SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


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

Previous Section Next Section Title Page Table of Contents

3. The transport processes: rotational mixing and microscopic diffusion

We calculate the destruction of lithium in F-type stars, assuming that rotational mixing is the only source of transport for angular momentum. The evolution of the interior radial differential rotation is calculated completely self-consistently, using the most complete description currently available for the following physical processes:

  • the advection of angular momentum by the meridional flow driven by the thermal imbalance in a rotating star, assuming that the rotation velocity is homogenized on isobars by anisotropic shear turbulence, as described by Zahn (1992);

  • the turbulent transport due to the vertical shear present in differentially rotating bodies, including the weakening effect of the thermal diffusivity on the density stratification (for details see e.g. Talon & Zahn 1997).

The complete equation for the transport of angular momentum is then

[EQUATION]

where we use standard notations for the radius r and the density [FORMULA] and where [FORMULA] is the vertical (turbulent) viscosity. [FORMULA] is the vertical component of the meridian velocity and is given by

[EQUATION]

where L is the luminosity, M the mass, g the gravity, P the pressure, [FORMULA] the specific heat at constant pressure and T the temperature. [FORMULA] and [FORMULA] depend respectively on the rotation profile and on the mean molecular weight gradients (for the complete expression, see Zahn 1992). The expression of the turbulent viscosity is

[EQUATION]

where N is the Brunt-Väisälä frequency and K is the thermal diffusivity. The coefficient [FORMULA] used here is the one that was found by Maeder (1995) when he rederived the criterion for shear instabilities assuming spherical geometry for the turbulent eddies. As was discussed by Talon & Zahn (1997), even though this is somewhat of an arbitrary choice, the exact value shouldn't differ much. In this study, we will use the value [FORMULA] and not consider it as a free parameter.

Microscopic diffusion of lithium, helium and metals, including gravitational and thermal settling, is taken into account (see Appendix for a description of the corresponding input physics).

Modeling the combination of the advective transport by the circulation and the strong horizontal diffusion [FORMULA] present in stratified media by an effective diffusivity [FORMULA] (cf. Chaboyer & Zahn 1992):

[EQUATION]

the evolution of a chemical concentration [FORMULA] is given by:

[EQUATION]

where [FORMULA] is the nuclear production/destruction rate and [FORMULA] is the microscopic diffusion; we assume [FORMULA]. The weakest point is this model is the magnitude of the horizontal diffusion coefficient. Here, we will use a parametric relation which links that coefficient to the advection of momentum:

[EQUATION]

where [FORMULA] is an unknown parameter of order unity (see Zahn 1992 for more details).

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1998

Online publication: June 26, 1998
helpdesk.link@springer.de