© ESO, 2012

1. Introduction

Any model-atmosphere calculation is strongly dependent on the available and reliable atomic data, which is a crucial input. Especially for highly ionized species and higher atomic mass, published data becomes rather sparse. A close inspection of the UV spectrum of the hot white dwarf RE 0503−289 by Werner et al. (2012) has shown that a large number of the hitherto unidentified observed spectral lines stem from trans-iron elements, namely Ga, Ge, As, Se, Mo, Sn, Te, and I.

Identification of the respective spectral lines is fairly straightforward because atomic databases like NIST¹ and Kelly’s database² have partly included the strongest lines of these elements with accurate wavelengths, whereas a quantitative analysis requires adequate spectral modeling. This is hampered by the fact that line strengths for trans-iron elements, when available at all, are relative intensities measured from emission line spectra. Exploratory atmosphere models that are based on the LTE assumption to calculate occupation numbers of the atomic levels of an ion and on log gf values scaled to match the relative line strengths may show that the line identifications are correct. A reliable abundance analysis, however, is impossible owing to the lack of measured or calculated transition probabilities.

The line identification was demonstrated by Werner et al. (2012) in the case of RE 0503−289. It is a hot (T_eff = 70   kK, log g = 7.5), helium-rich DO-type white dwarf (WD 0501−289, ${\mathit{\alpha }}_{\mathrm{2000}}\mathrm{=}{\mathrm{05}}^{\mathrm{h}}{\mathrm{03}}^{\mathrm{m}}\mathrm{55}\stackrel{\mathrm{s}}{.}\mathrm{513}$, ${\mathit{\delta }}_{\mathrm{2000}}\mathrm{=}\mathrm{-}\mathrm{28}°\mathrm{54}\prime \mathrm{34}\stackrel{\mathrm{″}}{.}\mathrm{57}$), which is well-suited to UV spectroscopy because its spectrum is only slightly contaminated by interstellar absorption. Werner et al. (2012) performed an abundance analysis of Kr and Xe where level energies and oscillator strengths of Kr VI, Kr VII, Xe VI, and Xe VII were already published. They determined log Kr = −4.3 ± 0.5 and log Xe = −4.2 ± 0.6 (mass fractions) and identified a variety of lines of the other trans-iron elements mentioned above.

Only level energies and (partly) relative line strengths were accessible for Ge. A test calculation of an H+Ge-composed model atmosphere with the relevant parameters (T_eff = 70   kK, log g = 7.5), log Ge = −4) shows that Ge V and Ge VI are dominant in the line-forming region (Fig. 1). Consequently, we calculated transition probabilities anew for Ge V and Ge VI (Sect. 2). In Sect. 3, we briefly introduce the available observed spectra, which are used for our Ge abundance analysis of RE 0503−289 that is presented in Sect. 4. In Sect. 5 we re-assess the effective temperature of RE 0503−289 based on the C III / C IV ionization balance. Results and conclusions are summarized in Sect. 6.

Fig. 1 Ionization fractions of Ge iii–vii. The formation depths of the Ge V and Ge VI line cores are marked at the top.

2. Transition probabilities in Ge v and Ge VI

There are not very many transition probabilities or oscillator strengths in Ge V and Ge VI ions. In Ge V, some pioneering HFR³ and MCDF⁴ (Grant & McKenzie 1980; Grant et al. 1980) results were reported by Quinet & Biémont (1990, 1991) but the work of these authors was limited to 3d–4p and 3d–4f transitions in nickel-like ions (Ge V–Pb LV). More recent work comes from Safronova and co-workers (Safronova et al. 2000; Hamasha et al. 2004; Safronova et al. 2006a,b; Safronova & Safronova 2006), who performed relativistic many-body calculations for multipole transitions (E1, M1, E2, M2, E3, M3) originating in the ground states.

In Ge VI, the available results are limited to forbidden transitions in 3d and 3d⁹ configurations (Biémont & Hansen 1989) and to the theoretical investigation of electric dipole transitions between 3d⁹ and d⁸p configurations in zinc, gallium, and germanium ions (Jucys et al. 1968).

As there is no uniform set of oscillator strengths available for all the transitions of Ge ions observed in the present work, we decided to perform the relevant calculations. The method adopted here is the relativistic Hartree-Fock approach frequently referred to in the literature as the HFR or Cowan’s method (Cowan 1981).

