Synchrotron and SSC Emission and the Blast-Wave Model of Gamma-Ray Bursts

We investigate the dynamics and radiation from a relativistic blast-wave which decelerates as it sweeps up ambient matter. The bulk kinetic energy of the blast-wave shell is converted into internal energy by the process of accreting external matter. If it takes the form of non-thermal electrons and magnetic fields, then this internal energy will be emitted as synchrotron and synchrotron self-Compton radiation. We perform analytic and numerical calculations for the deceleration and radiative processes and present time-resolved spectra throughout the evolution of the blast-wave. We also examine the dependence of the burst spectra and light curves on various parameters describing the magnetic field and non-thermal electron distributions. We find that for bursts such as GRB 910503, GRB 910601 and GRB 910814, the spectral shapes of the prompt gammaray emission at the peaks in νFν strongly constrain the magnetic fields in these bursts to be well below (∼< 10 −2) the equipartition values. These calculations are also considered in the context of the afterglow emission from the recently detected gamma-ray burst counterparts.