deletions | additions       diff --git a/subsection_Mode_Visibility_Here_we__.tex b/subsection_Mode_Visibility_Here_we__.tex  index dad3309..c5e736a 100644  --- a/subsection_Mode_Visibility_Here_we__.tex  +++ b/subsection_Mode_Visibility_Here_we__.tex 
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\begin{equation}  \dot{E}_{\rm leak} = E_{\rm ac} \frac{T^2}{2 t_{\rm cross}} ,  \end{equation}  where $T$ is the transmission coefficientfrom equation \ref{eqn:integral}, and  \begin{equation}  t_{\rm cross} \label{eqn:integral}  T  = \int^R_{r_2} \frac{dr}{v_s} \exp{\int^{r_2}_{r_1} i k_r dr} \simeq \exp{\int^{r_2}_{r_1} - \frac{\sqrt{\ell (\ell +1)}}{r} dr }  \, , \end{equation}  is which evaluates approximately to  the expression in equation \ref{eqn:integral}. The  wave crossing time across the for  acoustic cavity. The waves is  \begin{equation}  t_{\rm cross} = \int^R_{r_2} \frac{dr}{v_s} \, .  \end{equation}  A  suppressed mode is also damped by the same mechanisms as a normal mode. In the case of envelope modes for stars low on the RGB, this damping is created by convective motions near the surface of the star \citep{Dupret_2009}. The equilibrium energy of the suppressed mode is \begin{equation}  \label{eqn:esup}  \dot{E}_{\rm in} = \dot{E}_{\rm out} = E_{\rm ac} \bigg[\gamma_{\rm ac} + \frac{T^2}{2 t_{\rm cross}} \bigg],