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Astron. Astrophys. 335, 959-968 (1998)

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1. Towards a consistent description of rotation induced mixing

During the last decade, special efforts have been devoted to improve the description of the mixing processes related to stellar rotation. The most recent works (see for example Pinsonneault et al. 1989, Zahn 1992, Maeder 1995, Talon & Zahn 1997) describe the evolution of the internal distribution of angular momentum in a self-consistent manner under the action of meridional circulation and of shear turbulence. The mixing of chemicals is then linked directly to the rotation profile, whereas previous studies made use merely of a parametric relation between the turbulent diffusivity and the rotational velocity (cf. e.g. Schatzman et al. 1981, Zahn 1983).

Such a self-consistent treatment was applied successfully by Talon et al. (1997) in the study of a 9 [FORMULA] star, modeling the transport of angular momentum by the meridional circulation as a truly advective process. The only assumption in this theory is that the turbulence sustained by the shear is highly anisotropic and relies on two free parameters; the first one describes the magnitude of the horizontal shears (cf. Zahn 1992) and the second one, the erosion of the restoring force due to both the thermal and the mean molecular weight stratifications (cf. Maeder 1995, Talon & Zahn 1997). These authors reproduce the slight abundance anomalies measured in B stars by Gies & Lambert (1992). They also show that the widening of the main sequence, which is generally attributed to convective overshooting in massive stars, may be due to the rotational mixing present in stars having a "typical" velocity for the spectral type considered.

Concerning low-mass stars, it has been shown that the hydrodynamical models relying on meridional circulation and shear fail to reproduce the solar rotation profile given by the helioseismic observations (Brown et al. 1989, Kosovichev et al. 1997): at the solar age, those models still have large [FORMULA] gradients which are not present in the Sun (see Chaboyer et al. 1995 and Matias & Zahn 1997). That conclusion has been reached independently by two different groups, using different descriptions for the transport processes. On one hand, the Yale group computed the evolution of angular momentum in low mass stars with a simplified description of the action of the meridional circulation which was considered as a diffusive process rather than as an advective process. The whole evolution of momemtum and chemicals was then due to diffusion only, with a free parameter that had to be calibrated to differentiate the transport of the passive quantities with respect to that of vectorial ones. Pinsonneault et al. (1990) were then able to reproduce the surface Li abundances for low-mass cluster stars (with effective temperature lower than 6500K). However, they obtained large rotation gradients within these stars which are excluded by helioseismology (Chaboyer et al. 1995). On the other hand, Matias & Zahn (1997) performed a complete study for the evolution of the Sun's angular momentum, where they took into account the advective nature of the meridional circulation. They also concluded that meridional circulation and shear turbulence are not efficient enough to enforce the flat rotation profile measured by helioseismology.

These results indicate that another process participates in the transport of angular momentum in solar-type stars, while the so-called wind-driven meridional circulation (Zahn 1992) is successful in more massive stars. In order to study the transition between solar-type and more massive stars and to identify the mass range for which the present description for the transport of angular momentum and chemicals relying only on rotation fails, we propose to use the measures of lithium and rotational velocities in galactic cluster stars.

We first review the observations of lithium abundances and rotation in the Hyades main-sequence stars, and summarize the difficulties of the various models proposed so far to explain the Li dip in F stars (Sect. 2). We recall the equations that describe the evolution of angular momentum due to meridian circulation and shear turbulence as well as the associated transport of chemicals (Sect. 3). We study the impact of rotational mixing on the lithium abundance in galactic cluster F stars, and compare this to the observations. Our models include both element segregation and rotation-induced mixing, and we treat simultaneously the transport of matter and angular momentum. The internal rotation profile thus evolves completely self-consistently under the action of meridional circulation as described by Zahn (1992) (see also Matias et al. 1997), and of shear stresses which take into account the weakening effect of the thermal diffusivity, as was first shown by Townsend (1958) (Sect. 4). We show that the blue side of the lithium dip is well reproduced within this framework, and that the process responsible for the shape of the solar rotation profile should become efficient only for stars on the cool side of the Li dip, where the external convection zone is thick enough. By achieving efficiently momentum transport, the global effect of this process would be to reduce the mixing due to the rotational instabilities in stars with effective temperature lower than [FORMULA] 6500K. The most likely candidates for this transport process are the gravity waves generated by the external convection zone (Schatzman 1993; Zahn et al. 1997; Kumar & Quataert 1997) and the large-scale magnetic field which could be present in the radiative interior (Charbonneau & MacGregor 1993; Barnes et al. 1997).

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© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998