Astron. Astrophys. 336, L33-L36 (1998)

1. Introduction

Magnetic fields from about 40 kG to 1 GG have been detected in about about 50 (2%) of the 2100 known white dwarfs (McCook & Sion 1998). A list of all currently known magnetic white dwarfs is found in Jordan (1997). Magnetic fields in the low field range ( MG) in both hydrogen and helium rich magnetic white dwarfs can be detected by a relatively simple line pattern. Hydrogen line components have been identified in many objects, but until recently, helium was detected unambiguously only in the magnetic white dwarf Feige 7. Using He I line data calculated by Kemic (1974), Achilleos et al. (1992) found that the spectrum could be well reproduced with a dipole of strength 35 MG displaced by 0.15 white dwarf radii from the stellar center. Since the Kemic data were calculated by regarding the magnetic field as a small perturbation to the Coulomb interaction and are only valid up to about 20 MG, the Kemic tables had to be extrapolated for the Feige 7 analysis. The only other definite helium rich objects with fields of about 15-20 MG were discovered by Reimers et al. (1998) in the course of the Hamburg ESO survey.

Magnetic white dwarfs with field strengths MG containing hydrogen could be interpreted ever since the numerical calculations of energy level shifts and transition probabilities for bound-bound transitions by groups in Tübingen and Baton Rouge (Forster et al. 1984; Rösner et al. 1984; Henry and O'Connell 1984, 1985). With the help of these data Greenstein 1984 and Greenstein et al. 1985 could identify the hitherto unidentified features in Grw  with stationary components of hydrogen in fields between about 150 and 500 MG.

Since the magnetic field on the surface of a white dwarf is not homogeneous but e.g. better described by a magnetic dipole, the variation of the field strength from the pole to the equator (a factor of two for a pure dipole field) smears out most of the absorption lines at larger magnetic field strengths. However, a few of the line components become stationary, i.e. their wavelengths go through maxima or minima as functions of the magnetic field strength. These stationary components are visible in the spectra of magnetic white dwarfs despite a considerable variation of the field strengths.

About 80% of all known white dwarfs have nearly pure hydrogen atmospheres (spectral type DA). However, since most of the remaining stars have helium rich atmospheres, we would also expect a significant number of magnetic white dwarfs to belong to the spectral type DB in which He I lines are observed. Therefore it could be expected that the few magnetic white dwarfs with unidentified spectral features, that cannot be explained by the line data for hydrogen, are helium rich. The most famous example is GD 229, where Swedlund et al. (1974), Greenstein et al. (1974), Landstreet & Angel (1974), Liebert (1976), Greenstein & Boksenberg (1978), and Schmidt et al. (1996) found strong absorption features in the optical, infrared, and UV. Angel (1979) already proposed that the absorption bands in this star are due to stationary components of hydrogen or helium.

The basic difficulty in calculating energy levels and oscillator strengths for arbitrary field strengths lies in the fact that the Coulomb potential has a spherical symmetry whereas the magnetic field induces a cylindrical symmetry. This prevents a separation of variables and together with the nonlinear character of the interactions makes even the numerical solution a difficult problem. In particular the intermediate regime (), in which the majority of magnetic white dwarfs is found, is very complicated, since neither the magnetic nor the Coulomb interaction dominates and we therefore encounter a so-called nonperturbative regime where none of the interaction terms can be treated by perturbation theory. In the case of the two electron system He I the situation is even more difficult, since the number of degrees of freedom is enhanced significantly and the electron-electron interaction introduces a third competitive force which makes He I a complex system with a rich variability of the spectrum with changing field strength. The particular challenge of a comparison of atomic data with observational ones lies in the fact that the energies of many excited states have to be known with a high relative accuracy (usually ) and for a large number of field strengths in order to identify the stationary transitions.

Until this year the status of electronic structure calculations on He I was such (see Braun et al.1998, Jones et al. 1997, Ruder et al.1994 and references therein) that a conclusive comparison was impossible and the occurence of He I in the atmosphere of GD 229 had to be considered as a pure speculation as it was the case with respect to hydrogen in Grw  until 1984.

Therefore, several alternative explanations have been proposed. Engelhardt & Bues (1995) have tried to explain the regular almost periodical structure of the GD 229 spectrum by quasi-Landau resonances of hydrogen in a magnetic field of 2.5 GG. Östreicher et al. (1987) speculated that two of the features could be due to intersections of hydrogen components in a field of about 25-60 MG.

Now, the calculations performed in Heidelberg (Becken & Schmelcher 1998) have closed that gap and for the first time precise data for a large number of energy states have become available. In this paper we will show that most of the absorption features in the optical and UV spectrum of GD 229 can be identified as stationary line transitions of He I.

© European Southern Observatory (ESO) 1998

Online publication: July 20, 1998
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