deletions | additions       diff --git a/Early RGB.tex b/Early RGB.tex  index 96f2b29..cbf72e4 100644  --- a/Early RGB.tex  +++ b/Early RGB.tex 
...
Our calculations confirm the results of \citet{Eggenberger:2012}. Models that only include angular momentum transport due to rotational instabilities and circulations fail to reproduce the splittings observed in the RGB star $\KIC$ (which, using the relation $P_{c} \simeq (2\delta\nu_{\rm max}$)^{-1}, results in the estimate for the core rotation shown as a dot in Fig.~\ref{omega}). The resulting cores are so rapidly rotating that the the perturbative approach to the splitting calculation is no more justified. Even models with an extremely slow initial rotation of $1 \kms$ result in rotational splittings one order of magnitude larger than the observed ones, which clearly shows this class of models can not explain the observations. This is in perfect agreement with the calculations of \citet{Eggenberger:2012}, even if the implementation of the physics of rotation is quite different in the GENEVA code compared to MESA \citep[See Sec.6 in ][and references therein]{Paxton:2013}.   The evolution of core rotation during the early RGB for our models is shown in Fig.~\ref{period}. Here the value shown for $P_{\rm c}$ is a mass average of the rotational period in the region below the maximum of the energy generation $\epsilon_{\rm nuc}$ in the H-burning shell (see e.g. Fig.~\ref{kernels}). This is already showing that our cores seem to rotate about 1 to 3 orders of magnitude faster than the values inferred by asteroseismology. Note that during this phase the mass of the core increases only slightly (See Fig.~\ref{kipp.mass}).  The work of \citet{Mosser:2012} reveals that the cores of stars in the mass range 1.2...1.5$\mso$ {\bf spin down} ascending the early RGB as $P_{\rm c} \propto R^{0.7\pm0.3}$, while our stellar evolution calculations show spin up with different slopes ($P_{\rm c} \propto R^{-0.6}$ R^{-0.58}$  for models including ST and $P_{\rm c} \propto R^{-1.7}$ for models only including angular momentum transport by rotational instabilities), depending on the assumptions for angular momentum transport (Fig.~\ref{period}). This is clearly showing that the amount of torque between core and envelope during the RGB evolution is underestimated in the models. Of course to carefully compare the rotation rates in the models with the ones derived from the observations one has to calculate the relevant eigenfunctions for the mixed modes. This allows to calculate the rotational kernels $K_{n,\ell}(r)$ and compute the predicted splittings (See Fig.~\ref{kernels} and Sec.~\ref{splittings}). The results of a detailed comparison for the predicted splittings of $\KIC$ as function of different initial rotational velocities and physics of angular momentum transfer is shown in Fig.~\ref{splittings}. The splittings have been calculated using the ADIPLS code and the MESA background structure at the location that matches the asteroseismic properties of the star.  Overall we found that the models including angular momentum transport due to Spruit-Tayler magnetic fields \citep[which are generated by differential rotation in radiative regions][]{Spruit:2002} do a much better job, but still result in rotational splittings on the order of $1\mu$Hz (Fig.~\ref{splitting}) which overestimate the core rotation rates by a factor of $\sim10$ (See Fig.~\ref{omega} and Fig.~\ref{period}). We explored if an increase in the efficiency of the ST mechanism could reconcile the models with the observations. However even increasing the efficiency of the diffusion coefficient resulting from the magnetic torques by a factor 100 results in a very small change in the overall coupling.