deletions | additions       diff --git a/IGW_are_generated_by.tex b/IGW_are_generated_by.tex  index 1739694..5d489af 100644  --- a/IGW_are_generated_by.tex  +++ b/IGW_are_generated_by.tex 
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In Appendix \ref{wavestar}, we calculate characteristic wave frequencies $\omega_*(r)$ and AM fluxes $\dot{J}_*(r)$ entering the core during different phases of massive star evolution. During core He and shell C-burning, waves of lower frequency are somewhat attenuated by radiative photon diffusion. Neutrino damping is likely irrelevant at all times. During shell burning phases, the waves become highly non-linear as they approach the inner $\sim 0.5 M_\odot$, and we expect them to be mostly dissipated via non-linearly breaking before reflecting at the center of the star. For each phase, we calculate the characteristic IGW spin down time scale, $t_*(r)$, on which the waves can change the spin rate by an amount $\omega_*(r)$,  \begin{equation}  \label{eqn:tstar}  t_*(r) = \frac{I(r) \omega_*(r)}{dot{J}_*(r)} \omega_*(r)}{\dot{J}_*(r)}  \, , \end{equation}  where $I(r)$ is the moment of inertia interior to radius $r$.