deletions | additions       diff --git a/sectionSpin_Evolutio.tex b/sectionSpin_Evolutio.tex  index 0d18b9d..59f9310 100644  --- a/sectionSpin_Evolutio.tex  +++ b/sectionSpin_Evolutio.tex 
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\section{Stochastic Spin-up by Internal Gravity Waves}  \label{spinup}  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 At the end of the convective shell phase, the  total core AM is thus a superposition the sum  of the randomly oriented wave packet AM vectors. vectors emitted by the shell.  Each wave packet will contain an AM vector of length \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} \, ,