deletions | additions       diff --git a/Mode Visibility.tex b/Mode Visibility.tex  index 31c486f..87029df 100644  --- a/Mode Visibility.tex  +++ b/Mode Visibility.tex 
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%Most modes observed are within   %The value of $\nu_{\rm max}$ is determined by the evolutionary state of the star, and on the RGB %more evolved stars generally have smaller $\nu_{\rm max}$.   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 $\omega = L_l L_{\ell}  = \sqrt{l(l+1)} \sqrt{\ell(\ell+1)}  c_s/r$, where $c_s$ 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 the visibility of suppressed modes can be explained if wave energy leaking into the core never returns to the stellar envelope.