Radio and Optical Emission, Spectral Shapes and Breaks in GRB

Relativistic blast wave models predict the spectrum of the emitted synchrotron radiation. The electrons in the shocked region are heated to a Wien distribution whose ``temperature'' is $1/3$ of the mean electron energy. This energy scale determines a characteristic (break) frequency of synchrotron radiation. At much lower frequencies a spectrum $F_nu \propto \nu^{1/3}$ is predicted independently of details of the emitting region. This is consistent with the observed soft X-ray spectra of GRB. It implies low visible and radio intensities, unless there are collective emission processes.