Dynamically Stable Magnetic Fields in Relativistic Neutron Stars: A Diverse Landscape of GRMHD Equilibria
Neutron stars endowed with purely poloidal or purely toroidal magnetic fields are known to be unstable, and settle into mixed poloidal-toroidal configurations. The end state of these instabilities is still poorly understood. It is unclear whether this state is unique or whether the dynamically stable configuration has memory of the initial conditions. In this work, we perform long-term, fully general relativistic magnetohydrodynamic simulations of equilibrium configurations of slowly rotating neutron stars endowed with self-consistent mixed poloidal and toroidal magnetic fields. Our initial configurations differ in their initial magnetization and magnetic field geometry. We evolve the initial equilibria for tens of Alfvén timescales until well after any instabilities have saturated. Employing an array of diagnostic tools from visualizations to the structure of the plasma four-current and a vector spherical harmonic decomposition of the settled magnetic fields, we characterize the structure of the dynamically stable, settled magnetic equilibria. We find that the settled configurations are not unique. Instead, they exhibit diverse multipolar structures, with higher-order modes contributing substantially. Our findings demonstrate that there is memory of the magnetic-field initial conditions, and that there is no unique dynamically stable magnetic-field geometry for neutron stars. Nevertheless, we find that the angle-averaged radial profile of the magnetic field toroidal to poloidal amplitude in the bulk of the settled configurations exhibits some degree of universality with typical values of order \(20\)--\(40\%\).