Turbulent magnetic field amplification in binary neutron star mergers

Magnetic fields are expected to play a key role in the dynamics and the ejection mechanisms that accompany the merger of two neutron stars. General relativistic magnetohydrodynamic (MHD) simulations offer a unique opportunity to unravel the details of the ongoing physical processes. Nevertheless, current numerical studies are severely limited by the fact that any affordable resolution remains insufficient to fully capture the small-scale dynamo, initially triggered by the Kelvin-Helmholtz instability, and later sourced by several MHD processes involving differential rotation. Here, we alleviate this limitation by using explicit large-eddy simulations, a technique where the unresolved dynamics occurring at the subgrid scales (SGS) is modeled by extra terms, which are functions of the resolved fields and their derivatives. The combination of high-order numerical schemes, high resolutions, and the gradient SGS model allow us to capture the small-scale dynamos produced during the binary neutron star mergers, as shown in previous works. Here, we follow the first 50 milliseconds after the merger and, for the first time, we find numerical convergence on the magnetic field amplification, in terms of integrated energy and spectral distribution over spatial scales. Among other results, we find that the average intensity of the magnetic field in the remnant saturates at similar to 10(16) G around 5 ms after the merger. After 20-30 ms, both toroidal and poloidal magnetic field components grow continuously, fed by the winding mechanism that provides a slow inverse cascade, i.e., gradually transferring kinetic into magnetic energy. We find no clear hints for magnetorotational instabilities and no significant impact of the magnetic field on the redistribution of angular momentum in the remnant in our simulations, probably due to the very turbulent and dynamical topology of the magnetic field at all stages, with small-scale components largely dominating over the large-scale ones. Although the magnetic field grows near the rotation axis of the remnant, longer large-eddy simulations are necessary to further investigate the formation of large-scale, helical structures close to the rotational axis, which could be associated to jet formation.