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Matteo Cantiello added KIC8366239.tex
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\subsection{The red giant KIC 8366239}
We have chosen to model the red giant $\KIC$, for which \citet{Beck:2012} have observed a minimum rotational splitting of mixed modes of $\delta\nu_{n,\ell} = 0.135\pm0.008 \muhz$, arising from a p-dominated mode (mostly probing the slowly rotating stellar envelope). On the other hand the observed maximum values for the g-dominated mixed modes (mostly living in the stellar core) is on the order $0.2\muhz$. This confirmed the theoretical expectation that the core of this red giant is rotating faster than its envelope. However the inferred ratio is not very large, implying a ratio of order 10 in the rotation rate between core and envelope ($\Omega_{C}/\Omega_{E}$). This is at odd with the expectations coming from models that only include transport of angular momentum from rotational instabilities and circulations, predicting a ratio $\Omega_{C}/\Omega_{E} \ga 10^3$ for this object \citep[][, this work] assuming typical initial rotational velocities\footnote{Models with very slow initial rotation ($1\kms$) can not reproduce the observation either}. {Eggenberger:2012} compared to values. Similar to \citet{Eggenberger:2012} we adopt an initial mass of $1.5\mso$ and calculate models assuming different physics for angular momentum transport. We select the background structure of the different calculations by matching the global asteroseismic properties of $\KIC$ (the frequency of maximum oscillation power, $\nu_{\rm max}$, and the large frequency separation $\Delta \nu$). These are then used in ADIPLS to calculate the splitting of mixed modes for the different assumptions on the angular momentum transport mechanisms at work.
