deletions | additions       diff --git a/sectionSpin_Evolutio.tex b/sectionSpin_Evolutio.tex  index 8b8908c..7d1eef8 100644  --- a/sectionSpin_Evolutio.tex  +++ b/sectionSpin_Evolutio.tex 
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A stochastic influx of IGW into the core will also enforce a minimum expectation value of the core spin rate. Consider a non-spinning core being irradiated by IGW wave packets emitted from an overlying convective shell. The spherical symmetry of the background structure implies that the wave packets will contain randomly oriented AM vectors. Since we expect incoming waves to non-linearly dissipate before being reflected, the core will absorb their AM. The total core AM is thus a superposition of the randomly oriented wave packet AM vectors. Each wave packet will contain an AM vector of length  \label{AMvec} \begin{equation}  \label{eqn:AMvec}  J_w \sim \frac{2 \pi}{\bar{\omega}} \dot{J} \sim \frac{2 \bar{m} \pi}{\omega_{\rm con}^2} \mathcal{M} L_{\rm con}, con} \, ,  \end{equation}  which we have calculated using equations \ref{Ewaves} and \ref{Jwaves}, and assuming typical wave packets have angular frequency $\omega_{\rm con}$ and last for an eddy turnover time, $2 \pi/\omega_{\rm con}$. The expected magnitudes of the $x$, $y$, and $z$ components of the AM vector are $J_w/\sqrt{3}$.