deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 416f683..2f82be1 100644  --- a/untitled.tex  +++ b/untitled.tex 
...
\   The requirement of collimated relativistic flows leading to bi-polar jets in GRBs limit the central engines to only magnetars having 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 \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}). 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}). \citet{Kasen_2010} showed that magnetars with $B \sim 10^{14} \ \rm G$ and initial period $P $P_i  \sim 2-20 \ \rm ms$ can release rotational energy via magnetic dipole radiation on the spin-down timescale comparable to the effective diffusion time of the ejecta. They showed that these magnetars can enhance the peak luminosity to what given by Equation (4) in \citet{Kasen_2010}, which is exceeding $10^{43} \rm \ erg/s $, brighter than normal core-collapse Type II-P SNe. Figure 4 and 5 in \citet{Kasen_2010} show the dependence of peak luminosity and time to peak on $B$ and $P_i$ for ejecta mass of $5$ and $20 \ M_{\odot}$ respectively.