Jim Fuller edited Introduction.tex  almost 9 years ago

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Magnetic fields at stellar surfaces are routinely observed through their Zeeman spectral signature \cite{Landstreet_1992}. About 5-10\% of main sequence A stars are observed to have large scale, predominantly dipolar magnetic fields with surface strengths $0.3$-$30\, {\rm kG}$ (Ap stars, see e.g. \cite{Auri_re_2007}). Surface magnetic fields have also been detected in a handful of evolved red giant stars \cite{Auri_re_2015}. In Ap stars, the fields show little or no time evolution, which together with the existence of stable magnetic configurations \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., 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 \cite{Bedding_2014}. {\bf \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). Space-based asteroseismology has opened a window into the interiors of red giants. Mixed modes \cite{Beck_2011} have made it possible to distinguish between hydrogen and helium-burning red giants \cite{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 \cite{Beck_2012,Mosser_2012}.