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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 equal, so that  $\dot{E}_{\rm in} = \dot{E}_{\rm out} = E_{\alpha} \gamma_\alpha$. 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 is