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\subsection{Magnetic Greenhouse Effect}  \label{greenhouse}  The fate of magneto gravity waves in stellar interiors at the radius $r_{\rm MG}$ where they become evanescent is not totally clear. However, this issue has been examined in detail in the Sun's atmosphere, where outwardly propagating magneto-acoustic-gravity waves become magnetically dominated as they propagate upward  into regions of low plasma $\beta$. 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{Newington_2010}). (\cite{Newington_2009}).  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 matieral), as long as magnetic tension forces are strong as described above.  A similar effect likely occurs in stellar interiors, which we examine in more detail in the Supplementary Material. However, in either case, 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 dipolar ($\ell =1$, where $\ell$ is the spherical harmonic dependence of the angular structure of a wave) 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 completely trapped within the radiative core.\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.} 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.