Magnetic field configurations in neutron stars from MHD simulations

ABSTRACT We have studied numerically the evolution of magnetic fields in barotropic neutron stars, by performing non-linear magnetohydrodynamical simulations with the code pluto. For both initially predominantly poloidal and toroidal fields, with varying strengths, we find that the field settles down to a mixed poloidal–toroidal configuration, where the toroidal component contributes between ${\rm 10}$ and $20 {{\ \rm per\ cent}}$ of the total magnetic energy. This is, however, not a strict equilibrium, as the instability leads to the development of turbulence, which, in turn, gives rise to an inverse helicity cascade, which determines the final ‘twisted torus’ setup. The final field configuration is thus dictated by the non-linear saturation of the instability, and is not stationary. The average energy of the poloidal and toroidal components, however, is approximately stable in our simulations, and a complex multipolar structure emerges at the surface, while the magnetic field is dipolar at the exterior boundary, outside the star.

Exact solution of some exterior boundary value problems of elasticity in parabolic coordinates

The present work, by using the method of the separation of variables, states and analytically (exactly) solves the external boundary value problems of elastic equilibrium of the homogeneous isotropic body bounded by the parabola, when normal or tangential stresses are given on a parabolic border. Using MATLAB software, the numerical results and constructed graphs of the mentioned boundary value problems are obtained.