%0 Journal Article %T The radio to X-ray spectrum of GRB 970508 on May 21.0 UT %A T. J. Galama %A R. A. M. J. Wijers %A M. Bremer %A P. J. Groot %A R. G. Strom %A C. Kouveliotou %A J. van Paradijs %J Physics %D 1998 %I arXiv %R 10.1086/311425 %X We have reconstructed the spectrum of the afterglow of GRB 970508, on May 21.0 UT (12.1 days after the GRB), on the basis of observations spanning the X-ray to radio range. The low-frequency power law index of the spectrum, $\alpha=0.44\pm0.07$ ($F_\nu\propto\nu^\alpha$), 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 frequecies $\nu_{c}$ and $\nu_{m}$ on May 21.0 UT from a spectral transition from $F_{\nu} \sim \nu^{-0.6}$ to $F_{\nu} \sim \nu^{-1.1}$ 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. %U http://arxiv.org/abs/astro-ph/9804191v1