for polytropic models and $$\begin{aligned}
   U \equiv \int g(x) \, d^3 \Vec{r} \ ,\end{aligned}$$ $$\begin{aligned}
 g(x) = a\{ 8x^3 [(x^2 + 1)^\frac{1}{2} - 1]\} - p, \end{aligned}$$ for the Fermi gas configurations (see. @Chandrasekhar_stellar_structure), $$\begin{aligned}
   {\cal H} \equiv \int r \cdot \left(\frac{\Vec{j}}{c} \times \Vec{H} \right) \, d^3 \Vec{r} \ .\end{aligned}$$ $$\begin{aligned}
   K = \int (\nabla \times \Vec{A}) \cdot \Vec{A} \, d^3 \Vec{r}
   = \int \Vec{H} \cdot \Vec{A} \, d^3 \Vec{r} \ ,\end{aligned}$$ where $W$, $T$, $\Pi$, $U$, ${\cal H}$ and $K$ are the gravitational energy, rotational energy, total pressure, internal energy, magnetic field energy and magnetic helicity, respectively. In order to evaluate the structures of magnetic fields, we define some physical quantities related to the magnetic fields as follows: $$\begin{aligned}
   H_{sur} = \dfrac{\int_0^{2\pi} 
   \int_0^{\pi} \, 
 r_s^2(\theta) \, 
\sin \theta 
   |\Vec{H}(r_s, \theta)|
 \, d\theta
d\varphi
}{S} \ ,\end{aligned}$$ where $r_s(\theta)$ and $|H_{sur}|$ are the stellar radius in the direction of $\theta$ and the surface magnetic field strength, respectively, and the surface area of the star is defined as: $$\begin{aligned}
  S = \int_0^{2\pi} 
\int_0^{\pi}    \,  r_s^2(\theta) \sin \theta \, d\theta 
\, d \varphi .\end{aligned}$$ The volume-averaged magnetic field strength in the central region of the star is defined as $$\begin{aligned}
   H_\mathrm{c} = 
   