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Magnetic field configurations of a magnetar throughout its interior and exterior -- core, crust and magnetosphere

We obtained the magnetic field configurations, including both poloidal and toroidal components, throughout the interior and exterior of magnetars using a realistic equation of state. We divided the magnetized star into the hydromagnetic equilibrium core, Hall equilibrium crust and twisted force-free magnetosphere. We systematically and simultaneously calculated these regions under various boundary conditions using the Green function relaxation method, and noted the following interesting characteristics of these numerical results. First, the strength and structure of core magnetic fields affect the crustal magnetic fields. Second, the current sheet on the core-crust interface affects both internal and external magnetic field configurations. Third, the twisted magnetosphere makes a cross-point of magnetic field lines, such as X-point geometry, in the magnetosphere. The X-point geometry appears and disappears according to the strength of the twisted field in the magnetosphere or the core-crust boundary conditions. Our results mean that both Hall magnetohydrodynamics secular evolution and magnetospheric dynamical evolution are deeply affected by conditions of another region and the core-crust stress of magnetars.