| |
*Astron. Astrophys. 323, 831-838 (1997)*
## 1. Introduction
Rotation and shear mixing are becoming increasingly important
physical ingredients that are not to be omitted in the new run of
evolutionary calculations. They are both believed to be responsible
for the onset of macroscopic motions in the stellar plasma resulting
in enhanced mixing of chemical elements and the maintenance of angular
momentum transport phenomena. In recent years, in particular, shear
mixing has been frequently invoked to explain the unexpected degree of
enrichment in heavy elements in the atmospheres of massive MS stars
(Herrero et al. 1992; Venn 1995). Also, mixing processes can be
inferred to operate within the shear layer at the base of the
convective envelope of the Sun, thus possibly explaining the shallower
helium profile deduced by helioseismological data as compared to solar
model solutions with helium settling (Gough et al. 1996).
Unfortunately, the thresholds for shear induced instabilities and the
magnitude of the ensuing transport phenomena are badly known, and the
few works devoted to the study of their effects on stellar evolution
calculations remain in an exploratory phase.
The problem of the observed enrichment in metals at the surface of
fast rotating massive stars has been studied in a first paper by
Meynet & Maeder (1996), who remark that the common understanding
of the Richardson criterion proved of formidable efficacy in
preventing any significant mixing in regions where large
*µ*-gradients are generated in consequence of nuclear
evolution. In that respect let us recall that the Richardson
criterion, in its original form, imposes a threshold, namely
for shear mixing in a plane-parallel, radiative
zone (*U* being the horizontal velocity; the other symbols are
defined below). According to Maeder (1996), it is possible to solve
the present theoretical discrepancies if one *supposes* that a
fraction of the local energy excess available in radiative shear flows
is degraded by turbulence. This working hypothesis implies that even
in regions stable according to the Ledoux criterion, partial,
turbulent mixing occurs within a fraction of the hydrogen burning
timescale, determining the progressive erosion of the
*µ*-barriers and the consequent He- and N- enrichments in
fast rotating O-stars. Of course, the existence of *semiconvective
shear zones*, where the Richardson number ,
can only be assessed by confronting all their logical consequences
with carefully selected observations.
As a matter of fact, turbulent transport in stellar radiation zones
has a rather long history, which goes back to the first proposition of
Schatzman (1969) to explain the chemical composition at the surface of
the Sun and solar-like stars by a mild but efficient transport of
matter. Since then, much theoretical work has been devoted to the
study of its possible origin, soon recognizing that only shear
instabilities may reach a turbulent state strong enough to actually
mix the stellar material (Zahn 1983, 1990). In general, shear
instabilities depend on the exact profile of *U*, the horizontal
components are likely more vigorous and of larger extent, so that one
should account for the three dimensional character of the motion field
in deriving turbulent diffusivities that are necessarily anisotropic
(Zahn 1991). Here, however, and more modestly in view of the
aforementioned considerations on massive stars evolution, our purpose
is just to demonstrate that shear induced semiconvection is in fact a
natural prediction of a linear stability analysis of the basic
hydrodynamic equations. Our approach is an extension of the classical
work of Kato (1966) on chemically stratified Boussinesq mediums, when
the inertial corrections are included in the force law equation.
Additionally, we obtain a revised criterion for the onset of
convection, and provide a way to compute the diffusion coefficient of
scalar fields in presence of rotation, shear and thermal conductivity.
These results, of modest computational effort and easy implementation
in existing codes, could help in gaining some first order, deeper
insight on massive stellar structure and evolution.
© European Southern Observatory (ESO) 1997
Online publication: May 26, 1998
helpdesk.link@springer.de |