Constraints on the central engine of merger-driven long gamma-ray bursts

Recent observations have identified a new class of long-duration gamma-ray bursts (GRBs) likely produced by compact binary mergers. Using radio observations and lightcurve modelling, we investigate whether a magnetar remnant can power the long-lasting prompt emission observed in this merger-driven GRB sample. We derive constraints on the magnetars' rotational energy and magnetic-field strength, and assess whether the magnetar central-engine model is viable for the observed events. We conducted 2.1 GHz radio observations of seven nearby merger-driven GRBs (z<0.25) using the Australia Telescope Compact Array (ATCA), obtaining sensitive upper limits on late-time radio emission 520-6900 days post-burst. We modelled the expected radio light curves from magnetar-energized ejecta interacting with the circumburst medium and compared them to our observations. We separately tested the magnetar hypothesis against the extended gamma-ray emission using a fallback-accreting magnetar model. No radio counterpart is detected in any of the observed GRBs, with 3 σ flux density upper limits of 33-72 μ Jy at 2.1 GHz. Modelling the expected synchrotron emission from magnetar-energized ejecta interacting with the circumburst medium, we find that the radio non-detections remain compatible with energetic outflows in low-density environments. The analysis of the prompt gamma-ray emission provides complementary constraints on the spin period and magnetic field of the magnetar engine. Once fallback accretion and jet baryon-loading are considered, the parameter space is narrowly confined.