Expression (4.38), which is the main result of this work, shows that a µ-gradient can significantly reduce the velocity of the meridional circulation, since can be larger than by an order of a magnitude or even more.
Mestel (1963) was the first to take into account the gradient of chemical composition and he called "µ-currents" the contribution of the term to the meridional circulation (cf. 4.38). There are two differences here with his original treatment. First we no longer assume uniform rotation, but solve explicitely for the changes in the rotation profile. In other words, not only , but also evolves to stop the circulation in a star which does not lose angular momentum (Zahn 1992). And second the µ-gradient now enters in the entropy gradient: it acts there to reduce the strength of the meridional velocity (4.38).
Let us also note that the meridional circulation is generally studied in a purely radiative medium, i.e. with . In a semiconvective region, the usual expression without would predict an inverted circulation, going down at the pole and ascending at the equator in an uniformly rotating star. Also, it would predict an infinite velocity at the transition between the radiative and semiconvective zones. In case of alternance of radiative and semiconvective layers in massive stars, we would have a really strange situation! With expression (4.38) such an unphysical situation does not occur. Circulation behaves similarily in radiative and semiconvective zones, keeping its direction and the continuity of its amplitude.
Detailed numerical models are now being developed to quantitatively estimate the importance of the various effects studied in this work and to examine their consequences on stellar evolution and in particular for the surface abundance enrichments.
© European Southern Observatory (ESO) 1998
Online publication: June 2, 1998