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\section{Introduction}  Despite rapid progress in the discovery and characterization of magnetic fields at the surfaces of stars, very little is known abouttheir  internal stellar  magnetic fields. This has prevented the development of a coherent picture of stellar magnetism; for example magnetism. For example,  it is not clear if some of the magnetic flux observed at the surface of main sequence stars can be conserved through the various phases of stellar evolution and be responsible for the existence of strongly magnetized compact remnants (magnetic such as magnetic  white dwarfs and neutron stars \citep{Wickramasinghe_2000,Duncan_1992}). \cite{Wickramasinghe_2000,Duncan_1992}.  Magnetic fields at stellar surfaces are routinely observed through their Zeeman spectral signature \citep{Landstreet_1992}. %A star's magnetic flux can be inherited from the gas cloud from which the star is formed, or generated by a dynamo \citep{Brandenburg_2005}. \cite{Landstreet_1992}.  About 5-10\% of main sequence A stars are observed to have large scale, predominantly dipolar magnetic fields with surface strengths 0.3-30kG $0.3$-$30\, {\rm kG}$  (Ap stars, see e.g. \citealt{Auri_re_2007}). \cite{Auri_re_2007}).  Surface magnetic fields have also been detected in a handful of evolved red giant stars \citep{Auri_re_2015}. \cite{Auri_re_2015}.  In Ap stars, the fields show little or no time evolution, which together with the existence of stable magnetic configurations \citep{Braithwaite_2004,Duez_2010} \cite{Braithwaite_2004,Duez_2010}  supports the notion that they are not generated by a contemporary magnetic dynamo but rather inherited from the star formation phase (i.e. (i.e.,  a fossil field). After exhausting hydrogen in their cores, most main sequence stars evolve up the red giant branch (RGB). During this phase, the stellar structure is characterized by an expanding convective envelope and a contracting radiative core. Acoustic waves (p modes) in the envelope can couple to gravity waves (g modes) in the core \citep{Bedding_2014}. \cite{Bedding_2014}.  Consequently, non-radial stellar oscillation modes become mixed modes that probe both the envelope (the p mode cavity) and the core (the g mode cavity). % Acoustic waves excited by turbulent convection in the envelope can propagate through the star and be used to %probe Space-based asteroseismology has opened a window into  the stellar interiors. Asteroseismology of thousands interiors  of red giants has just become giants. Mixed modes \cite{Beck_2011} have made it  possiblethanks to the %space satellites CoRoT and Kepler. During the red giant branch (RGB) the frequency of stochastically generated %acoustic waves (p-modes) becomes comparable  to the frequency of internal gravity waves (g-modes) in the radiative %core of the star. In this situation a crosstalk distinguish  between p-modes hydrogen  and g-modes becomes possible if enough energy can %leak through the evanescent region, which is located between the acoustic cavity and the gravity-waves cavity and %which extent depends on the harmonic degree ($\ell$) of the mode.  %This gives rise to standing waves with a mixed nature (mixed modes). helium-burning red giants \cite{Bedding_2011,Mosser_2014}.  Therestoring force for these waves is the %pressure gradient in the envelope and gravity in the core.   %The  rotational splitting of mixed modes has been used to determine the degree of radial  differential rotation in red %giants interiors, giants,  revealing that the core cores  of these red giant  stars is rotating about 10 times rotate  faster than their envelope %\cite{Beck_2011}. envelopes \cite{Beck_2012,Mosser_2012}.  %This is because, as a red giant increase its radius, the frequency $\omega$ The amplitudes  ofp-modes decreases and becomes comparable to  the frequency of waves in stellar oscillations depend on  the g-mode cavity.  %In this situation some interplay between driving and damping  of the energy in the p-modes can leak into the g-modes cavity, where waves modes \cite{Dupret_2009}. Interestingly, a significant group of red giants  with frequency $\omega < N$ can be excited ($N$ is suppressed dipole modes were identified using {\it Kepler} observations (e.g., \cite{Mosser_2011}, see Figure \ref{fig:moneyplot}). These stars have normal radial pulsation modes (spherical harmonic degree $\ell=0$), but exhibit low-amplitude dipole ($\ell=1$) modes. Until now,  the Brunt-Vaisala frequency). suppression mechanism was unknown \cite{Garcia_2014}. Below, we demonstrate that dipole mode suppression results from strong magnetic fields within the cores of these red giants.  Space-based asteroseismology has opened a window into the interiors of red giants. Mixed modes \citep{Beck_2011} have made it possible to distinguish between hydrogen and helium-burning red giants \citep{Bedding_2011,Mosser_2014}. The rotational splitting of mixed modes has been used to determine the degree of radial differential rotation in red giants, revealing that the cores of red giant stars rotate faster than their envelopes \citep{Beck_2012,Mosser_2012}  %but much slower than predicted by theory \citep{Cantiello_2014}.   The amplitudes of these oscillations depend on the interplay between driving and damping of the modes \citep{Dupret_2009}. Interestingly, a significant group of red giants with suppressed dipole modes were identified using {\it Kepler} observations (e.g., \citealt{Mosser_2011}, see Figure \ref{fig:moneyplot}). These stars have normal radial pulsation modes (spherical harmonic degree $\ell=0$), but exhibit low-amplitude dipolar ($\ell=1$) modes.  %They comprise about $20 \%$ of stars on the early red giant branch (RGB) in the sample presented in \citet{Mosser_2011}.   Until now, the suppression mechanism was unknown \citep{Garcia_2014}. Below, we demonstrate that dipole mode suppression results from strong magnetic fields within the cores of these red giants.  %Here, we demonstrate that the presence of a strongly magnetized core suppresses the visibility of dipolar modes via a ``magnetic greenhouse" effect. We show that magnetic suppression reduces the visibility of dipole modes to the level observed by \citet{Mosser_2011} in suppressed dipolar pulsators, suggesting these stars host strong magnetic fields in their cores. We develop a novel asteroseismic technique that places tight constraints on (and in some cases yields measurements of) the magnetic fields in red giant cores.