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:
where we use standard notations for the radius r and the density and where is the vertical (turbulent) viscosity. is the vertical component of the meridian velocity and is given by
where L is the luminosity, M the mass, g the gravity, P the pressure, the specific heat at constant pressure and T the temperature. and 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
where N is the Brunt-Väisälä frequency and K is the thermal diffusivity. The coefficient 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 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 present in stratified media by an effective diffusivity (cf. Chaboyer & Zahn 1992):
where is the nuclear production/destruction rate and is the microscopic diffusion; we assume . 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:
where is an unknown parameter of order unity (see Zahn 1992 for more details).
© European Southern Observatory (ESO) 1998
Online publication: June 26, 1998