| Summary: | The electron energy distribution index, p, is a fundamental parameter of the process by which electrons at shock fronts are accelerated to relativistic speeds and by which they radiate, via synchrotron emission. This acceleration process is applicable to a myriad of astronomical jet sources such as AGN, X-ray binaries and gamma-ray bursts (GRBs), as well as to particle acceleration in the solar wind and supernovae, and the acceleration of cosmic rays. The accurate measurement of the distribution of p is of fundamental importance to differentiate between the possible theories of electron acceleration at any relativistic shock front; there is division as to whether p has a universal value or whether it has a distribution, and if so, what that distribution is.Here one such source of synchrotron emission is examined: the blast waves of GRB afterglows observed by the Swift satellite. Within the framework of the GRB blast wave model, the constraints placed on the distribution of p by the observed X-ray spectral and temporal indices are examined and the distribution parametrized. The results show that the observed distribution of spectral indices is inconsistent with an underlying distribution of p composed of a single discrete value but consistent with a Gaussian distribution centred at p = 2.4 and having a width of 0.6. This finding disagrees with theoretical work that argues for a single, universal value of p, but also demonstrates that the width of the distribution is not as wide as has been suggested by some authors.
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