Spectra and Light Curves of Gamma-Ray Burst Afterglows

The recently discovered GRB afterglow is believed to be described reasonably well by synchrotron emission from a slowing down relativistic shell that collides with an external medium. To compare theoretical models with afterglow observations we calculate here the broad band 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. The light curve is constructed under two limiting models for the hydrodynamical evolution of the shock: fully adiabatic and fully radiative. We compare the results with observations of $\gamma$-ray burst afterglows.