A 450 Day Light Curve of the Radio Afterglow of GRB 970508: Fireball Calorimetry

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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 subrelativistic expansion at t ~ 100 days. This allows us to perform "calorimetry" of the explosion. The derived total energy, E0 ~ 5 × 1050 ergs, is well below the ~5 × 1051 ergs 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°. Our analysis also allows determination of the energy fractions carried by the electrons and magnetic field and the density of the ambient medium surrounding the fireball. We find that during the subrelativistic expansion, the electrons and magnetic field are close to equipartition and the density of the ambient medium is ~1 cm -3. The inferred density rules out the possibility that the fireball expands into a strongly nonuniform medium, as would be expected, e.g., in the case of a massive star progenitor.