A self-consistent analytical magnetar model: The luminosity of $\gamma$-ray burst supernovae is powered by radioactivity

Understand

We present an analytical model that considers energy arising from a magnetar central engine.

• The results of fitting this model to the optical and X-ray light curves (LCs) of five long-duration $\gamma$-ray bursts (LGRBs) and two ultra-long GRBs (ULGRBs), including their associated supernovae (SNe), show that emission from a magnetar central engine cannot be solely responsible for powering an LGRB-SN.
• While the early AG-dominated phase can be well described with our model, the predicted SN luminosity is underluminous by a factor of $3-17$.
• We use this as compelling evidence that additional sources of heating must be present to power an LGRB-SN, which we argue must be radioactive heating.