Equilibrium configurations of magnetized rotating polytropes: Effects of strong toroidal magnetic fields in addition to poloidal magnetic fields

We have constructed many equilibrium sequences of magnetized polytropic stars with infinite conductivity for polytropes of indices N = 0.5, 1, and 3. Not only poloidal magnetic fields but also toroidal magnetic fields have been included in addition to rotation. By choosing simplified forms for arbitrary functions appearing in the formulation of magnetized barotropic equilibrium stars, we have obtained strongly magnetized polytropes whose toroidal magnetic fields are of comparable strength to those of poloidal magnetic fields. The exterior magnetic fields of the obtained stars consist of dipole-like poloidal fields, which decrease as r^-3 when r → ∞. On the other hand, the interior magnetic fields are mixed poloidal-toroidal, which are composed of tori of twisted field lines around the symmetry axis and of untwisted poloidal fields that continue to the exterior fields penetrating the surfaces of the stars.