Hydrodynamical instabilities in the envelopes of main-sequence stars - Constraints implied by the lithium, beryllium, and boron observations

The abundances of lithium, beryllium, and boron in main-sequence stars are studied in view of their implications on the hydrodynamics in stellar interiors. Since they are destroyed by nuclear reactions relatively close to the surface, these elements can give a clue to the macroscopic transport processes occurring in stellar envelopes. Furthermore, as beryllium is destroyed deeper than lithium, their relative abundances tell us about the variation of the macroscopic transport with depth. The determination of the macroscopic transport can also indicate in which stars "micro- scopic" diffusion processes can be important. Throughout this paper, "microscopic diffusion" stands for the diffusion of elements due to the effect of the gravity, the radiation force, the temperature gradient, and the concentration gradient, while "turbulent diffusion" is used for the macroscopic diffusion due to turbulence. Theoretical variations of the abundances of lithium, beryllium, and boron induced by a combination of either a laminar meridional circulation or a turbulent diffusion with microscopic diffusion and nuclear destruction have been computed. The microscopic diffusion and nuclear destruction of these elements have been computed exactly. The velocity of meridional circulation and the turbulent diffusion coefficient have been introduced as parameters. A fitting of the theoretical abundance variations with the observed ones give severe constraints on the allowed macroscopic motions in main-sequence stars. A consistent model emerges, for which we suggest observational tests. In the Sun, overshooting is probably the basic transport process below the convection zone. Neither microscopic diffusion nor laminar meridional circulation coupled with nuclear destruction can account for the observations. Turbulence is the only process which can lead to both the observed abundance of lithium (1/100 of normal) and of beryllium (roughly normal). The turbulent diffusion coefficient must decrease with depth and have a value larger than 1000cm2 s ' in the lithium nuclear destruction zone, and smaller than 500 cm2 s -` in the beryllium one. In F stars, overshooting below the convection zone can be as important as in the Sun. In rapidly rotating F stars, meridional circulation can also become important and prevent diffusion processes under the "overshooting zone," where the turbulent diffusion coefficient induced by overshooting becomes smaller than the microscopic diffusion coefficient. This will occur if the circulation velocity is larger than about 10- `0/p cm s-'. However, the circulation velocity must be smaller than about 10 - 8/p cm s -` for lithium to remain normal in these stars. In slowly rotating F stars, it is possible that microscopic diffusion occurs below the overshooting zone and leads to lithium and beryllium depletion. In this frame the Be-deficient stars (observed at effective temperatures between 6600 K and 7400 K by Boesgaard) can be a prolongation of the Am sequence. An observational test for this model would be found in a detailed spectroscopic analysis of these stars, as we would expect random abundance variations of metals in their atmospheres. If this hypothesis were ruled out by the observations, we would have to turn to some internal effects (as a rapidly rotating core) to account for these stars. In slowly rotating A stars (e.g., Am stars), we expect either overabundances or underabundances of the light elements. The Be and B deficiencies in Sirius observed by Praderie et al. can be accounted for by microscopic diffusion processes within the general explanatory scheme for Am stars. Subject headings: convection - hydrodynamics - stars: abundances - stars: interiors