Implications of the Radio Afterglow from the Gamma‐Ray Burst of 1997 May 8

Radio observations of the afterglow of the gamma-ray burst GRB970508 provideunique new constraints on afterglow models. The quenching of diffractivescintillation at 4 week delay provides the first direct estimate of source sizeand expansion rate. It implies an apparent size $R\sim10^{17}$cm and expansionat a speed comparable to that of light at 4 weeks delay, in agreement with thefireball model prediction $R=10^{17}(t/week)^{5/8}$cm. The radio flux and itsdependence on time and frequency at 1--5 week delay are in agreement with themodel and imply a fireball energy (assuming spherical symmetry) of order10^{52}erg, consistent with the value inferred from observations at shorterdelay. The observed radio behavior deviates from model predictions at delayslarger than 5 weeks. This is expected, since at this delay the fireball is intransition from highly-relativistic to sub-relativistic expansion, with Lorentzfactor \gamma<2. Deviation may be due to a change in the physical processesassociated with the shock wave as it becomes sub-relativistic (e.g. a decreasein the fraction of energy carried by magnetic field), or to the fireball beinga cone of opening angle $1/\gamma\sim0.5$. We predict the future behavior ofthe radio flux assuming that the latter interpretation is valid. Thesepredictions may be tested by radio observations in the frequency range0.1--10GHz on time scale of months.Comment: Submitted to ApJ (15 pages, LaTeX