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

4. The new Montreal models

4.1. New results with the NMM

The NMM include the diffusion of all major elements up to nickel consistently by using monochromatic opacity tables of the Livermore group (Iglesias & Roger 1996) to compute the opacity and the radiative forces accurately at all points in the star and for the local chemical composition; the basic procedures were outlined by Turcotte et al. (1998a) and Richer et al. (1998).

The evolution of the abundances and of the structure is completely consistent through the opacity. One very important property of these models is the presence of a convectively unstable zone around  K where iron-group elements dominate the opacity. This convection zone appears naturally as the consequence of abundance changes if they are large enough. The NMM then assume that this deeper convection zone is connected to the helium and hydrogen convection zones through convective overshoot.

The large depth of the convective mixing relative to standard models for chemically peculiar stars results in much smaller surface-abundance variations, more in line with observations. Richer et al. (2000) showed that the radiative forces at the base of the iron convection zone follow the correct pattern over a relatively narrow region for the Am signature to be recovered without additional assumptions. A quantitative agreement with observed abundances for Am stars does require additional turbulence below the superficial convective envelope. In the NMM, the mixing necessary to reproduce the abundances observed in Am stars prevents the formation of this convection zone.

A significant result in the context of stellar pulsations is that helium is still substantially present in the HeII driving region in these new models. Also, as the opacity in the vicinity of the so-called "metal opacity bump" ² is increased relative to standard models, one can expect that this region will contribute to the excitation of longer-period modes. On the other hand, in some extreme cases this region might be convective in contrast to standard models, which would reduce the radiative flux and by consequence the driving in that region.

We shall examine the consequence of these results on the possible instability of Am stars. As a complement, we shall also estimate the effect of mild abundance anomalies on predicted pulsations of  Scuti stars.

4.2. The basic properties of the NMM

The NMM include the detailed diffusion of 21 major elements from H through Ni plus several light elements and isotopes for a total of 28 species. The opacity data used in the evolution code and in the following analysis are the OPAL monochromatic opacity tables (Iglesias & Rogers 1996) which allow us to calculate accurate Rosseland mean opacities and radiative forces for any peculiar chemical composition necessary. At low temperatures, for which the OPAL data is lacking, we supplement them with the Kurucz (1991) opacity tables. Although it would be desirable to take into account changes in the composition of individual heavy elements in the atmosphere, the transition occurs at such low temperatures that it might be of little consequence for the stellar interior.

The models incorporate standard procedures for the equation of state and the nuclear reaction rates. The mixing-length formalism for convection is used and is calibrated using the Sun (Turcotte et al. 1998a). All models have an identical, homogeneous, initial chemical composition as specified by Turcotte et al. (1998b). All models are one-dimensional, non-rotating, and non-magnetic.

Individual models for a given stellar mass only differ in the parameters adopted for the coefficient of turbulent diffusion. In all calculations presented in this paper, the coefficients are chosen so that the zone mixed by turbulence goes from the surface to somewhat below the iron convection zone. The coefficient of turbulent diffusion is modeled with the following three-parameter expression

where the free parameters are , and n. The evolution of the abundances is very sensitive to the depth of the mixing but not so much to the profile of . The models are named with reference to the number R which specifies the ratio of to the coefficient of atomic diffusion of helium at the point where the density is equal to the reference value . For example, model 1.90R1000-2 is a 1.90  star with and ; for simplicity, `10K' is used to refer to models with . In all the models discussed in this paper is g cm^-3. The reader is referred to Richer et al. (2000) and Richard et al. (2000) for further details.

For every stellar mass examined, one model that does not include any effects of diffusion is also included. For computational efficiency this comparison model uses the mean Rosseland opacity tables of Iglesias & Rogers (1996). Assuming that there is no separation of elements in the star implies that some unspecified mixing is necessarily assumed. This mixing is required to be large and deep enough to keep superficial regions at a constant chemical composition without mixing too deeply, to avoid dredging up nuclearly processed matter to the surface. They are named according to the mass and are labeled with the tag "ND" (e.g. , 1.90-ND).

© European Southern Observatory (ESO) 2000

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