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In principle, it is possible that another symmetry-breaking mechanism within the core could suppress dipole mode amplitudes. The only other plausible candidate is rapid core rotation. In order for rotation to strongly modify the incoming waves such that they will be trapped in the core, the core must rotate at a frequency comparable to $\nu_{\rm max}$, roughly two orders of magnitude faster than the values commonly observed in red giant cores \cite{Beck_2011,Mosser_2012,deheuvels_2014}. The suppressed pulsator KIC 8561221 \cite{Garcia_2014} does not exhibit rapid envelope rotation and disfavors the rotation scenario.  A magnetic field of amplitude $B > 10^4 \, {\rm G}$ (see Figure \ref{fig:Bc}) could be present in the core of a red giant if it retains a fossil field from star formation, or if a convective core dynamo was at work during the main sequence (supplementary online text). These strong fields may reside within the inner core with little external manifestation apart from the suppressed visibility of the dipole modes. However, 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}. The {\bf inferred core field strength of $B_r \gtrsim 1.5 \times 10^7 \, {\rm G}$ in KIC 8561221} KIC8561221}  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. A detailed analysis of a large population of red giants with suppressed dipole modes will put strong constraints on the amplitude and evolution of internal magnetic fields in stars of different masses. The asteroseismic technique described in this paper can also be extended to red clump stars burning helium in their cores. Observations of dipole mode suppression (or lack thereof) in clump stars will also put important constraints on the internal magnetic fields of the immediate progenitors of white dwarfs. 
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