deletions | additions       diff --git a/During_each_shell_bu.tex b/During_each_shell_bu.tex  index cd64a22..c6495cd 100644  --- a/During_each_shell_bu.tex  +++ b/During_each_shell_bu.tex 
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\begin{equation}  \label{eqn:omex}  \Omega_{\rm ex} = \sqrt{\frac{4 \omega_c T_{\rm shell} }{3 \pi^2}} \frac{J_w}{I_c} \, .  \end{equaion} \end{equation}  In MLT, the quantity $\mathcal{M} L_{\rm conv} \propto \omega_c^4$. Therefore, we find approximate scaling $\Omega_{\rm ex} \propto \omega_c^{5/2} T_{\rm shell}^{1/2}$. Thus, more vigorous burning phases with higher convective turnover frequencies will lead to larger minimum core rotation rates. However, the later burning phases tend to have a much shorter life $T_{\rm shell}$, which largely counteracts their increased vigor.