deletions | additions       diff --git a/IGW_are_generated_by.tex b/IGW_are_generated_by.tex  index c86115c..7c3b6cf 100644  --- a/IGW_are_generated_by.tex  +++ b/IGW_are_generated_by.tex 
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\end{equation}  Turbulent convection generates waves with a spectrum of azimuthal numbers $m$ and angular frequencies $\omega$, the values given above are characteristic values which dominate the AM flux. The waves carrying the most AM flux sometimes damp before they reach the core, and might not be able to affect the spin of the core. Then the waves with $\bar{m}$ and $\bar{\omega}$ would not dominate the AM flux to the core; instead, other waves in the turbulent spectrum become important (see Appendix \ref{wavestar}).   As a first check to see if IGW can have any affect on the spin of the core of the star, we assume all waves can propagate to the core. We conjecture suppose  that IGW could be important for the spin evolution if they are able to carry an amount of AM comparable to that contained in a young NS, which contains $J_{NS} \approx 10^{48} \, g \, {\rm cm}^2 \, {\rm s}^{-1}$ for a rotation period of $P_{\rm NS} = 10 \, {\rm ms}$. Then the characteristic timescale on which waves could affect the AM of the core is \begin{equation}  \label{eqn:twave}  t_{\rm waves} = \frac{J_{\rm NS}}{\dot{J}} \, .  \end{equation}  Table 1 lists shell burning stage lifetimes $T_{\rm shell}$ and wave spin-down time scales $t_{\rm waves}$, evaluated using $\dot{E} \propto \mathcal{M}$, $\bar{m}=1$ and $\bar{\omega}=\omega_c$. In all phases, $t_{\rm waves} \ll T_{\rm shell}$ for our model, indicating that waves may be able to have a substantial impact on the spin rate of the core. We examine this impact in the following sections.