deletions | additions       diff --git a/Results2.tex b/Results2.tex  index 1e4e69c..ce2e58a 100644  --- a/Results2.tex  +++ b/Results2.tex 
...
\subsection{RGB}  We show in Fig.~\ref{omega} the evolution of the core angular velocity in a rotating $1.5\mso$ model for different assumptions of the internal angular momentum transport. The star is initially rotating with a surface velocity of about $50\kms$. %$150\kms$  The plot shows how the contraction of the core leads to different rates of spin up for the different models. On the other hand the expanding envelope slows down substantially, following the expected $P_{\rm rot} \propto R^2$ scaling from homologous expansion and angular momentum conservation (no substantial mass is lost in this phase). First we note that models including angular momentum transport due to rotation couple very weakly core and envelope, resulting on the lower RGB in very similar core rotation rates than in models with homologous contraction and angular momentum conservation (no angular momentum transport).   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 $\delta\nu_{n,\ell=1} $P_{c}  \simeq \frac{1}{2} \frac{\Omega_{c}}{2\pi}$, \frac{1}{2\delta\nu_{\rm max}}$,  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.   In particular 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 ($P_{\rm c} \propto R^{-0.6}$ for models including ST and $P_{\rm c} \propto R^{-1.7}$ for models only including rotational angular momentum transport), 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.