A 450-day light curve of the radio afterglow of GRB 970508: Fireball calorimetry

Abstract

We report on the results of an extensive monitoring campaign of the radio afterglow of GRB 970508, lasting 450 days after the burst. The spectral and temporal radio behavior indicate that the fireball has undergone a transition to sub-relativistic expansion at t~100 days. This allows us to perform "calorimetry" of the explosion. The derived total energy, ~5\times 10^{50} erg, is well below the ~5\times 10^{51} erg inferred under the assumption of spherical symmetry from gamma-ray and early afterglow observations. A natural consequence of this result, which can also account for deviations at t<100 days from the spherical relativistic fireball model predictions, is that the fireball was initially a wide-angle jet of opening angle ~30 degrees. Our analysis also allows to determine the energy fractions carried by electrons and magnetic field, and the density of ambient medium surrounding the fireball. We find that during the sub-relativistic expansion electrons and magnetic field are close to equipartition, and that the density of the ambient medium is ~1/cm^3. The inferred density rules out the possibility that the fireball expands into a strongly non-uniform medium, as would be expected, e.g., in the case of a massive star progenitor.