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\section{Discussion}  The striking agreement between the theoretical expectations for the $\ell=1$ modes visibility and the observations of \citet{Mosser_2011} conclusively shows that the energy sink for suppressed dipolar oscillations is located in the stellar core (see Fig.~\ref{fig:moneyplot}). The core acts as an efficient energy sink: all the waves leaking through the evanescent region never couple back to the envelope modes. In this situation dipole modes are modes only in the envelope, with part of their energy leaking into the  core as running waves. Mixed modes do not exist in stars with suppressed $\ell=1$ modes. We have shown that the magnetic greenhouse effect can provide the required maximally efficient trapping, thanks to the symmetry breaking enforced by any plausible geometry of a (strong enough) magnetic field.  While it is possible that other symmetry breaking mechanisms could play a role similar to a strong magnetic field, we believe this is an unlikely explanation for the bulk of the suppressed dipoles sample (see details in the supplementary material). This is because the rotation rate required to modify the incoming waves such that they will be trapped in the core, is two orders of magnitude higher than the values commonly observed in the cores of these stars \citep{Beck_2011,Mosser_2012}. 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. The early subgiant star KIC 8561221 displays this exact behavior \citep{Garcia_2014}, demonstrating the reality of the magnetic greenhouse effect.