The radio-to-X-Ray spectrum of GRB 970508 on 1997 May 21.0 UT

We have reconstructed the spectrum of the afterglow of GRB 970508 on 1997 May 21.0 UT (12.1 days after the gamma-ray burst) on the basis of observations spanning the X-ray-to-radio range. The low-frequency power-law index of the spectrum, alpha =0.44+/-0.07 ( F_nu~ nu ^alpha ), is in agreement with the expected value alpha =1/3 for optically thin synchrotron radiation. The 1.4 GHz emission is self-absorbed. We infer constraints on the break frequencies nu c and nu m on 1997 May 21.0 UT from a spectral transition from F_nu~ nu ^{-0.6} to F_nu~ nu ^{-1.1} in the optical passband around 1.4 days. A model of an adiabatically expanding blast wave emitting synchrotron radiation, in which a significant fraction of the electrons cool rapidly, provides a successful and consistent description of the afterglow observations over nine decades in frequency, ranging in time from trigger until several months later.