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

¹ Université Paris-Saclay, Université Paris-Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
e-mail: paul.barrere@cea.fr
² Max Planck Institute for Gravitational Physics (Albert Einstein Institute), 14476 Potsdam, Germany
³ Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany

Received: 2 June 2022
Accepted: 11 October 2022

Abstract

Magnetars are isolated young neutron stars characterised by the most intense magnetic fields known in the Universe, which power a wide variety of high-energy emissions from giant flares to fast radio bursts. The origin of their magnetic field is still a challenging question. In situ magnetic field amplification by dynamo action could potentially generate ultra-strong magnetic fields in fast-rotating progenitors. However, it is unclear whether the fraction of progenitors harbouring fast core rotation is sufficient to explain the entire magnetar population. To address this point, we propose a new scenario for magnetar formation involving a slowly rotating progenitor, in which a slow-rotating proto-neutron star is spun up by the supernova fallback. We argue that this can trigger the development of the Tayler-Spruit dynamo while other dynamo processes are disfavoured. Using the findings of previous studies of this dynamo and simulation results characterising the supernova fallback, we derive equations modelling the coupled evolution of the proto-neutron star rotation and magnetic field. Their time integration for different accreted masses is successfully compared with analytical estimates of the amplification timescales and saturation value of the magnetic field. We find that the magnetic field is amplified within 20 − 40 s after the core bounce, and that the radial magnetic field saturates at intensities between ∼10¹³ and 10¹⁵ G, therefore spanning the full range of a magnetar’s dipolar magnetic fields. The toroidal magnetic field is predicted to be a factor of 10–100 times stronger, lying between ∼10¹⁵ and 3 × 10¹⁶ G. We also compare the saturation mechanisms proposed respectively by H.C. Spruit and J. Fuller, showing that magnetar-like magnetic fields can be generated for a neutron star spun up to rotation periods of ≲8 ms and ≲28 ms, corresponding to accreted masses of ≳ 4 × 10⁻² M_⊙ and ≳ 1.1 × 10⁻² M_⊙, respectively. Therefore, our results suggest that magnetars can be formed from slow-rotating progenitors for accreted masses compatible with recent supernova simulations and leading to plausible initial rotation periods of the proto-neutron star.