deletions | additions       diff --git a/Mode Visibility.tex b/Mode Visibility.tex  index e42e4c5..f4e124a 100644  --- a/Mode Visibility.tex  +++ b/Mode Visibility.tex 
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\section{Mode Visibility}  Solar-like oscillations are created by standing waves with frequencies near $\nu_{\rm max}$ that are driven by stochastic energy input from turbulent near-surface convection. These waves The value of $\nu_{\rm max}$ is determined by the evolutionary state of the star: more evolved stars have smaller $\nu_{\rm max}$. Waves excited near the stellar surface  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 local sound speed and $r$ is the radial coordinate. At this boundary, part of the wave flux is reflected, and part of it tunnels into the core. The wave resumes propagating inward as a gravity wave in the radiative core where $\omega < N$, where $N$ the buoyancy 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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\end{equation}  where $\Delta \nu \simeq (2 t_{\rm cross})^{-1}$ \citep{Chaplin_2013} is the large frequency separation, and $\tau_{0}$ is the damping time of a radial mode with similar frequency. The value of $T^2$ can be easily calculated from a stellar model, whereas the envelope life-time $\tau_{0} \sim 10 \, {\rm days}$ \citep{Dupret_2009,Corsaro_2012,Corsaro_2015} for stars ascending the red giant branch (RGB).  Fig.~\ref{fig:moneyplot} compares our estimate for suppressed dipole mode visibility (equation \ref{eqn:vis}) with the observations of \cite{Mosser_2011}. Our estimate closely aligns with the branch of stars classified by \cite{Mosser_2011} as suppressed pulsators. The striking agreement holds over a large baseline in $\nu_{\rm max}$. max}$ extending from the sub-giant branch to near the luminosity bump.  %The predicted visibility of equation \ref{eqn:vis} has no free parameters, although there is some uncertainty in the value of $\tau_0$. Additional scatter can be accounted for by a range of stellar masses, metallicities, and inclinations in the the observed sample.  We conclude that the cores of stars with suppressed dipole modes host a mechanism able to efficiently trap waves tunneling through the evanescent region. This is further supported by the normal $\ell=0$ mode visibility in suppressed pulsators (since radial modes do not propagate within the core) and the lack (or perhaps smaller degree) of suppression observed in $\ell=2$ modes by \citet{Mosser_2011}, as quadrupole modes have a smaller transmission coefficient $T$.