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\subsection{Magnetic Greenhouse Effect}  \label{greenhouse}  The fate of magneto In stars with field strengths exceeding $B_c$ (equation \ref{eqn:Bc}) somewhere in their core, incoming dipolar  gravity waves in stellar interiors will become evanescent  at the radius $r_{\rm MG}$ where they become evanescent is not totally clear. However, $B>B_c$. At  this issue has been examined in detail point, the waves must either reflect or be transmitted into the strongly magnetized region as Alfven waves. In both cases, we argue the waves will be prevented from returning to the surface of the star to be observed as solar-like oscillations.  An analogous process occurs  in the Sun's atmosphere, where outwardly propagating magneto-acoustic-gravity waves become magnetically dominated as they propagate upward into regions where the magnetic pressure is larger than the gas pressure. In this case, the reflection or transmission of the wave depends on the geometry of the magnetic field (\cite{Zhugzhda_1984}). Radial fields typically reflect outgoing waves, whereas sufficiently oblique (nearly horizontal) fields allow for transmission into Alfven waves which then propagate along the field lines. A similar effect likely occurs in stellar interiors (although large magnetic pressure is not required, see discussion in supplementary material), as long as magnetic tension forces are strong as described above. In RGB cores, the reflection/transmission process modifies the waves such that they will become trapped in the radiative zone. Let’s first consider waves that are transmitted into Alfven waves at $r_{\rm MG}$. The number of Alfven modes that can be excited is likely very high, due to the fact that the magnetic field has a large range of values and a non-trivial geometry in the region (stable magnetic equilibria require a mixture of toroidal and poloidal magnetic fields, (\cite{Braithwaite_2004,Braithwaite_2006,Duez_2010}). In fact the spectrum of Alfven modes is likely continuous (\cite{Reese_2004,Levin_2006}). An incoming $\ell=1$ magneto-gravity wave is therefore transmitted into Alfven waves with a broad spectrum of $\ell$ values. The Alfven waves will travel along field lines and could eventually transmit their energy back into magneto-gravity waves. However, even if this occurs, the energy will be spread over a large number of $\ell$ values.   Once a dipolar wave has its energy spread to a broad spectrum of $\ell$, it is doomed to remain within the core. The reason is that higher $\ell$ waves are trapped within the radiative core by a thicker evanescent region (see equation \ref{eqn:integral2}) separating the g-wave cavity in the core from the acoustic wave cavity in the envelope. Therefore, any wave energy with $\ell \gtrsim 3$ will be almost  completely trapped within the radiative core. Moreover, higher multipole magneto-gravity waves have shorter wavelengths and damp out more quickly than dipole waves. Hence, an initially dipolar magnetically altered wave will become trapped in the core until it dissipates, unable to tunnel back toward the surface to create an observable signature. %\footnote{For the same reason, mixed modes with $\ell \gtrsim 2$ are usually not observable in any red giants. Only the envelope modes can be seen, because the gravity-dominated modes in the core of the star are insulated by the thick evanescent evanescent region between core and envelope.}  
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We emphasize that the magnetic greenhouse effect arises not from the alteration of incoming wave frequencies, but rather due to modification of the wave angular structure. Such angular modification originates from the inherently non-spherical structure (since $\nabla \cdot {\bf B} = 0$) of even the simplest magnetic field configurations.  Finally, we note that magneto-gravity waves which are reflected at $r_{\rm MG}$ may be reflected onto the slow branch of magneto-gravity waves, since this branch has the same wavenumber as the fast branch at $r=r_{\rm MG}$. This process is known to occur for reflected waves in the solar atmosphere (\cite{Newington_2009,Newington_2011}). In our case, as the slow waves propagate back outward into regions with weaker magnetic fields, their wavenumber increases rapidly (see Figure \ref{fig:Prop}). supplementary material).  The slow waves will thus dissipate very rapidly via radiative diffusion or non-linear effects, diffusion,  the end result being that they will not be observed as oscillations at the stellar surface.