A new scenario for magnetar formation: Tayler-Spruit dynamo in a proto-neutron star spun up by fallback

Magnetars are isolated young neutron stars characterized by the most intensemagnetic fields known in the universe. The origin of their magnetic field isstill a challenging question. In situ magnetic field amplification by dynamoaction is a promising process to generate ultra-strong magnetic fields infast-rotating progenitors. However, it is unclear whether the fraction ofprogenitors harboring fast core rotation is sufficient to explain the entiremagnetar population. To address this point, we propose a new scenario formagnetar formation, in which a slow-rotating proto-neutron star is spun up bythe supernova fallback. We argue that this can trigger the development of theTayler-Spruit dynamo while other dynamo processes are disfavored. Usingprevious works done on this dynamo and simulations to characterize thefallback, we derive equations modelling the coupled evolution of theproto-neutron star rotation and magnetic field. Their time integration fordifferent fallback masses is successfully compared with analytical estimates ofthe amplification timescales and saturation value of the magnetic field. Wefind that the magnetic field is amplified within $20$ to $40$s after the corebounce, and that the radial magnetic field saturates at intensities$10^{14}-10^{15}$G, therefore spanning the full range of magnetar's dipolarmagnetic fields. We also compare predictions of two proposed saturationmechanisms showing that magnetar-like magnetic fields can be generated forneutron star spun up to rotation periods $\lesssim8$ms and $\lesssim28$ms,corresponding to fallback masses $\gtrsim4\times10^{-2}{\rm M}_{\odot}$ and$\gtrsim10^{-2}{\rm M}_{\odot}$. Thus, our results suggest that magnetars canbe formed from slow-rotating progenitors for fallback masses compatible withrecent supernova simulations and leading to plausible initial rotation periodsof the proto-neutron star.