Tayler-Spruit dynamo in stably stratified rotating fluids: Application to proto-magnetars

¹ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
² Observatoire de Genève, Université de Genève, 51 Ch. Pegasi, 1290 Versoix, Switzerland
³ Université Paris Cité, Université Paris-Saclay, CNRS, CEA, AIM, 91191 Gif-sur-Yvette, France
⁴ Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam, Germany

^⋆ Corresponding author; paul.barrere@cea.fr

Received: 1 July 2024
Accepted: 13 February 2025

Abstract

The formation of highly magnetized young neutron stars, called magnetars, is still a strongly debated topic. One promising scenario invokes the amplification of the magnetic field by the Tayler-Spruit dynamo in a proto-neutron star (PNS) that is spun up by fall-back. Our previous numerical study supports this scenario by demonstrating that this dynamo can generate magnetar-like magnetic fields in stably stratified Boussinesq models of a PNS interior. To further investigate the Tayler-Spruit dynamo, we performed 3D magnetohydrodynamic (MHD) numerical simulations with the MagIC code, varying the ratio between the Brunt-Väisälä frequency and the rotation rate. We first demonstrated that a self-sustained dynamo process can be maintained for a Brunt-Väisälä frequency about four times higher than the angular rotation frequency. The generated magnetic fields and angular momentum transport follow the scaling laws derived in prior analytical investigations, confirming our earlier results. We also report, for the first time, the existence of an intermittent Tayler-Spruit dynamo. For a typical PNS Brunt-Väisälä frequency of 1 kHz, the axisymmetric toroidal and dipolar magnetic fields range between 1.2 × 10¹⁵–2 × 10¹⁶ G and 1.4 × 10¹³–3 × 10¹⁵ G, for rotation periods of 1 − 10 ms. Moreover, the total magnetic field remains ≳10¹⁴ G for periods of ≲60 ms. Thus, our results suggest that our scenario is promising to form classical fast-rotating magnetars and magnetars with weaker magnetic dipoles for slower rotations. We offer a calibration of the analytical scaling laws based on our simulations, with a dimensionless normalisation factor of the order of 10⁻². As the Tayler-Spruit dynamo is often invoked for the angular momentum transport in stellar radiative zones, our results are of particular significance to asteroseismology as well.