For Ge V, configuration interaction has been considered among the configurations 3d¹⁰, 3d⁹ns (n = 4–7), 3d⁹nd (n = 4–7), 3d⁸4s², 3d⁸4p², 3d⁸4d², 3d⁸4f², 3d⁸4sns (n = 5–7), 3d⁸4snd (n = 4–7), and 3d⁸4p4f for the even parity, and 3d⁹np (n = 4–7), 3d⁹nf (n = 4–7), 3d⁸4snp (n = 4–7), 3d⁸4snf (n = 4–7), and 3d⁸4p4d for the odd parity. Using experimental energy levels reported by Sugar & Musgrove (1993) and Churilov et al. (1997), the radial integrals (average energies, Slater integrals, spin-orbit parameters) of 3d¹⁰, 3d⁹ns (n = 4–7), 3d⁹np (n = 4–6), 3d⁹nd (n = 4,5), 3d⁹4f and 3d⁸4s4p were optimized by a well-established least-squares fitting procedure. In this process, the 3d⁹4d ¹S₀ level at 493 765.5 cm^-1 (Sugar & Musgrove 1993) and the 3d⁸4s4p (J = 1) level at 673 405 cm^-1 (Churilov et al. 1997), affected by larger uncertainties, were not considered.

For Ge VI, the configurations included in the HFR model were 3d⁹, 3d⁸4s, 3d⁸5s, 3d⁸4d, 3d⁸5d, 3d⁷4s², 3d⁷4p², 3d⁷4d², 3d⁷4f², 3d⁷4s5s, 3d⁷4s4d, and 3d⁷4s5d for the even parity and 3d⁸4p, 3d⁸5p, 3d⁸4f, 3d⁸5f, 3d⁷4s4p, 3d⁷4s5p, 3d⁷4s4f, 3d⁷4s5f, and 3d⁷4p4d for the odd parity. In this case, the semi-empirical process was performed to optimize the radial integrals corresponding to 3d⁹, 3d⁸4s, and 3d⁸4p configurations using the experimental levels reported by Sugar & Musgrove (1993). The 3d⁹4f levels were excluded from the fit because many of these were found to be mixed with experimentally unknown levels belonging notably to the 3d⁹5p configuration.

The experimental and calculated energy levels for Ge V, expressed in cm^-1, are reported in Table 1 which also shows the differences between both sets of results (ΔE) and, in the last column, the percentage composition in LS-coupling (only the first three components over 5% are given). This last piece of information is useful because oscillator strengths for transitions connecting strongly perturbed levels are more sensitive to configuration interaction effects.

The calculated HFR oscillator strengths on a logarithmic scale (log gf) and transition probabilities (gA, in s^-1) for Ge V are reported in Table 2 with the corresponding wavelengths (in Å) and energy levels (in cm^-1). In the last column, we give the cancellation factor CF as defined by Cowan (1981). Low values of this factor indicate strong cancellation effects in the calculations. The corresponding transition probabilities could be very inaccurate so need to be considered with some care. It does appear, however, from the last column of the table that very few transitions are affected by such effects.

The experimental and calculated energy levels for Ge VI appear in Table 3 and the corresponding calculated HFR oscillator strengths and transition probabilities are reported in Table 4. Here too, very few transitions are affected by cancellation effects so that for most of the transitions, the f values should be reliable.

3. Observations

For our analysis, we mainly use the FUSE spectrum of RE 0503−289 that is described in detail by Werner et al. (2012). In addition, we use UV spectra that were obtained with ORFEUS⁵/BEFS⁶, ORFEUS/GHRS⁷ and IUE⁸. The BEFS spectrum (909–1222 Å) is co-added from five observations (ObsIds: BEFS2003, BEFS2126, BEFS2128, BEFS2133, BEFS2173; with a total observation time of 6826 s). The GHRS spectrum (1228–1275 Å, 1339–1375 Å, 1610–1655 Å) is co-added from eight observations (ObsIds: Z3GM0204T, Z3GM0205T, Z3JU0104T, Z3JU0107T, Z3JU0108T, Z3JU0109T, Z3JU010AT, Z3JU010BT; 5155 s). The IUE spectrum (1153–1947 Å) is the co-added spectrum (ObsIds: SWP46428, SWP49788, SWP52796, SWP52803; 136 193 s) provided by the IUE NEWSIPS data base⁹ (Holberg et al. 1998).

Optical spectra were taken in the framework of the SPY¹⁰ project (Napiwotzki et al. 2001, 2003) with UVES¹¹ at ESO’s¹² VLT¹³.

4. The photospheric Ge abundance in RE 0503−289

Ge V and Ge VI are the dominant ionization stages in the line-forming region of RE 0503−289 (Fig. 1). Thus, we constructed a Ge iii–vii model atom (Table 5, Fig. 2). We used level energies from NIST for all ions. For Ge IV, we considered the oscillator strengths of Nath Dutta & Majumder (2011) and, where missing, approximated values from the isoelectronic C IV. Ge V and Ge VI include our newly calculated oscillator strengths (Sect. 2). Analogously to Werner et al. (2012) in the case of Kr and Xe, the unknown f values (Table 5) of these two ions were set to 10^-4 within a spin and to 10^-6 otherwise. Test calculations have shown that the Ge line profiles in the UV do not change when we set f = 0 for these lines. Photoionization rates were computed with hydrogen-like crosssections. Electron collisional excitation and ionization rates were evaluated with the usual approximation formulae following van Regemorter (1962) and Seaton (1962), respectively. This enabled us to build on the HeCNOKrXe models for RE 0503−289 described by Werner et al. (2012) and to consider Ge opacities as well as iron-group opacities (elements Ca-Ni, own determination of upper abundance limits) in addition. Compared to Werner et al. (2012), we reduced the N abundance to match the N IV 2p ³P^o–2p²³P multiplet (921–924 Å, Fig. 3).

