deletions | additions       diff --git a/Mode Visibility.tex b/Mode Visibility.tex  index f75d146..21f2e87 100644  --- a/Mode Visibility.tex  +++ b/Mode Visibility.tex 
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Red giant oscillation modes are standing waves that are driven by stochastic energy input from turbulent near surface-convection \cite{Goldreich_1977}. Waves excited near the stellar surface propagate downward as acoustic waves until their angular frequency $\omega$ is less than the local Lamb frequency for waves of angular degree $\ell$, i.e., until $\omega = L_l L_{\ell}  = \sqrt{l(l+1)} \sqrt{\ell(\ell+1)}  v_s/r$, where $v_s$ is the local sound speed and $r$ is the radial coordinate. At this boundary, part of the wave flux is reflected, and part of it tunnels into the core. The wave resumes propagating inward as a gravity wave in the radiative core where $\omega < N$, where $N$ is the local buoyancy frequency. In normal red giants, wave energy that tunnels into the core eventually tunnels back out to produce the observed oscillation modes. We show here that suppressed modes can be explained if wave energy leaking into the core never returns back to the stellar envelope.  The degree of wave transmission between the core and envelope is determined by the tunneling integral through the intervening evanescent zone. The transmission coefficient is   \begin{equation}  \label{eqn:integral2}  T \sim \bigg( \frac{r_1}{r_2} \bigg)^{\sqrt{l(l+1)}} \bigg)^{\sqrt{\ell(\ell+1)}}  \, , \end{equation}  where $r_1$ and $r_2$ are the lower and upper boundaries of the evanescent zone, respectively. The fraction of wave energy transmitted through the evanescent zone is $T^2$. For waves of the same frequency, larger values of $\ell$ have larger values of $r_2$, thus equation \ref{eqn:integral2} demonstrates that high $\ell$ waves have much smaller transmission coefficients through the evanescent zone.  
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