it describes the steady angular velocity profile. We apply the same initial [*dimesionless*]{} profile of the angular velocity, which was taken from @Howe2011JPh, to all rotational periods studied in the paper. This profile is used as the reference state. We subtract the reference state from the Eq.(\[eq:angm\]) to find the equation for perturbations of the angular velocity profile from the reference state due to effects of the large- and small-scale Lorentz forces]{}: $$\begin{aligned}
\sin\theta\frac{\partial\delta\Omega}{\partial t} & = & \frac{1}{\rho r^{4}}\frac{\partial}{\partial r}r^{3}\bigg(T_{r\phi}\left(\Omega_{\odot}+\delta\Omega,\Omega^{*},\beta\right)\\
 & - & T_{r\phi}\left(\Omega_{\odot},\Omega^{\star},\beta=0\right)-\frac{B}{4\pi r^{2}}\frac{\partial A}{\partial\mu}\bigg)\nonumber \\
 & - & \frac{1}{\rho r^{2}\sin\theta}\frac{\partial}{\partial\mu}\sin^{2}\theta\bigg(T_{\theta\phi}\left(\Omega_{\odot}+\delta\Omega,\Omega^{*},\beta\right)\nonumber \\
 & - & T_{\theta\phi}\left(\Omega_{\odot},\Omega^{*},\beta=0\right)-\frac{B}{4\pi r\sin\theta}\frac{\partial A}{\partial r}\bigg),\nonumber \end{aligned}$$ where $\beta={\displaystyle
  \frac{\left|\overline{B}\right|}{\sqrt{4\pi\overline{\rho}u'^{2}}}}$ characterizes the strength of the magnetic field, $\Omega_{\odot}=\Omega_{0}^{\odot}f\left(r,\theta\right)$, $f\left(r,\theta\right)$ the angular velocity profile given by helioseismology, $T_{\left(\theta,r\right)\phi}\left(\Omega_{\odot},\Omega^{*},\beta=0\right)$ are the turbulent stresses (see, Eqs(\[eq:trf\],\[eq:ttf\])) in initial state when there is no large-scale magnetic field. The same is applied for the star rotating with the different period than the Sun. We assume that the sum of the radial turbulent and the Maxwell stresses is zero at the boundaries. This guarantees the conservation of the angular momentum in the model. [In the absence of the large-scale magnetic field any perturbation $\delta\Omega$ evolves to zero.]{} The details of the 