Spectral Energy Distributions of Gamma‐Ray Bursts Energized by External Shocks

Sari, Piran, and Narayan have derived analytic formulas to model the spectrafrom gamma-ray burst blast waves that are energized by sweeping up materialfrom the surrounding medium. We extend these expressions to apply to generalradiative regimes and to include the effects of synchrotron self-absorption.Electron energy losses due to the synchrotron self-Compton process are alsotreated in a very approximate way. The calculated spectra are compared withdetailed numerical simulation results. We find that the spectral and temporalbreaks from the detailed numerical simulation are much smoother than theanalytic formulas imply, and that the discrepancies between the analytic andnumerical results are greatest near the breaks and endpoints of the synchrotronspectra. The expressions are most accurate (within a factor of ~ 3) in theoptical/X-ray regime during the afterglow phase, and are more accurate whenepsilon_e, the fraction of swept-up particle energy that is transferred to theelectrons, is <~ 0.1. The analytic results provide at best order-of-magnitudeaccuracy in the self-absorbed radio/infrared regime, and give poor fits to theself-Compton spectra due to complications from Klein-Nishina effects andphoton-photon opacity.Comment: 16 pages, 7 figures, ApJ, in press, 537, July 1, 2000. Minor changes in response to referee report, corrected figure