LOFAR detectability of prompt low-frequency radio emission during gamma-ray burst X-ray flares

The prompt emission in long gamma-ray bursts arises from within relativistic outflows created during the collapse of massive stars, and the mechanism by which radiation is produced may be either magnetically- or matter-dominated. In this work we suggest an observational test of a magnetically-dominated Poynting flux model that predicts both gamma-ray and low-frequency radio pulses. A common feature among early light curves of long gamma-ray bursts are X-ray flares, which have been shown to arise from sites internal to the jet. Ascribing these events to the prompt emission, we take an established Swift XRT flare sample and apply a magnetically-dominated wind model to make predictions for the timing and flux density of corresponding radio pulses in the ~100-200 MHz band observable with radio facilities such as LOFAR. We find that 44 per cent of the X-ray flares studied would have had detectable radio emission under this model, for typical sensitivities reached using LOFAR's rapid response mode and assuming negligible absorption and scattering effects in the interstellar and intergalactic medium. We estimate the rate of Swift gamma-ray bursts displaying X-ray flares with detectable radio pulses, accessible to LOFAR, of order seven per year. We determine that LOFAR triggered observations can play a key role in establishing the long debated mechanism responsible for gamma-ray burst prompt emission.