Impact of rotation on magnetic field stability and orientation in isolated neutron stars

Neutron stars are the most compact horizonless objects in the Universe, exhibiting the strongest known magnetic fields. They are potential sources of coincident gravitational waves and electromagnetic radiation across the entire spectrum. However, the internal configuration of their magnetic fields and the mechanisms that stabilize them remain open questions. As a step forward in understanding the timescale for the emergence of magnetic instabilities that disrupt stellar field configurations, we study the impact of stellar rotation using three-dimensional general relativistic numerical simulations of uniformly rotating, isolated neutron stars threaded by strong, poloidal, pulsar-like magnetic fields. The initial stellar configurations assume perfect conductivity and are stationary and axisymmetric. We explore a range of angular velocities, from non-rotating stars to those near the mass-shedding limit. We find that the stars spontaneously develop differential rotation, which triggers the appearance of a strong toroidal magnetic field component. Non-rotating neutron stars are unstable to the Tayler and Parker instabilities, which significantly change the magnetic field geometry. These instabilities lead to a rapid reduction of the initial magnetic energy by $\sim 99\%$ within $\sim 4$ Alfvén times of their onset. In contrast, rotation significantly delays the development of these instabilities and, in some cases, mitigates their effects. Highly rotating models retain up to $\sim 30\%$ of their magnetic energy for at least $\sim 10$ Alfvén times. Our results suggest that rotation plays a crucial role in stabilizing the magnetic field of neutron stars, regardless of its initial configuration.