Time-resolved spectra of six short gamma-ray bursts (sGRBs), measured by the {em Swift} telescope, are used to estimate the parameters of a plerion-like model of the X-ray afterglow. The unshrouded, optically thin component of the afterglow is modelled as emanating from an expanding bubble of relativistic, shock-accelerated electrons fuelled by a central object. The electrons are injected with a power-law distribution and cool mainly by synchrotron losses. We compute posteriors for model parameters describing the central engine (e.g. spin frequency at birth, magnetic field strength) and shock acceleration (e.g. power-law index, minimum injection energy). It is found that the central engine is compatible with a millisecond magnetar, and the shock physics is compatible with what occurs in Galactic supernova remnants, assuming standard magnetic field models for the magnetar wind. Separately, we allow the magnetic field to vary arbitrarily and infer that it is roughly constant and lower in magnitude than the wind-borne extension of the inferred magnetar field. This may be due to the expansion history of the bubble, or the magnetization of the circumstellar environment of the sGRB progenitor.
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