Implications of the radio afterglow from the $\gamma$-ray burst of May 8, 1997

Radio observations of the afterglow of the gamma-ray burst GRB970508 provide unique new constraints on afterglow models. The quenching of diffractive scintillation at 4 week delay provides the first direct estimate of source size and expansion rate. It implies an apparent size $R\sim10^{17}$cm and expansion at a speed comparable to that of light at 4 weeks delay, in agreement with the fireball model prediction $R=10^{17}(t/week)^{5/8}$cm. The radio flux and its dependence on time and frequency at 1--5 week delay are in agreement with the model and imply a fireball energy (assuming spherical symmetry) of order 10^{52}erg, consistent with the value inferred from observations at shorter delay. The observed radio behavior deviates from model predictions at delays larger than 5 weeks. This is expected, since at this delay the fireball is in transition from highly-relativistic to sub-relativistic expansion, with Lorentz factor \gamma