Multi-Peaked Non-Thermal Light Curves from Magnetar-Powered Gamma-Ray Bursts

Binary neutron star mergers and collapsing massive stars can both create millisecond magnetars. Such magnetars are candidate engines to power gamma-ray bursts (GRBs). The non-thermal light curve of the resulting transients can exhibit multiple components, including: the GRB afterglow, pulsar wind nebula (PWN), and ejecta afterglow. We derive the timescales for the peak of each component and show that the PWN is detectable at radio frequencies, dominating the emission for $\sim$ 6 years for supernova/long GRBs (SN/LGRBs) and $\sim$ 100 days for kilonova/short GRBs (KN/SGRBs) at 1 GHz, and $\sim$ 1 year for SN/LGRBs and $\sim$ 15 days for KN/SGRBs at 100 GHz. The PWN emission has an exponential, frequency-dependent rise to peak that cannot be replicated by an ejecta afterglow. We show that PWNe in SN/LGRBs can be detected out to $z \sim 0.06$ with current instruments and $z \sim 0.3$ with next-generation instruments and PWNe in KN/SGRBs can be detected out to $z \sim 0.3$ with current instruments and $z \sim 1.5$ with next-generation instruments. We find that the optimal strategy for detecting PWNe in these systems is a multi-band, high cadence radio follow-up of nearby KN/SGRBs with an x-ray plateau or extended prompt emission from 10 - 100 days post-burst.