Three-dimensional numerical simulations of ambipolar diffusion in NS cores in the one-fluid approximation: instability of poloidal magnetic field

We numerically model evolution of magnetic fields inside a neutron star under the influence of ambipolar diffusion in the weak-coupling mode in the one-fluid MHD approximation. Our simulations are 3D and performed in spherical coordinates. Our model covers the neutron star core and includes crust where the magnetic field decay is due to Ohmic decay. We discover an instability of poloidal magnetic field under the influence of ambipolar diffusion. This instability develops in the neutron star core and grows on a time-scale of 0.2 dimensionless times, reaching saturation by 2 dimensionless times. The instability leads to formation of azimuthal magnetic field with azimuthal wavenumber m = 14 (at the moment of saturation) which keeps merging and reaches m = 4 by 16 dimensionless times. Over the course of our simulations (16 dimensionless times) the surface dipolar magnetic field decays, reaching 20 per cent of its original value and keeps decaying. The decay time-scale for the total magnetic energy is six dimensionless times. The ambipolar diffusion induces electric currents in the crust where these currents dissipate efficiently. Strong electric currents in the crust lead to heating, which could correspond to luminosities of ≈10²⁹ erg s¯¹during hundreds of Myrs for an initial magnetic field of 10¹⁴ G. Ambipolar diffusion leads to formation of small-scale magnetic fields at the neutron star surface.