4. Alternative models
In this section we discuss alternative models to explain the observed spectral features of HS 0209+0832.
Stratified atmosphere. The favored explanation for the DB gap predicts a small layer of hydrogen on top of a helium atmosphere for stars inside the gap. However, the presence of photospheric metals is in contradiction with this assumption, because it is difficult to understand why helium has settled down, whereas metals are still in the photosphere. Elements heavier than helium should sink down much faster. We have, nevertheless, tested whether HS 0209+0832 could have a stratified hydrogen-helium atmosphere, where the hydrogen layer is thin enough so that helium lines are still visible, in order to test the assumption of a homogeneously mixed atmosphere.
We have calculated stratified models with hydrogen and helium being in diffusion equilibrium. A general description of the physics and the computational methods has been given by Jordan & Koester (1986). Similar to the homogeneous case, we started with K and , determined the mass of the hydrogen layer from the strengths of the He I 4471 Å line, and used a technique to calculate and . It turned out that the shape of the He II 1640 Å line cannot be reproduced in detail and that the equivalent widths of the He II and He I line cannot be reproduced simultaneously. We have, therefore, used the optical line only. Two iterations were needed until the procedure converged with K, , and for the mass of the hydrogen layer.
Fig. 8 shows the observed He II line at 1640 Å together with the stratified model, which can reproduce the optical He I line and the Balmer lines. The formal fit to the hydrogen lines is slightly worse than with homogeneous atmospheres ( compared to ); the change of is only small mainly due to the low signal-to-noise of the optical spectrum (). However, the 1640 Å line of the stratified model is far too broad (Fig. 8) and the slope of the UV continuum is also reproduced worse than in the homogeneously mixed case. Therefore, a stratified hydrogen-helium atmosphere in diffusion equilibrium is not able to explain the spectrum of HS 0209+0832. This confirms the conclusion of Jordan et al. (1993).
Non-uniform surface composition. Both models discussed so far assume that the elements are distributed uniformly over the surface of the star. A possibility to explain variable helium features as observed by Heber et al. (1997) is a slowly rotating star with a composition that varies over the surface. Such models have been applied with different success to several DAB white dwarfs (e.g. Achilleos et al. 1992, Kidder et al. 1992, Beauchamp et al. 1993, Koester et al. 1994). However, an inhomogeneous surface composition with extreme abundance variations - e.g. small helium spots in a pure hydrogen atmosphere - which has been discussed for some DABs is not suited to explain the spectrum of HS 0209+0832. This can be demonstrated with the strength of the UV He II line and the non-detection of the He I lines at 3187 Å and 2945 Å.
Let us consider first an equal temperature for the spots and the rest of the atmosphere. A pure DB model with K has already a He II 1640 Å line with about the same strengths as in the DAB model with K: The depths of the line is equal and only the wings are somewhat broader in the DB. Therefore, it is not possible to reproduce this line with a pure hydrogen atmosphere and additional helium spots of the same temperature. The pure helium region would have to contribute a significant amount of the total flux observed. This can only be achieved if it is hotter than the rest of the surface. This assumption is rather unlikely and cannot explain the whole spectrum either: If the equivalent width of the 1640 Å line is reproduced by a model, the He I lines at 3187 Å and 2945 Å would also be visible, unless the helium region is hotter than 50 000 K, but in the latter case, the He II 1640 Å line is broader than observed.
Fig. 9 illustrates this behaviour: A composite model consisting of a DA spectrum of K originating from 85 % of the surface and a DO of K covering 15 % has a He II line which is too broad and too shallow although the model can reproduce the strengths of both the Balmer and 4471 Å lines. For comparison, a DB model with K, which can reproduce the He II line, is also plotted.
The only remaining possibility to explain the spectrum of HS 0209+0832 with a static inhomogeneous surface composition would be a less extreme abundance variation - something like on one half of the star and on the other.
DA+DB double star. Jordan et al. (1993) have considered the possibility that HS 0209+0832 is a double star consisting of a DA and a DB white dwarf. This explanation has been sucessfully applied for the DABs MCT 0128-3846 and MCT 0453-2933 (Wesemael et al. 1994). Jordan et al. have found that a combination of a DA at K with a DB at 15 000 K can reproduce and He I 4471 Å. However, the slope of the IUE spectrum indicated a higher temperature of the DA. The detection of the He II line at 4686 Å by Heber et al. (1997) and our finding of 1640 Å clearly rules out a cool DB as companion. The combination with a hotter DO would have the same problems as a helium spot model. Therefore, the spectrum cannot be explained with a DA+DB/DO binary.
© European Southern Observatory (ESO) 2000
Online publication: October 2, 2000