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Astron. Astrophys. 361, 629-640 (2000)

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5. Possible scenarios for HS 0209+0832

A successful model for HS 0209+0832 has to explain the (almost) homogeneous hydrogen-helium atmosphere, the presence of elements heavier than helium, and the variability at least of the helium features. In the following we discuss possible scenarios.

Accretion from the interstellar medium. Helium in atmospheres of DA white dwarfs is subject to downward diffusion on time scales much shorter than the cooling age so that the observed helium abundance in HS 0209+0832 cannot be of primordial origin. Radiation pressure is not strong enough to prevent helium from sinking: For [FORMULA] K the expected abundance of helium is less than [FORMULA] (Vennes et al. 1988). It could be assumed that helium has indeed left the outer parts of the atmosphere so that a small hydrogen layer floats on top of the helium, but the analysis with stratified hydrogen-helium models in diffusion equilibrium shows that this scenario cannot reproduce the observations.

A rather homogeneous distribution of helium as it is implied by our analysis could be reached if helium has been accreted very recently from the interstellar medium onto the white dwarf. This scenario can also explain the observed variability of the helium abundance, if HS 0209+0832 has passed through regions with different densities and therefore experienced different accretion rates during the last years. A lower rate would reduce the abundance within a few months due to the short diffusion time scale. If we assume that the primordial helium has settled down then the outer hydrogen layer must have a mass of at least [FORMULA] [FORMULA]. Otherwise, the underlying helium would disturb the observed spectral features. Koester (1989) has shown that hydrogen and helium are separated within nine months in a layer of this mass in a white dwarf with [FORMULA] K; this is consistent with the possibility of a helium line strength variation within eight months as found by Heber et al. (1997).

The presence of heavy elements supports the assumption of recent accretion. In white dwarfs with [FORMULA] K metals can be supported against gravity by selective radiation pressure. However, this explanation is not possible for HS 0209+0832. Chayer et al. (1995) predict [FORMULA], [FORMULA], and [FORMULA]. No recent calculations exist for titanium, nickel, and zinc but the nickel abundance should be similar to the iron abundance (Chayer et al. 1994), which is predicted to be less than [FORMULA]. The theoretical abundances are lower than the observed values for carbon, calcium, and nickel but higher for silicon. This implies that radiative levitation cannot account for the element abundances.

It is interesting to note that the atmosphere of HS 0209+0832 contains among others those metals (Ca, Ti, Al, Ni) which show the highest depletion factors of up to 1000 in the gas phase of the interstellar medium (e.g. in [FORMULA] Oph, Savage & Sembach 1996). This is commonly explained by their high condensation temperatures (cf. Spitzer 1978, Fig. 9.1). The large depletion of elements like calcium and titanium is a result of initial grain condensation in a dense and warm gas, e.g. in the winds of cool giants, where all calcium and titanium is condensed. Later, in a cooler medium, elements with lower accretion temperatures are accreted onto the condensation nuclei. It might be speculated that during infall from the interstellar medium the former condensation nuclei mostly survive the accretion process and reach the white dwarf surface while metals with lower condensation temperatures evaporate earlier and do not reach the atmosphere. However, the presence of zinc with a much lower condensation temperature does not fit into this scenario.

Accretion from a late-type companion. An alternative to accretion from the interstellar medium is accretion of helium and metals from a close companion. This scenario is discussed for some DAO white dwarfs at [FORMULA] K (e.g. Tweedy et al. 1993, Dobbie et al. 1999, Vennes et al. 1999). These objects and HS 0209+0832 have several similarities: Helium is distributed homogeneously in the atmosphere, an equilibrium stratified composition can be ruled out from the shape of the He II 1640 Å line (Vennes et al. 1999), the helium abundance of one object (EUVE J0720-317) seems to vary by one order of magnitude on a time scale of a year (Finley et al. 1997) or may be distributed inhomogeneously over the surface (Dobbie et al. 1999), and photospheric carbon is also detected (Thorstensen et al. 1996, Vennes et al. 1999). The main differences besides the temperature are that the helium abundance in HS 0209+0832 is about one order of magnitude higher and that the optical spectrum does not show any signs of emission lines from the companion whereas these lines are clearly detected in these DAO stars.

We have tested if a close, possibly interacting, M dwarf could be detected in the optical spectra of HS 0209+0832. The observed flux at 5500 Å and the theoretical visual magnitude according to the evolutionary tracks of Wood (1994, "thick" hydrogen layers) give a distance modulus of [FORMULA] for HS 0209+0832. The spectra of an M1V and an M5V star taken from the compilation of Jacoby et al. (1984) were scaled according to the distance modulus and the calibrated absolute magnitudes for these stars (Schmidt-Kaler 1982). The M dwarf spectra were than added to the synthetic DAB spectrum for HS 0209+0832 which was also scaled to the visual magnitude. The result is that even an M5V star would cause detectable absorption bands around 6200 Å. If there is indeed a companion star then the spectral type must be later than M5.

Magnetic fields. In the case of Feige 7 it has been discussed that a magnetic field between about 17 MG and 57 MG is the reason for the inhomogeneous surface composition (Achilleos et al. 1992): In regions of higher field strengths convection may be suppressed so that the outer hydrogen layer is not mixed fully with the underlying helium. However, this scenario can be ruled out here because the photosphere of HS 0209+0832 is convectively stable.

From the observed line shapes of the hydrogen lines we derive a maximum line splitting of [FORMULA] 10 Å for [FORMULA] and [FORMULA] and [FORMULA] 1.5 Å for [FORMULA]. This translates into an upper limit of 0.5 MG for the magnetic field strength. A sharper limit of [FORMULA] 0.1 MG can be calculated from the C IV and Si IV lines and a maximum splitting of 0.05 Å due to anomalous Zeeman effect. Therefore, we believe that magnetic fields are not important in HS 0209+0832.

Rotation and meridional circulation. A mechanism that could explain a rather homogeneous distribution of helium would be large-scale meridional circulation in a rotating star. For a 0.8 [FORMULA] white dwarf with [FORMULA] [FORMULA] and a rotation velocity of [FORMULA] Tassoul & Tassoul (1983) have found that mixing due to meridional circulation is completely negligible. The effect may be significantly stronger in HS 0209+0832 with [FORMULA] [FORMULA] and [FORMULA] [FORMULA]. However, from the metal lines we derive an upper limit of [FORMULA] for [FORMULA] so that rotation should be not important unless the star is seen pole-on. Fig. 10 presents an example for the broadening due to rotation.

[FIGURE] Fig. 10. Observed Si IV lines compared to rotational broadened models. From top to bottom: [FORMULA], 12.5, 6, [FORMULA]

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Online publication: October 2, 2000