The impact of superconductivity and the Hall effect in models of magnetized neutron stars

Understand

Equilibrium configurations of the internal magnetic field of a pulsar play a key role in modeling astrophysical phenomena, from glitches to gravitational wave emission.

• In this paper we present a numerical scheme for solving the Grad-Shafranov equation and calculating equilibrium configurations of pulsars, accounting for superconductivity in the core of the neutron star, and for the Hall effect in the crust of the star.
• Our numerical code uses a finite-difference method in which the source term appearing in the Grad-Shafranov equation, used to model the magnetic equilibrium is nonlinear.
• We obtain solutions by linearizing the source and applying an under-relaxation scheme at each step of computation to improve the solver's convergence.