deletions | additions       diff --git a/IGW_are_generated_by.tex b/IGW_are_generated_by.tex  index b2d4030..41f42a6 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 burning, waves of lower frequency are significantly attenuated by radiative photon diffusion. Neutrino damping is likely irrelevant at all times. During C/O/Si shell burning phases, the waves become highly non-linear as they approach the inner $\sim 0.3 M_\odot$, and we expect them to be mostly dissipated via non-linearly breaking before reflecting at the center of the star.   The AM deposited by IGW is only significant if it is larger than the amount of AM contained within the core of the star. A typical massive star has a zero-age main sequence equatorial rotation velocity of $v_{\rm rot} \sim 150 \,{\rm km \ s}^{-1}$ \citep{de_Mink_2013}, corresponding to a rotation period of $P_{\rm MS} \sim 1.5 \, {\rm d}$ for our stellar model). model.  Using this rotation rate,we caluclate the AM $J_0(M)$ contained within the mass coordinate $M(r)$, given rigid rotation on the main sequence. In the absence of AM transport, this AM is conserved, although the core will spin-up as it contracts. Of course, magnetic torques may extract much of this AM and thus $J_0$ represents an upper limit to the AM contained within the mass coordinate $M(r)$. Both $J_0$ and the corresponding rotation profile are shown in the bottom panel of Figure \ref{fig:MassiveIGWtime}. In the top panel of Figure \ref{fig:MassiveIGWtime}, we plot the amount of AM capable of being extracted by IGW during each burning phase,   \begin{equation}