deletions | additions       diff --git a/Mode Visibility.tex b/Mode Visibility.tex  index fffb4c8..fd35b4b 100644  --- a/Mode Visibility.tex  +++ b/Mode Visibility.tex 
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\subsection{Mode Visibility}  In the absence of magnetic suppression, each mode receives a stochastic energy input $\dot{E}_{\rm in}$ \cite{Dupret_2009}. At its time-averaged equilibrium amplitude, the energy input and damping rates of the mode are equal: $\dot{E}_{\rm in} = \dot{E}_{\rm out} = E_{\alpha} \gamma_\alpha$, where $E_{\alpha}$ is the energy contained in the mode and $\gamma_\alpha$ is its damping rate.  Modes suppressed via the magnetic greenhouse effect have an extra source of damping determined by the rate at which energy leaks through the evanescent region separating the acoustic cavity from the g-mode cavity. For suppressed modes, we assume that any mode energy which leaks into the g-mode cavity is completely lost via the magnetic greenhouse effect.   Given some mode energy contained within the acoustic cavity, $E_{\rm ac}$, the rate at which mode energy leaks into the core depends on the transmission coefficient through the evanescent region ($T$) and the wave crossing time $\tau_{\rm cross}$ across the acoustic cavity. The suppressed mode is also damped by the same mechanisms as a normal mode, which is mostly occurring in the acoustic cavity at a rate $\gamma_{\rm ac}$. One can show that the expression for the ratio of visibilities between modes that are suppressed by the the magnetic greenhouse effects and normal modes is   \begin{equation}  \label{eqn:vis} 
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\end{equation}  Where we used the fact that the large frequency spacing is $\Delta \nu \simeq (2 t_{\rm cross})^{-1}$ \citep{Chaplin_2013} and have defined $\tau_{\rm ac} = \gamma_{\rm ac}^{-1}$.  The value of $T^2$ can be easily calculated from a stellar model, whereas the envelope life-time $\tau_{\rm ac}$ is approximately equal to the life-time of radial modes (because they have all their energy in the acoustic cavity). For stars ascending the RGB below the bump, $\tau_{\rm ac} \sim 10 \, {\rm days}$ \citep{Dupret_2009}.  A comparison between the theoretical prediction for the visibility of dipole modes suppressed by the magnetic greenhouse effect and the observations of \cite{Mosser_2011} is shown in Fig.~\ref{fig:moneyplot}.