Three-dimensional numerical simulations of neutron star cores in the two-fluid MHD approximation: simple configurations

Abstract

Magnetic field evolution in neutron star cores is not fully understood. We describe the field evolution both for one barotropic fluid as well as two collisionally coupled barotropic fluids with different density profiles using the anelastic approximation and the Navier-Stokes equations to simulate the evolution in three dimensions. In the one-fluid case, a single fluid describes the motion of the charged particles. In the two-fluid model, the neutral fluid is coupled to the electrically conductive fluid by collisions, the latter being dragged by the magnetic field. In this model, both fluids have distinct density profiles. This forces them to move at slightly different velocities, resulting in a relative motion between the two barotropic fluids -- ambipolar diffusion. We develop a code based on Dedalus and study the evolution of simple poloidal dipolar and toroidal magnetic fields. Previous 2D studies found that poloidal magnetic fields evolve towards a stable Grad-Shafranov equilibrium. In our 3D simulations we find an instability of the two-fluid system similar to the one in the barotropic fluid system. After the instability saturates, a highly non-linear Lorentz force introduces small-scale fluid motion that leads to turbulence, development of a cascade and significant, non-axially symmetric changes in the magnetic field configuration. Fluid viscosity plays an essential role in regularizing the small-scale fluid motion, providing an energy drain.