The electron energy distribution index, p, is a fundamental parameter of the synchrotron emission from a range of astronomical sources. Here we examine one such source of synchrotron emission, Gamma-Ray Burst afterglows observed by the Swift satellite. Within the framework of the blast wave model, we examine the constraints placed on the distribution of p by the observed X-ray spectral indices and parametrise the distribution. We find that the observed distribution of spectral indices are inconsistent with an underlying distribution of p composed of a single discrete value but consistent with a Gaussian distribution centred at p = 2.36 and having a width of 0.59. Furthermore, accepting that the underlying distribution is a Gaussian, we find the majority (>94%) of GRB afterglows in our sample have cooling break frequencies less than the X-ray frequency.
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