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\section{Discussion and Conclusions}  %The striking agreement between our calculation of suppressed dipole mode visibility and the observations of \citet{Mosser_2011} (see Figure \ref{fig:moneyplot}) conclusively demonstrates that the dipole mode suppression arises from a phenomenon within the core.  We %We  have demonstrated that strong magnetic fields in the cores of red giants create a greenhouse effect, trapping mode energy within the core and suppressing mode visibility at the surface. Dipole ($\ell=1$) modes are most sensitive to the core and therefore are affected the most. We predict that $\ell=0$ modes in suppressed oscillators will be unaffected (since they do not propagate within the core), while $\ell=2$ modes will be slightly suppressed, and $\ell=3$ modes should exhibit very little suppression. The magnetic greenhouse mechanism that operates in suppressed dipole oscillators is unrelated to the suppression of solar-like oscillations in stars exhibiting surface magnetic activity \citep{Chaplin_2011}. In the latter case, the suppression likely arises from magnetic inhibition of convective motions and suppresses the amplitudes of all oscillation modes, not just the dipole modes. 
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%but we argue this is an unlikely explanation for most suppressed pulsators (see details in the supplementary material). Moreover the magnetic greenhouse effect makes a clear prediction: that for stars with frequency of maximum power similar to the critical magneto gravity frequency $\nu_{\rm c}$, dipole modes with $\nu >\nu_{\rm c}$ will be unaffected, while those with $\nu <\nu_{\rm c}$ should show suppression. KIC 8561221 displays this exact behavior, supporting the magnetic greenhouse mechanism.  For the magnetic greenhouse effect to operate, stars red giants  must have magnetic fields with a radial component $B\gtrsim 10^4 10^4-10^5  \, {\rm G}$ (see Figure \ref{fig:Bc}) around the location of the H-burning shell. Fields of similar amplitude have been discussed in order to explain the suppression of thermohaline mixing in a small fraction of red giant stars, as inferred from the observations of their surface abundances \cite{Charbonnel_2007}. Core magnetic fields with these characteristics could be present if the star retained a fossil field with surface amplitude $\sim 1 {\rm kG}$ on the main sequence, from star formation,  or if a convective core dynamo was at work during the main sequence. These strong fields may reside within the inner core with little external manifestation apart from the suppressed visibility of the dipole modes. In the early red giant KIC 8561221 (\cite{Garcia_2014}), we have The  calculated a radial core  field strength of  $B_r \approx 1.5 \times 10^7 \, {\rm G}$ at the H-burning shell. This star demonstrates that in KIC 8561221 shows  very strong magnetic fields ($B \gg 10^6 \, {\rm G}$) can exist within the radiative cores of early RGB stars. Since these fields are likely inherited from previous stages of stellar evolution, slightly weaker ($B \gg 10^5 \,{\rm G})$ fields likely exist within the cores of some main sequence stars. %(sub-equipartition magnetic fields are easily above $B \sim 10^4 {\rm G}$).