deletions | additions       diff --git a/Mode Visibility.tex b/Mode Visibility.tex  index ba182ab..c3a5bfd 100644  --- a/Mode Visibility.tex  +++ b/Mode Visibility.tex 
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where $r_1$ and $r_2$ are the lower and upper boundaries of the evanescent zone, respectively. 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. The fraction of wave energy transmitted through the evanescent zone is $T^2$.  %while the fraction of reflected energy is $R^2=1-T^2$.  To estimate the reduced mode visibility due to energy loss in the core, we assume any mode energy which leaks into the g-mode g mode  cavity is completely lost. Therate at which  mode loses a fraction $T^2$ of its  energy leaks into the core depends on the transmission coefficient through the evanescent region ($T$) and in a time $2 t_{\rm cross}$, where $t_{\rm cross}$ is  the wave crossing time $t_{\rm cross}$ across of  the acoustic cavity. We show (see Supplementary Material) that the ratio of visibility between a suppressed mode and its non-suppressed counterpart is \begin{equation}  \label{eqn:vis}  \frac{V_{\rm sup}^2}{V_\alpha^2} = \bigg[1 + \Delta \nu \tau_{0} T^2 \bigg]^{-1} \, ,