, is less than or similar to 0.1. The analytic results provide at best order-of-magnitude accuracy in the self-ab sorbed radio/infrared regime and give poor fits to the self-Compton spectra because of complications from Klein-Nishina effects and photon-photon opac ity.