figures, there are no discontinuities of the magnetic fields at the stellar surfaces. Due to the choice of the functional form of the arbitrary function $\hat{\kappa}(\hat{\Psi})$ and the distribution of the magnetic flux function, [*toroidal*]{} magnetic fields appear only in the region that is bounded by the outermost closed [*poloidal*]{} magnetic field line inside the star (thick line). Thus the toroidal magnetic fields exist inside the torus region.

As the value of $m$ is increased, i.e. from top panels to bottom panels, the ratio of $H_c / H_{sur}$ decreases (see left panels in Fig. \[fig:magnetic\_structure\]) because the [*poloidal*]{} magnetic field becomes weaker. This is also related to the fact that the interior [*poloidal*]{} magnetic field lines are much more localized near the axis for negative $m$ models. The contours of magnetic field strength also display the same tendency. For the $m = 1.0$ model, the contour of $|\Vec{H}| = H_{sur}$ (thick line) shows the stellar surface and the shapes of contours are nearly spherical. By contrast, the contours of the $m=-2.0$ model are highly distorted near the axis. The strength of the [*poloidal*]{} magnetic fields for the negative $m$ models could exceed $10^{17}$G near the central region. Fig. \[fig:beta\] shows 