Physical Constraints on GRB 970508 from Its Radio Afterglow

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Abstract
Model-independent lower limits on the energy stored in the electrons emitting the radio afterglow from GRB 970508 are derived. These limits arise from the optically thick synchrotron source function and the synchrotron cooling timescale. The primary free parameters for these limits are the dimensionless synchrotron frequency, the bulk Lorentz factor Γ, and the source diameter θ. When one assumes θ is related to Γ alone, one finds that the energy stored in electrons is more than 1051 ergs for a 3 μas source size and more than 1049 ergs for a 6 μas source size. These limits are inconsistent with the energy storage expected for a relativistic shell from a destructive solar mass source.