2 v 1 2 9 Se p 20 04 Rotation and Mixing in Massive Stars : Principles and

The main instabilities induced by rotation in stellar interiors are described. We derive from first principles the general equation describing the transport of the angular momentum. The case of the transport of the chemical species is also discussed. As long as the mass loss rates are not too important, meridional currents, by advecting angular momentum from the inner regions to the outer layers, accelerate the stellar surface during the Main Sequence phase. A 9 M ⊙ stellar model at solar metallicity with an equatorial velocity at the beginning of the core H–burning phase equal to 340 km s −1 reaches the break– up limit during the MS phase. The model with an initial velocity of 290 km s −1 approaches this limit without reaching it. The models with 290 km s −1 and 340 km s −1 predict enhancements of the N/C ratio at the end of the MS phase equal to 2.8 and 3.2 times the initial value respectively. 1. The main instabilities in a rotating star Recent discussions of the various instabilities induced by rotation may be found in Maeder & Meynet (2000), Heger & Langer (2000), and Talon (2004). Among the most important instabilities are the secular shear instability and the merid-ional circulation. These instabilities drive the transport of the chemical species and of the angular momentum. Let us briefly recall the physical principles underlying these two instabilities. In a rotating star local radiative equilibrium cannot be achieved (Von Zeipel 1924; Eddington 1925; Vogt 1925). As a result some parts of the star are heated while others are cooled. The buoyancy forces then drive a large scale motion, called the meridional circulation. Meridional circulation, contraction/expansion of the stellar layers, and convection create gradients of the angular velocity inside the star. These gradients produce instabilities known as shear instabilities. The physical reason for this instability lies in the fact that the minimum energy state of a differentially rotating fluid is solid body rotation. The star will tend to approach this state by homogenizing the angular velocity by turbulent mixing. In a radiative zone, the vertical stable density stratification counteracts both the shear and meridional instability. In that respect the µ–gradients play a key role as a stabilizing agent. These gradients may even, depending on the physics involved in the model, completely inhibit the mixing (Meynet & Maeder 1997). There are different methods in the literature for accounting for …