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Astron. Astrophys. 341, 560-566 (1999)

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5. Numerical estimates of the diffusion velocity

Here the typical drift velocity is calculated for two model stars. The stellar models have been provided by M. Salaris (private communication) and are computed according to the evolution code described in Salaris et al. (1997) and references therein. The two models correspond to (2.0[FORMULA], 1.8[FORMULA] [FORMULA]K) and (5.0[FORMULA], 3.0[FORMULA] [FORMULA]K) main sequence stars. These models are computed with no rotation and solar composition. Although below the models are used to represent non-solar composition rotating stars, it is unlikely that this slight inconsistency will introduce a large error.

The calculation of the atomic parameters [FORMULA] and [FORMULA] are lengthy and cumbersome, and so the parameters given by Alecian et al. (1993) for iron are assumed (their Table 4), derived using Opacity Project data. These are for the states FeIX- FeXVII. For a given temperature in the model stars, the atomic parameters used are interpolated between those for the dominant, and next dominant ions (the temperatures at which ions are dominant is given in Eq. 3 of Alecian et al. 1993). These temperatures also give the applicable range used in the calculation: [FORMULA] to cover all the ions used.

Although the models are calculated with solar metallicity, the drift velocity [FORMULA] is calculated for two values of iron abundance: solar abundance [FORMULA] and [FORMULA] solar. Although strictly this is inconsistent, the error associated in doing so will be very small.

In Fig. 2, the radial radiative acceleration is shown for the two stars with solar iron abundance, and should be compared with Fig. 4 of Alecian et al. (1993). It can be seen that the interpolation used here to calculate the atomic parameters is not introducing any large errors in the calculation.

[FIGURE] Fig. 2. Numerical estimates of the radial radiative acceleration [FORMULA] for the two model stars.

Fig. 3 shows the value of [FORMULA] as a function of the fractional mass exterior to that point [FORMULA] for the two models. The stars is assumed to rotate at 0.7 of their break up velocities (0.89 of its break-up angular velocities), equal to [FORMULA] and 320 km s-1 respectively for the 2[FORMULA] and 5[FORMULA] stars. The top panel of Fig. 3 corresponds to the 5[FORMULA] star, and the lower to the 2[FORMULA] star. In each panel, the lines refer to [FORMULA], [FORMULA], [FORMULA] and [FORMULA] with the uppermost line corresponding to [FORMULA] decreasing downwards. The solid and dotted lines correspond to iron abundance of solar and [FORMULA]solar respectively.

[FIGURE] Fig. 3. Numerical estimates of [FORMULA] from Eq. 14. The four lines in each panel refer to velocities at [FORMULA], [FORMULA], [FORMULA] and [FORMULA] with the uppermost line corresponding to [FORMULA] decreasing downwards. The solid (dashed) lines correspond to solar ([FORMULA] solar) abundance of iron.

In three of the four models, the drift velocity exceeds [FORMULA] cm s-1 in the outer layers at some latitude. This indicates that there may be regions in the envelope where iron may start to diffuse round the star. For the 5[FORMULA] star the outer [FORMULA] ([FORMULA]) of the solar ([FORMULA] solar) composition model may suffer latitudinal drift of iron. For the 2[FORMULA] star, at [FORMULA] solar composition the situation is similar - [FORMULA] cm s-1 in the outer [FORMULA] of the star. However for solar composition, there may be no effect as the radiative acceleration on iron is smaller. In this case the turbulence may homogenise the star faster than the metals may drift due to the radiation. Taken at face value, Fig. 3 indicates that stars rotating at significant fractions of their break-up velocity may be prone to latitudinal metallic drift in their outer envelopes.

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© European Southern Observatory (ESO) 1999

Online publication: December 4, 1998