We discuss the spectrum arising from synchrotron emission by fast cooling electrons, which are continually accelerated into relativistic thermal energies by a strong blast wave. The fast cooling spectrum was so far believed to consist of four power law segments divided by three break frequencies: . We show that emission from different depths behind the shock front, where the electrons had suffered a different degree of cooling, results in a new spectral slope and a new break frequency in the optically thick regime: , for and for . It is shown that different relative orderings of the break frequencies result in two additional cases for the shape of the spectrum: and . We discuss possible applications for GRBs and their afterglow, in the context of the internal-external shock model, and provide useful expressions for the various break frequencies and the flux density.
Fifth Huntsville Gamma Ray Burst Symposium
Hunsville, Alabama, USA
18-22 October, 1999