Twisted-torus equilibrium structures of magnetic fields in magnetized stars

We have investigated the "universality" of the twisted-torus equilibrium structures of the magnetic fields in deformed stars. The Tomimura-Eriguchi scheme for equilibrium structures of uniformly rotating magnetized stars is extended to treat equilibrium configurations of differentially rotating and meridional circulation-free magnetized polytropes with infinite conductivity. Characteristics of the magnetic fields obtained are summarized as follows: The exterior magnetic fields of the stars behave like dipolar poloidal fields, which decrease as r^-3 when r → ∞. The interior magnetic fields are a mixture of poloidal and toroidal fields. Their geometric structures are tori of twisted field lines around the symmetry axis and of untwisted poloidal fields that penetrate the surface of the stars to continue to the exterior fields. It has been found that these structures of magnetic fields in stationary magnetic stars are robust and universal in the sense that they are nearly independent of the compressibility of the matter, rotation laws, and degrees of differential rotation. This universality is a consequence of the natural assumption that the electric current should be confined inside the star and of the integrability condition of the basic equation, i.e., that the electric current in the meridional plane is a function of the flux function, whose behavior is governed by a partial differential equation of the elliptic type.