deletions | additions       diff --git a/Around_the_same_time_that__.tex b/Around_the_same_time_that__.tex  index 5f8514b..522ef07 100644  --- a/Around_the_same_time_that__.tex  +++ b/Around_the_same_time_that__.tex 
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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.}  The newly formed neutron star then loses its rotational energy quickly due to electromagnetic torque, generating electric fields that accelerate particles to ultra-relativistic energies, which eventually give out $\gamma$-ray. The energy released time scale due to magnetic dipole luminosity and gravitational wave emission of $\sim 20 \ \rm s$ for a typical magnetar is consistent with the timescale of long-duration GRBs \cite{Usov_1992}.  Near the magnetar's surface out to the light cylinder, the optical depth to this radiation due to Compton scattering, absorption, and pair-cration is large. The radiation has to propagate out to a photosphere radius of $\sim 10^8 \ \rm cm$ before it is released. The typical radiated $\gamma$-ray energies of $0.1-1 \ \rm MeV$ is also  consistent with those observed from GRBs. GRBs \cite{Usov_1992}.  Numerous works have been done