## 4. Effects of the rotationally induced mixingTo study the effects of the rotationally induced mixing, we have computed a 40 model with , including in addition to the hydrostatic effects discussed above, the effects of mixing of the chemical elements. The mixing of the chemical species, modelised through a diffusion equation in our rotating stellar models, intervenes through three hydrodynamical processes: the horizontal and vertical turbulence induced by the shear and the meridional circulation. The diffusion coefficient , which accounts for the effects of the horizontal turbulence induced by the shear and of the meridional circulation, exerts its effect whenever turbulent and circulation motions are sustained. The same is true for the action of , which describes the effects of the vertical turbulence induced by the shear. But its action is in addition submitted to the Richardson criterion which states when the shear is large enough to produce vertical mixing. Let us recall that for a radiative zone, the Richardson stability criterion becomes (Maeder & Meynet 1996) where and , measure
the strength of the shear and that of the where . Current symbols are used (Kippenhahn & Weigert 1990, see also Maeder & Meynet 1996). On Fig. 5, we present the profiles of various physical quantities inside the model with a hydrogen mass fraction at the centre equal to . Let us first concentrate on the semiconvective zone. We can note the following points: 1) The semiconvective zone encompasses nearly all the region where
there is an important
The same situations occur during the whole H-burning phase.
Comparing Figs. 6 and 7 which show the profiles of the diffusion
coefficients and of the hydrogen in seven models during the H-burning
phase, one immediately sees that where
From these considerations, one can conclude that the rotationally
induced mixing will have a very limited impact on the chemical
profiles and subsequently on the stellar structure. This is indeed the
case. On Fig. 8 the profile of the hydrogen mass fraction, at the
end of the MS, inside the stellar model obtained with rotationally
induced mixing, is compared with the one in the standard model
(without rotation). The action of in the
rotating model gives birth to a series of intermediate convective
zones which are nearly totally absent in the standard model. Apart
from these differences the general shapes of the two profiles are
quite similar. In particular, the sizes of the convective cores are
the same and no significant changes of the surface abundances are
observed in the rotating model. The main sequence lifetimes of the two
models differ by less than 0.4%. The similarity of the two models is a
consequence of the very strong inhibiting effect of the
Let us note that this conclusion on the inhibiting effect of the
© European Southern Observatory (ESO) 1997 Online publication: June 30, 1998 |