Gamma‐Ray Burst Afterglows as Probes of Environment and Blast Wave Physics. II. The Distribution ofpand Structure of the Circumburst Medium

We constrain blast wave parameters and the circumburst media of a subsample of 10 BeppoSAX gamma-ray bursts (GRBs). For this sample we derive the values of the injected electron energy distribution index, p , and the density structure index of the circumburst medium, k , from simultaneous spectral fits to their X-ray, optical, and NIR afterglow data. The spectral fits have been done in count space and include the effects of metallicity, and are compared with the previously reported optical and X-ray temporal behavior. Using the blast wave model and some assumptions which include on-axis viewing and standard jet structure, constant blast wave energy, and no evolution of the microphysical parameters, we find a mean value of p for the sample as a whole of 2.04 + 0.02 −0.03 . A statistical analysis of the distribution demonstrates that the p -values in this sample are inconsistent with a single universal value for p at the 3 σ level or greater, which has significant implications for particle acceleration models. This approach provides us with a measured distribution of circumburst density structures rather than considering only the cases of k = 0 (homogeneous) and k = 2 (windlike). We find five GRBs for which k can be well constrained, and in four of these cases the circumburst medium is clearly windlike. The fifth source has a value of 0 ⩽ k⩽ 1, consistent with a homogeneous circumburst medium.