Persistent Counterparts to GRBS

The recent discovery of persistent GRB counterparts at lower frequencies permits several important conclusions to be drawn. The spectrum of GRB970508 is not consistent with an external shock origin for both the prompt GRB and the persistent emission, suggesting that at least the prompt radiation is produced by internal shocks. Comparisons among three GRB with counterparts (or upper limits on them) establishes that GRB are not all scaled versions of similar events. The angular size inferred from the apparent observation of self-absorption in the radio spectrum of GRB970508 a week later implies that its expansion had slowed to semi-relativistic speeds. This permits a remarkably low upper bound to be placed on its residual energy, suggesting either that radiation has been $> 99.7$ efficient or that the initial outflow was strongly collimated. Observations of self-absorbed radio emission from future GRB may permit direct measurement of their expansion and determination of their parameters and energetics. We estimate initial Lorentz factors for GRB970228 and GRB970508 $\gamma_0 \sim 100$, and present a solution for the evolution of a blast wave with instantaneous cooling. The visible flux is predicted to rise initially as a power of $t$ slightly less than unity, in agreement with observations of GRB970508.