Gamma-Ray Burst Afterglows as Probes of Environment and Blastwave Physics II: The Distribution of p and Structure of the Circumburst Medium

We constrain blastwave parameters and the circumburst media of a subsample of BeppoSAX Gamma-Ray Bursts. 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 behaviour. Assuming the fireball model, we can find a mean value of p for the sample as a whole of 2.035. 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 3sigma level or greater. 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 (wind-like). We find five GRBs for which k can be well constrained, and in four of these cases the circumburst medium is clearly wind-like. The fifth source has a value of 0 less than or equal to k less than or equal to 1, consistent with a homogeneous circumburst medium.