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Astron. Astrophys. 332, 204-214 (1998)

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5. Clues on the nature of the extra-mixing process on the rgb

The results described previously were obtained using observational constraints only, and did not rely on any special prescription for the extra-mixing. We can nevertheless check whether the value we get for [FORMULA] is consistent with what is expected in a very simplified rotation framework. Let us follow the suggestion by Huppert & Spiegel (1977) according to which meridional currents can penetrate into a region with a stable gradient of molecular weight within a scale height given by [FORMULA], where r is the local radius, [FORMULA] is the angular rotation velocity, and [FORMULA] the buoyancy frequency due to the µ-gradients. We can derive then a critical µ-gradient by specifying that h must be a small fraction of r ([FORMULA]): [FORMULA], where all the quantities are computed at the place where the actual [FORMULA] is equal to the critical one.

For each of our 3 models, we computed [FORMULA] for a stellar rotation velocity of 2.5 km sec-1, typical on the RGB for the stellar masses in consideration (De Medeiros et al. 1996). The [FORMULA] we obtain in this model-dependent approach are shown in Figs. 4 to 8 (thick cross). They are in perfect agreement with the constraints coming from the observations discussed in Sect. 4. This result tends to indicate that the extra-mixing process on the RGB is related to rotation.

However, we have to be cautious in our conclusions. Indeed, [FORMULA] is derived here in a simplified framework. Complete computations with rotation-induced mixing have to be performed. The transport of chemicals and angular momentum should be treated simultaneously to properly handle the development of µ-barriers (despite rotational mixing) during stellar evolution. Different stellar rotational histories also have to be considered, which may result in different efficiencies of the extra-mixing, and lead to a dispersion of chemical anomalies from star to star. Observational support for this approach may exist from the variations of oxygen abundances and rotational velocities in blue horizontal branch stars in three globular clusters (Peterson et al. 1995).

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© European Southern Observatory (ESO) 1998

Online publication: March 10, 1998
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