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\subsection{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. 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}  \frac{V_{\rm sup}^2}{V_\alpha^2} = \bigg[1 + \Delta \nu \tau_{\rm ac} T^2 \bigg]^{-1} \, ,