Broadband modelling of short gamma-ray bursts with energy injection from magnetar spin-down and its implications for radio detectability

B. P. Gompertz, A. J. van der Horst, P. T. O'Brien, G. A. Wynn, K. Wiersema

Published 2014-11-20Version 1

The magnetar model has been proposed to explain the apparent energy injection in the X-ray light curves of short gamma-ray bursts (SGRBs), but its implications across the full broadband spectrum are not well explored. We investigate the broadband modelling of four SGRBs with evidence for energy injection in their X-ray light curves, applying a physically motivated model in which a newly-formed magnetar injects energy into a forward shock as it loses angular momentum along open field lines. By performing an order of magnitude search for the underlying physical parameters in the blast wave, we constrain the characteristic break frequencies of the synchrotron spectrum against their manifestations in the available multi-wavelength observations for each burst. The application of the magnetar energy injection profile restricts the succesful matches to a limited family of models that are self-consistent within the magnetic dipole spin-down framework. Because of this, we are able to produce synthetic light curves that describe how the radio signatures of these SGRBs ought to have looked at a variety of frequencies, given the restrictions imposed by the available data. We discuss the detectability of these signatures in the context of present day and near future radio telescopes. Our results show that previous observations were not deep enough to place meaningful constraints on the model, but that both ALMA and the upgraded VLA are now sensitive enough to detect the radio signature within two weeks of trigger in most SGRBs, assuming our sample is representative of the population as a whole. We also find that the upcoming Square Kilometer Array will be sensitive to depths greater than those of our lower limit predictions.