2025MNRAS.544...53H

Relativistic jets generated in gamma-ray bursts (GRBs) produce luminous transient events, yet the fundamentals of jet composition and radiation mechanisms remain unclear. One means of identifying a magnetically dominated outflow would be detection of prompt, coherent radio emission at low frequencies, and we are able to search for this using the LOw Frequency ARray (LOFAR) coupled with modelling of high-energy pulses detected by the Neil Gehrels Swift Observatory (Swift). We present the rapid response mode follow-up LOFAR observations of four long GRBs, each beginning within a few hundred seconds of the initial Swift-Burst Alert Telescope (BAT) trigger. We interpreted our findings under the framework of a magnetic wind model, predicting coherent radio emission analogous to prompt emission pulses. Using 60 and 180 s time-sliced imaging at 120-168 MHz, we obtain upper limits on radio pulse emission, finding no significant signals. In the case of GRB 200925B, we observed a small increase of radio flux seen at ${\sim}$60-360 s post-burst. In this model, this could represent the radio emission related to the Swift-BAT pulses, for a redshift of $z=1.8$, however, with a low signal-to-noise ratio of ${\sim} 2$, it is not deemed significant enough to confirm coincident prompt radio and gamma-ray emission. Instead, we can constrain the $\epsilon _{B}$ parameter, deriving upper limits of $\epsilon _{B} < 4.2 \times 10^{-4}$ for GRB 200925B. In GRB 240414A, with a reported redshift of $z=1.833$, we constrain $\epsilon _{B} < 2.8 \times 10^{-4}$. We discuss these results in the context of our whole LOFAR rapid response sample of six long GRBs, finding our $\epsilon _{B}$ values are generally consistent with previous GRB studies.