Samaporn Tinyanont edited untitled.tex  almost 8 years ago

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\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 $\tau \simeq 0.6 B_{15}^{-2} (P/1 \ {\rm ms})^2 \ \rm hr$ \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.   \  Around the same time that magnetars were proposed, a realization had emerged that GRBs could have cosmological origin. This would require a total energy of $\sim 10^{51} \ \rm erg$ to explain the observed flux assuming isotropic emission (e.g. \citealp{Paczynski_1991}). Interestingly, \citet{Usov_1992} proposing highly magnetized neutron stars as central engines of these bursts was published only a day after \citet{Duncan_1992}. The proposed scenario is such that a magnetar forms from a white dwarf via accretion induced collapse (AIC). The WD magnetic field of $\sim 10^9 \ \rm G$ is amplified to $10^{15} \rm \ G$ by magnetic flux conservation. The rotational period of $\sim 1 \ \rm ms$ is a result of angular momentum conservation.   \footnote{\citet{Duncan_1992} also briefly mentioned this scenario as a possible explanation for cosmological GRBs.}