Temporal behaviour of the thermal model of hard X-ray bursts

A simple, analytic model is presented of a hot, thermal hard X-ray source, continuously heated, bounded by ion-acoustic conduction fronts, and expanding in a loop. The model is used to investigate the assumption that the 'rise time' of the X-ray emission is approximately given by the loop length divided by the ion-sound speed appropriate to the peak temperature. It is found that a freely-expanding source does not behave in this way; instead, the rise time is symptomatic of the timescale for primary energy release. If the energy release rate does not fall significantly before the source fills the loop, however, then this assumption may be approximately satisfied, if a condition on the temporal behavior of the energy release is satisfied. Finally, some remarks on the relative timing of temperature and emission measure peaks are made, and possible further applications mentioned of the results presented herein.