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Astron. Astrophys. 355, 308-314 (2000)

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2. The effect of the magnetic field on the fluxes

In Paper 1, a figure demonstrated that as the metallicity increased for models with [FORMULA] = 8400 K, log g = 3.30 the fluxes exhibit an increase in the size of the [FORMULA]5200 feature. This also occurs at other temperatures and surface gravities. Most investigators believe that the mCP stars are indeed metal rich, but are cautious about the degree of enhancement due to the effects of the magnetic field. The Zeeman effect produced by the stellar magnetic field desaturates strong lines and strengthens those lines which are above the linear part of the curve of growth. For lines with Zeeman patterns having many components, one can treat the effects of a weak magnetic field as pseudo-microturbulence. But very sensitive lines exhibit the Paschen-Back effect even for moderately strong magnetic field strengths.

Paper 1 did not account for the effects of the magnetic field on the fluxes of magnetic CP stars. ATLAS9 uses Opacity Distribution Functions (odfs) to model the metal line opacity. To calculate valid odfs for mCP stars is complicated. As the magnetic field strength varies over the photosphere, a proper calculation probably requires several odfs for a variety of field strengths and compositions as well as an integration over the visible hemisphere. Further the photosphere of a mCP star may not be spherical.

Nevertheless, let us try to include magnetic field affects on the line opacity in an approximate manner. According to the radiation diffusion scenario (Michaud & Proffitt 1993), the atmospheres of the mCP stars should be quiescent. Thus the true microturbulence should be zero. But when we examine the spectra of most mCP stars and attempt to find microturbulences by standard techniques, we find non-zero values due to line broadening produced by the Zeeman effect acting as a pseudo-microturbulence. The magnetic field redistributes the line opacity so that it is more uniform with wavelength and tends to close opacity holes. Such effects are likely to be most important in the spectral regions where most of the flux is emitted and for hot stars this is the ultraviolet. The use of scaled solar odfs also may be non-optimal due to the abnormal compositions. Further the distribution of opacity with wavelength is unique for each atomic species. Effects of this sort can be explored using ATLAS12 (Kurucz 1996) models and might be important especially for some remaining details.

Fig. 1 shows predicted optical region energy distributions for ATLAS9 model atmospheres with [FORMULA] = 10000 K, log g = 4.00, and log Z = +1.0 odfs. The fluxes from top to bottom correspond to microturbulences of 0, 2, 4, and 8 km s-1, respectively. The offset between fluxes for pairs of models is 0.5 mag with the scale being correct for the 0 km s-1 model. As the microturbulence increases so does the size of the [FORMULA]5200 feature near 1.9 [FORMULA] and the Lyman continuum becomes more depressed and exhibits additional structure. In addition the Balmer continuum brightens slightly (about 0.1 magnitude over the range of exhibited microturbulence) and the mean line strength increases.

[FIGURE] Fig. 1. The optical region fluxes of ATLAS9 model atmospheres with [FORMULA] = 10000 K, log g = 4.00, and log Z = +1.0 odfs. The fluxes correspond from top to bottom to microturbulences of 0, 2, 4, and 8 km s-1. The offset between pairs of models is 0.5 mag. As the microturbulence increases so does the size of the [FORMULA]5200 feature near 1.9 [FORMULA] and the Lyman continuum becomes more depressed and exhibits more features.

Hence to fit the energy distribution of a mCP star, one can adjust both the metallicity and the microturbulence. One is constrained since the spectrum synthesized from the model should match that of the star. If the elements which produce the [FORMULA]5200 feature and the elements which produce most of the observed lines are not the same and are enhanced by sufficiently different amounts, then the matching process may be able to reveal such effects. Each element is enhanced by a different average amount and these anomalies are affected by the changing strength of the magnetic field over the photosphere. In some spectrum variables lines of different elements are known to vary in strength out of phase with one another. To model such effects, it may be necessary to use an opacity sampling model atmospheres program such as ATLAS12 (Kurucz 1996) and to integrate the predicted fluxes over the surface.

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© European Southern Observatory (ESO) 2000

Online publication: March 17, 2000
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