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Neutron stars typically have magnetic fields of $\sim 10^{12} \rm \ G$. However, if a neutron star's rotation period is comparable to the convective overturn time, magnetic fields can be amplified by helical motion in a mechanism called mean field dynamo. These highly magnetized neutron stars, magnetars, are born with short periods of $\sim$ 1 ms, which allow them to support an efficient $\alpha-\Omega$ dynamo, resulting in large magnetic dipole fields of $10^{14}-10^{15} \rm \ G$ \cite{Duncan_1992}.
%They were first proposed by \cite{Duncan_1992} to explain Soft Gamma Repeaters (SGRs).
A magnetar of mass $1.4 M_{\odot}$, $R = 10 \ \rm km$, and $P = 1 \ \rm ms$ has a rotational energy of
\begin{equation}
\nonumber
E_{\rm rot} = I \omega^2 /2 = \dfrac{1}{5}MR^2 \left(\dfrac{2\pi}{P}\right)^2 \simeq 4 \times 10^{51} \ \rm erg
\end{equation}
assuming the solid sphere moment of inertia as an approximation. The strong magnetic stresses and torques damped the rotation and release a large fraction of $E_{\rm rot}$ on the time scale of
\begin{equation}
\label{timescale} \label{eqn:timescale}
\tau \simeq 0.6 B_{15}^{-2} (P/1 \ {\rm ms})^2 \ \rm hr
\end{equation} \cite{Duncan_1992}. This amount of energy is similar to that released in $\gamma$-ray bursts and superluminous supernovae (SLSNe), thus making magnetar an attractive candidate for the central engine that power these explosions. In the past two decades, a connection has been made between supernovae and at least some subclass of long-duration $\gamma$-ray bursts (GRBs), supporting the case that they are powered by the same mechanism.
...
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The requirement of collimated relativistic flows leading to bi-polar jets in GRBs limit the central engines to only magnetars having
mimimal minimal periods of $1 \ \rm ms$ and magnetic fields of $\sim 10^{15} \ \rm G$. However, their less extreme population can still power quite fantastic cosmic fireworks. \cite{Duncan_1992} noted that the spin down timescale given in
\eqref{timescale} \ref{eqn:timescale} is shorter than the SN shock breakout time, making SNe that create magnetars brighter than usual. These subclasses of brighter Type II SNe are indeed observed (e.g.
\citealp{Richardson_2002} \citealp{Richardson_2002}). Recently, a number of rare superluminous SNe (SLSNe) are discovered, emitted the total radiation energy of $\sim 10^{51} \ \rm erg$ (e.g. SN\,2005ap \cite{Quimby_2007}; SN\,2008es \cite{Miller_2008}).