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Samaporn Tinyanont edited untitled.tex
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Magnetars are neutron 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 $10^{14}-10^{15} \rm \
G$. This field strength is higher than that of normal neutron stars by a factor of $\sim 10^2$. They 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}
E_{\rm rot} = I \omega^2 /2 = \dfrac{1}{5}MR^2 \left(\dfrac{2\pi}{P}\right)^2 \simeq 4.4 \times 10^{51} \ \rm erg
\end{equation}