distribution compared with the models with $m=1.0$ and $m = 0.0$. Thus the value of $\log \beta$ becomes dramatically small within the $\hat{r} [0:0.1]$ region and the minimum value of $\beta$ can reach about $\sim$ 20 in the central part. Therefore, in the central region of the model with $m=-2.0$ the influence of magnetic field on the local structure of the star is no longer negligible.

Here we explain the reason why this kind of highly localized [*poloidal*]{} magnetic field configuration can be realized. We need to note the distribution of the [*toroidal*]{} current density $\hat{j}_\varphi$ in order to analyse our models properly, because the current density is related to the magnetic field closely by the two equations (\[Eq:rotH\]) and (\[Eq:current\]). In Fig. \[fig:j\_phi\] we show the distributions of the [*toroidal*]{} current density for models with different values of $m$. As seen from Fig. \[fig:j\_phi\], the distribution of the [*toroidal*]{} current density is concentrated toward the magnetic axis for the configuration with negative values of $m$. This is due to the dependence of $\hat{\mu}$ on the value of $m$. The current density distribution spreads over a large region inside the star as the value of $m$ [*increases*]{} (from left panel 