Matteo Cantiello edited Introduction.tex  over 10 years ago

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\section{Introduction}  %Rotation in stars  Stars are gravitationally bound, rotating spheroids of plasma, with rotation potentially playing an important role in their evolution and observable properties \cite{Maeder:2009}. To account for the changes in the distribution of internal angular momentum during the long timescales of stellar evolution, modern stellar evolution codes include a treatment of angular momentum and chemical mixing due to rotational instabilities. In fact it has been shown that it is still possible to treat this problem in 1D if the star is well mixed on horizontal surfaces. The existence of strong anisotropic turbulence in stars is expected to enforce a constant composition and angular velocity on isobaric surfaces, the so-called ``shellular'' approximation \citep{Zahn:1992}. The impact of the centrifugal term can be easily included in the equation of stellar structure \citep{Endal:1976}, while the effect of transport of angular momentum and chemicals in the radial direction requires a simplified treatment of the rotational instabilities and circulations expected to arise in a rotating star \citep[See e.g.][]{Heger:2000,Maeder:2000}. Dynamo action seems to be ubiquitous in astrophysical plasma, and   the presence of magnetic fields can lead to efficient transport of angular momentum through magnetic torques. In radiative zones the presence of magnetic fields has been discussed to explain the final rotation rate of compact remnants \citep[both white dwarfs and neutron stars,][]{Suijs:2008,Heger:2005}.   % Effect of Rotation  This impacts observable properties of the star, as well as its evolution. Surface rotation can be measured using spectroscopic observations or from the modulation of surface features (e.g. stellar spots). Beneath the surface rotational instabilities and circulations do not only transport angular momentum, but can also lead to compositional mixing. Surface abundances can therefore change already during the main sequence of a rotating star \citep{Meynet2000,Maeder2012}.   The bulk of the redistribution of angular momentum occurs in the star due to structural changes. For example at the end of the main sequence most stars, after contracting due to the exhaustion of Hydrogen in their cores, ignite Hydrogen in a shell. Above this shell the star begins to expand, while the core continues its contraction. In the absence of a strong coupling between core and envelope, conservation of angular momentum implies that the core has to spin up considerably while the envelope spins down. This leads to very rapidly rotating stellar cores. Stellar evolution calculations that include only angular momentum transport from rotational instabilities predict very rapidly rotating compact remnants (white dwarfs, neutron stars and black holes) \cite{Heger_Langer_Woosley_2000,larends_Yoon_Heger_Herwig_2008}.