Initial Configuration

Neutron Star

We construct the initial magnetized equilibria by solving the Einstein equations, Maxwell's equations, and ideal MHD equations self-consistently under the assumptions of stationarity and axisymmetry. Case A is a rapidly rotating neutron star with a polytropic equation of state with adiabatic index $\Gamma=2$. Case B is a moderately rotating neutron star with a polytropic equation of state with $\Gamma=3$. All magnetars have magnetic energy which is at most 4.4% of their gravitational potential energy. Most of this energy is poloidal in nature since the toroidal magnetic field is confined to a region just below the surface of the NS, therefore its volume is much smaller than the corresponding one for the poloidal field, which extends to infinity. However, the maximum values of the toroidal and the poloidal magnetic fields are of the same order.