Spectra and Light Curves of Gamma-Ray Burst Afterglows

The recently discovered gamma-ray burst afterglow is believed to be described reasonably well by synchrotron emission from a decelerating relativistic shell that collides with an external medium. To compare theoretical models with afterglow observations, we calculate here the broadband spectrum and corresponding light curve of synchrotron radiation from a power-law distribution of electrons in an expanding relativistic shock. Both the spectrum and the light curve consist of several power-law segments with related indices. The light curve is constructed under two limiting models for the hydrodynamic evolution of the shock: fully adiabatic and fully radiative. We give explicit relations between the spectral index and the temporal power-law index. Future observations should be able to distinguish between the possible behaviors and determine the type of solution.