deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 2b7e06e..4416439 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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%Stars are gravitationally bound, rotating spheroids of plasma, with rotation potentially playing an important role in their evolution and observable properties %\cite{Maeder:2009}. Despite this, we know little about their internal rotation profile and the mechanisms that contribute to angular momentum transport.   Different classes of transport mechanisms have been proposed, in particular hydrodynamical instabilities and circulations induced by rotation \citep[see][for a review]{Maeder:2000}, magnetic torques \citep{Gough:1998,Spruit:1999,Spruit:2002,Spada:2010} and internal gravity waves \citep[see e.g.,][]{Charbonnel:2005}. In the absence of strong mass loss, the bulk of the redistribution of angular momentum is expected to occur when shearing is generated during evolutionary episodes of expansion or contraction.   Most stars ignite hydrogen in a shell at the end of the main sequence. Above this shell the star begins to expand, while the core contracts. In the absence of a strong coupling between the core and the envelope, conservation of angular momentum implies requires  that the core spins up while the envelope spins down. This implies very rapidly rotating stellar cores and a shear layer between core and envelope. Evolutionary calculations that include angular momentum transport from rotational instabilities and circulations also predict rapidly rotating stellar cores at the end of stellar evolution \citep[e.g.,][]{Heger_Langer_Woosley_2000,larends_Yoon_Heger_Herwig_2008,Eggenberger:2012,Marques:2013}. This is at odds with the observed rotation rate of white dwarfs (WD) and neutron stars (NS). This can be somewhat remedied by including angular momentum transport due to magnetic torques in radiative regions \citep[Tayler-Spruit dynamo (TS)][]{Spruit:2002,Heger:2005,larends_Yoon_Heger_Herwig_2008}. In the era of space asteroseismology, the \textit{Kepler} satellite enabled the measurement of the core rotation in many red giants using the splitting of mixed modes \citep{Beck:2012,Deheuvels:2012,Mosser:2012}. Mixed modes are oscillations that have an acoustic component (p-mode) in the envelope and are g-modes (restoring force is gravity) in the stellar core \citep[see e.g.,][]{Beck:2011}.  \citet{2012A&A...548A..10M} showed that it is the rotation rate 
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the splitting of mixed modes \citep[see also][]{2013A&A...549A..74M}. This measurement   of the interior rotational state of an evolved star provides a new test for   theoretical ideas of angular momentum transport.  Similar to the case of compact remnants, models solely including angular momentum transport due to rotational mixing and circulations predict rotation rates 2 to 3 orders of magnitude higher than observed \citep{Eggenberger:2012,Marques:2013,Ceillier:2013}. While the adopted treatment of angular momentum transport is approximate approximate,  \citet{Marques:2013} have shown that even the most extreme of the physically motivated hydrodynamic mechanisms included in their code cannot yield the observed values. %They claim that ``the seismology of red-giant stars emphasize that an additional mechanism is needed to achieve a %slower core rotation of red-giant stars''.  Our goal is to assess whether models including transport due to TS magnetic fields agree more closely with the observations.  While the physics of the Tayler instability is secure, the existence of the Tayler-Spruit dynamo loop is debated on both analytical and numerical grounds \citep{Braithwaite:2006,Zahn:2007}. However observations of the spin rates of compact objects (WD and NS) are in much better agreement with models including this angular momentum transport mechanism \citep{Heger:2005,larends_Yoon_Heger_Herwig_2008}, which has also been discussed in the context of the rigid rotation of the solar core \citep{Eggenberger:2005}, but see also \citet{Denissenkov:2010}.  In Sec.~\ref{stev} we present the stellar evolution calculations and the details of the implemented physics.   Results for the evolution of core rotation during the early RGB are shown in Sec.~\ref{earlyrgb} for different angular momentum transport mechanisms. Results are compared to \Kepler \textit{Kepler}  asteroseismic observations of mixed modes in red giants. In Sec.~\ref{splittings} we show how the rotational splittings of mixed mode are calculated from the stellar evolution models using \ADIPLS. Sec.~\ref{beyond} presents the angular momentum evolution of our models beyond the early RGB. Predictions for the core rotation rates past the luminosity bump (Sec.~\ref{bump}), during core He-burning (Sec.~\ref{clump}) and in the WD stage (Sec.~\ref{wd}) are shown and compared to the asteroseismically derived values.   %In particular we begin showing models including different physics of angular momentum transport to explain the %rotational splittings observed in the red giant star KIC 8366239 \citep{Beck:2012}.   Overall %Overall  our results show that it is difficult, even in the presence of magnetic torques due to TS magnetic fields, to fully %fully  account for the evolution of the core rotation rate from the end of the main sequence to the WD stage. In Sec.~\ref{conclusions} we draw our conclusions and discuss possible future work.  %we discuss our results and up and show that it is difficult, even in the presence of magnetic torques due to TS %magnetic fields, to fully account for the evolution of the core rotation rate from the end of the main sequence to the %WD stage. We also show that a constant diffusivity, as discussed in \citet{Eggenberger:2012}, can not explain the full %core angular momentum evolution past core H exhaustion.