deletions | additions       diff --git a/Mode Visibility.tex b/Mode Visibility.tex  index 25132c6..e40dd21 100644  --- a/Mode Visibility.tex  +++ b/Mode Visibility.tex 
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where $\Delta \nu \simeq (2 t_{\rm cross})^{-1}$ \cite{Chaplin_2013} is the large frequency separation between overtone modes, and $\tau$ is the damping time of a radial mode with similar frequency. The value of $T^2$ can be calculated from a stellar model, whereas {\bf $\tau \approx 5 \! - \! 10 \, {\rm days}$} {\bf \cite{Dupret_2009,Corsaro_2012,Grosjean_2014,Corsaro_2015} } for stars ascending the RGB.  Most observed modes are near the frequency $\nu_{\rm max}$, which is determined by the evolutionary state of the star. On the RGB, more evolved stars generally have smaller $\nu_{\rm max}$.   Figure \ref{fig:moneyplot} compares our estimate for suppressed dipole mode visibility (equation \ref{eqn:vis}) with {\it Kepler} observations \cite{Mosser_2011,Garcia_2014}. The {\bf objects identified by \cite{Mosser_2011} as depressed dipole modes} stars lie very close to our estimate. The striking agreement holds over a large baseline in $\nu_{\rm max}$ extending from the very early red giants KIC 8561221 \cite{Garcia_2014} and KIC 9073950 at high $\nu_{\rm max}$ to near the luminosity bump at low $\nu_{\rm max}$. {\bf The observations appear to be consistent with near nearly  total wave energy loss in the core, as partial energy loss would create stars with less-depressed modes, which seem to be rare.} We conclude that the cores of stars with {\bf depressed} dipole modes efficiently {\bf trap or disrupt} waves tunneling through the evanescent region. This is further supported by their normal $\ell=0$ mode visibility, {\bf because radial modes do not propagate within the inner core and because much larger field strengths are required to alter acoustic waves}. {\bf The absence (or perhaps smaller degree) of depression} observed for $\ell=2$ modes (\cite{Mosser_2011}) {\bf occurs because quadrupole modes have a smaller transmission coefficient $T$, and less of their energy leaks into the core.} 
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