Astron. Astrophys. 360, 603-616 (2000)

11. Conclusion

We have investigated the impact of diffusion on the stability of A-type main-sequence Population I stars. The models include the consistent abundance evolution of all important elements and its impact on stellar structure. In these models helium remains present in the HeII ionization zone and the opacity in the iron opacity bump increases substantially, raising the possibility of a strong relationship between variability and diffusion.

We present evidence that young Am stars are stable against driving from the mechanism and that, as the stars evolve, they become unstable, but only when near the red edge of the instability strip. Hot Am stars need to be more evolved than cool Am stars before variability can occur. The blue edge of the instability strip for metallic A stars is sensitive to the magnitude of the abundance variations and is thus indicative of the depth of mixing by turbulence.

The stability of A stars is more sensitive to the evolution of the abundance of helium than to the accumulation of iron-peak elements. In stars with very little turbulence the iron-peak driving region can become convectively unstable thereby reducing the radiative flux there and negating the driving effect of the enhanced opacity bump. However, in the models which are representative of Am stars, the turbulence is high enough to prevent the formation of that iron convection zone while allowing a significant increase of the opacity bump due to iron-peak elements. Still, only a marginal positive effect can be seen in the long-period g modes. The higher-frequency modes depend mostly on the helium abundance and somewhat on the hydrogen abundance.

There are a number of caveats relevant to the present work.

There is no direct link between the normalized growth rates and the actual amplitude of the pulsations as evidenced by the lower number of modes observed in  Scuti stars relative to their predicted number. Additionally, comparisons to models at solar composition by J. Christensen-Dalsgaard and W. Dziembowski have shown that the growth rates are sensitive to the details of the modeling. In general, in the stars we compared at 1.8 and 1.9 , the growth rates were lower in our models than in either of their models.

The treatment of convection in the present work is simplistic. Convection and turbulence are known to damp pulsation to a certain extent. The most striking and well known evidence of the effect of convective damping is the red edge of the instability strip [Gough (1977); Gonczi & Osaki (1980); Balmforth & Gough (1988); see also Buchler et al. (1999) for a recent review]. Turbulence affects pulsations in two ways: 1) through turbulent viscosity, which always dampens pulsations, and 2) through the phase difference between entropy variations and the modulation of the convective flux, which can either excite or dampen pulsations. It is the latter effect which is responsible for the red edge of the classical instability strip. While the interaction between turbulent convection and pulsations has been studied, the effect of turbulence outside of the convection zones is unknown.

In the models including diffusion, the coupling between turbulence and diffusion might be very important. For the present models reproducing Am stars, the turbulence extends to a significant depth below the convection zone. While the energy flux related to the turbulence is expected to be very small, the effect of turbulent viscosity might not be negligible. For stars in which the iron convection zone is allowed to form, three separate convection zones exist with highly turbulent regions between them. The behavior of pulsations in such stars might be heavily affected by a proper treatment of convective effects.

While it is true that our analysis does not take this into account, one should not forget that in the standard models without diffusion an ad hoc mixing mechanism is implied to prevent the formation of abundance gradients. This presumably turbulent mixing (at least in the more slowly rotating  Scuti stars) is also never taken into account. It is, by hypothesis, larger than that in the models where atomic diffusion is important. Under these circumstances, we may perhaps consider the simple treatment of convection and turbulence applied here as adequate for identifying the differential effect of diffusion on stellar stability.

The NMM used here still contain an element of arbitrariness in that they extend turbulent mixing a little beyond that expected from iron convection zones, without providing a physical mechanism for this extension. This extension is required to fit the observed surface abundances of Am stars. The extension is, however, sufficient to cause the iron-peak abundances to decrease sufficiently for the convection zone to disappear in models representative of these stars. The models do not include the potential effects of mass loss or rotation, although differential rotation is one mechanism that is now being investigated as a source of the instabilities that could provide this mixing zone extension.

When compared against each other the present models do, however, illustrate the effect of diffusion on the stability of main-sequence A stars as well as present modeling allows.

© European Southern Observatory (ESO) 2000

Online publication: August 17, 2000
helpdesk.link@springer.de