deletions | additions       diff --git a/Asteroseismic Calculations.tex b/Asteroseismic Calculations.tex  index 674cd24..437cd88 100644  --- a/Asteroseismic Calculations.tex  +++ b/Asteroseismic Calculations.tex 
...
{\bf TBD (Chris/JCD): Details about the ADIPLS calculations?}  \subsection{The red giant KIC 8366239}  We have chosen to model in detail the red giant $\KIC$, for which \citet{Beck:2012} have observed a minimum rotational splitting of mixed modes of $\delta\nu_{n,1} = 0.135\pm0.008 \mu$Hz, 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 $0.2-0.25\mu$Hz. 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 that the core is rotating only about 10 times more rapidly than the core. This is at odd with the expectations coming from models that only include transport of angular momentum from rotational instabilities and circulations, which assuming typical initial rotational velocities\footnote{Models with very slow initial rotation of $1\kms$ can not reproduce the observation either} either, see Fig.~\ref{splitting}}  predict a ratio of order $10^3$ between the angular velocity of the core and that of the envelope \citep[][ this work]{Eggenberger:2012}. Similar to \citet{Eggenberger:2012} for $\KIC$ 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 $\KIC$ (frequency of maximum oscillation power, $\nu_{\rm max}$, and large frequency separation $\Delta \nu$), as derived by \citet{Beck:2012}. The MESA background structure and rotational profiles are then used in ADIPLS to calculate the splitting of mixed modes for the different assumptions on the angular momentum transport. We show in Fig.~\ref{kernels} an example of the background rotational profile calculated by MESA, together with the radial integrals of the rotational kernels $K_{n,\ell}$ for $\ell=1,2$ calculated using ADIPLS. This figure shows how the p-dominated modes mostly probe the envelope of the star, where the angular velocity is quite low. The gravity dominated modes on the other hand tend to probe the radiative region below the H-burning shell, in which the angular velocity is higher. Note that higher $\ell$ modes have higher Lamb frequencies, implying a larger tunneling zone between the acoustic cavity in the envelope and the gravity modes region in the core. As a consequence a the modes become ``less mixed'', with $\ell=2$ p-modes (g-modes) being more p-like (g-like) than their $\ell=1$ analogue.