## 4. The efficiency of rotational mixing in F-stars## 4.1. Constraints from the observed surface rotation in galactic cluster F starsAs can be seen in Fig. 1, the stars of the Li dip are peculiar as far as their rotational history is concerned. From the observational data, one may conclude that the physical processes responsible for the surface velocity are different or operate with different time scales when one goes to lower effective temperature: stars hotter than 6900 K still have their initial velocities (when compared to the velocity distribution observed in younger clusters) while stars cooler than 6400 K have been very efficiently spun down at the age of the Hyades (700 Myr). This behavior is linked to the variation of the thickness of the external convection zone (Fig. 2 top). Indeed, the hottest stars have only a very shallow surface convection zone which is not an efficient site for magnetic generation via a dynamo process. The coolest stars have a deeper surface convection zone, thus sustaining a strong magnetic field which spins down the outer layers efficiently. The rapid diminution with increasing effective temperature in the efficiency of magnetic braking observed for stars of the Li dip is a clear signature of the rapid decrease in mass of the envelope convection zone in stars of the corresponding effective temperature. Let us note that the diminution of the moment of inertia of the convective envelope as the effective temperature increases implies an even more drastic change in the magnitude of the magnetic torque than the variation of the surface velocities indicate.
We calculate Li destruction in models of different stellar masses within the theoretical framework described in Sect. 3. We use the statistical study of rotation velocities in the Hyades performed by Gaigé (1993) in order to estimate the spin down associated to stars of different masses: we take an initial velocity of 100 km/s that corresponds to the mean velocity of hot stars ( K) and that is consistent with velocities of cooler stars measured in younger clusters. The resulting velocity at the age of the Hyades (Fig. 2 bottom) corresponds to the average value for stars of a given effective temperature. We also calculate the dispersion expected in the Li abundances from different rotational histories using the values from Gaigé's study. The corresponding initial velocities are 50 and 150 km/s. The main characteristics of the stellar models, together with the rotation velocities and the lithium and beryllium depletion factors at different ages (corresponding to the ages of the clusters shown in Figs. 6 and 7) are given in Table 1.
## 4.2. The depletion on the blue side of the Li dip
The predictions for the lithium abundance at different ages are given in Figs. 6 and 7, and compared to observations in galactic clusters. We also show predictions for models with [Fe/H]=-0.15 in Fig. 7, in order to take into account the metallicity differences between the various clusters. At the age of the Hyades, rotational mixing described in Sect. 3 perfectly explains the shape of the blue side of the Li dip, as well as the observed dispersion. This clearly indicates that, in this effective temperature range, the process which participates to the transport of angular momentum in the Sun is not yet efficient.
We computed the effect of rotational mixing on beryllium, which
burns at a slightly higher temperature than lithium
( 3.5 10
## 4.3. The red side of the Li dip
We rather propose that the red side of the dip corresponds to a transition region where some other physics for angular momentum transport, which is known to be present in the Sun, starts to become efficient. In that case, the magnitude of both the meridional circulation and shear turbulence is reduced, as well as the Li depletion by rotation-induced mixing. We suggest that this increase of efficiency is linked to the growth of the surface convection zone (see Fig. 2 top). This efficient transport mechanism for angular momentum could be due to gravity waves or to a magnetic field in the radiative interior (see references given in the first part). A complete description of the efficient mechanism for the transport of angular momentum is required in order to calculate self-consistently the Li destruction in this region, and has not been attempted here.
Two important remarks have to be done on the transition region. Firstly, it was shown by Balachandran (1995) that the location of
the Li dip in different clusters depends on the effective temperature
Secondly, the measures of Li abundances in the Hyades stars of 66006200 exhibit a large dispersion while it is much smaller in cooler stars. This can be again linked to different rotational histories of stars of the same mass. Indeed, when these are young, the fast rotators have a larger convective zone than their slower counterparts (see Table 1 and Fig. 2 top). Therefore, in the early stages meridional circulation could be lower than expected, leading to a smaller Li destruction. Even though the magnitude of this change of may seem small, it is not negligible compared to the size of the transition region. A detailed description of angular momentum transport by the "efficient" process is however required in order to quantify the magnitude of this effect. © European Southern Observatory (ESO) 1998 Online publication: June 26, 1998 |