deletions | additions       diff --git a/Mode Visibility.tex b/Mode Visibility.tex  index 6423f03..7230ea3 100644  --- a/Mode Visibility.tex  +++ b/Mode Visibility.tex 
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\section{Mode Visibility}  Solar-like oscillations are driven by stochastic energy input in the acoustic cavity, which is located in the convective envelope. At its time-averaged equilibrium amplitude, the energy input and damping rates of the mode are equal \cite{Dupret_2009}.   %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.   Waves with angular frequency $\omega \sim \omega_{\rm max} = 2 \pi \nu_{\rm max}$ are excited via convective motions, the waves propagate downward as acoustic waves until their frequency is less than the local Lamb frequency for waves of angular degree $\ell$, i.e., until $\omega = L_l = \sqrt{l(l+1)} c_s/r$, where $c_s$ is the sound speed. At this boundary, part of the wave flux is reflected, and part of it tunnels through. The wave resumes propagating inward as a gravity waves when in reaches the radiative core where $\omega < N$, with $N$ is the Brunt-Vaisala 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. 
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\label{eqn:integral2}  T \simeq \bigg( \frac{r_1}{r_2} \bigg)^{\sqrt{l(l+1)}} \, ,  \end{equation}  where $r_1$ and $r_2$ are the boundaries of the evanescent region. In this case, the upper boundary occurs where $\omega=L_{\ell}$ and the lower boundary occurs where $\omega=N$, where $N$ is the Brunt-Vaisala frequency. $\omega=N$.  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 transmitted energy flux through the evanescent region 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 cavity is completely lost.   %via the magnetic greenhouse effect.