We used the Tübingen Model-Atmosphere Package (TMAP¹⁴Werner et al. 2003) to calculate state-of-the-art, plane-parallel, chemically homogeneous model atmospheres in hydrostatic and radiative equilibrium. The considered model atoms are those that are provided via the Tübingen Model-Atom Database (TMAD¹⁵, Rauch & Deetjen 2003).

Fig. 2 Grotrian diagram of our Ge IV (top), Ge V (middle), and Ge VI (bottom) model ions. Thick black and thin gray lines represent radiative transitions with known and unknown f values, respectively. The identified lines (red) are labeled with their respective wavelengths in Å.

We compared the available UV spectra of RE 0503−289 (Sect. 3) with our TMAP model (and wavelength positions given by NIST and Kelly’s database) in order to identify Ge lines. The line lists in that energy region, especially for the highly ionized trans-iron elements that are encountered, are rather incomplete, and thus, lines that are not considered in the models may contribute to the assumed isolated Ge lines. Ga V λλ   1054.560,1069.450 Å are two examples (Fig. 3). The consideration of Ga in the model-atmosphere calculation would improve the fit of the blends with Ge V λλ   1054.588,1069.419 Å. However, we identify four Ge IV, 37 Ge V, and six Ge VI lines (Table 6). All Ge IV and Ge V lines are in general reproduced in both strength and width by our model simultaneously at log Ge = −3.81 ± 0.3 (Fig. 3). There is only one line, Ge V λ   1123.744 Å, that is much too strong in our model. The reason is unknown. The Ge VI lines are weak in our model and just emerge from the noise in the FUSE observation, but they do agree. Ge VI λλ   986.721,1039.890 Å are too weak to reproduce the observed absorption features, most likely due to unknown blends at their positions that are not considered in the model. However, the large number of identified Ge lines and their modeling give convincing evidence that our model and the determined Ge abundance are realistic.

Fig. 3 Ge IV (top), Ge V, and Ge VI (bottom) lines in FUSE, ORFEUS/BEFS (Ge IV λ   1189 Å), and IUE (Ge V λ   1222 Å, Ge IV λ   1229 Å) observations compared with a Teff = 70   kK/log g = 7.5 TMAP model. The abundances (top right) are logarithmic mass fractions. IG denotes a generic model atom (Rauch & Deetjen 2003), which comprises Ca, Sc, Ti, V, Cr, Mn, and Co. The synthetic spectra a convolved with a Gaussian of 0.05 Å (FWHM, 0.1 Å for the IUE comparison) to match the instrument resolution. A radial-velocity shift of vrad = 23   km   s-1 is applied to the observation.

5. Effective temperature and surface gravity of RE 0503−289

Both T_eff and log g were adopted from Werner et al. (2012) for this analysis. Figure 3 shows that the C III multiplet 2p ³P^o–2p²³P (1174–1176 Å) in our model is too weak. Since an increased C abundance would strengthen C IV lines as well, e.g. C IV λλ   948.09,948.21 Å (Fig. 3), this is evidence that T_eff of the model is too high and/or log g is too low. A respective variation would change the C III/C IV ionization equilibrium towards the lower ionization and improve the agreement of the C III lines. Figures 4 and 5 demonstrate this for T_eff = 70   kK and T_eff = 65   kK. We compared theoretical He I, He II, C III, C IV, O IV, and O V line profiles with FUSE and GHRS UV observations and optical UVES observations. The most prominent C III λ   977.020 Å has a strong, blue-shifted interstellar component and is not well suited to an analysis. The better agreement of C III λλ   1175 Å in the line cores favors T_eff = 65   kK, while the “shoulders” between the C III λλ   1175 Å components are better matched at T_eff = 70   kK. The lower T_eff is supported by the Ge IV/Ge V ionization balance (Fig. 6), if we judge e.g. Ge IV λ   936.765 Å. The Ge V lines appear almost with same strengths in both (T_eff = 70   kK and T_eff = 65   kK) models. On the other hand, Kr VI/Kr VII favors T_eff = 70   kK (Werner et al. 2012), and He I λ   4471 Å is too strong in the model at T_eff = 65   kK (Fig. 6). The O IV/O V ionization appears unchanged between T_eff = 65   kK and T_eff = 70   kK.

It is worthwhile mentioning that a lower T_eff would strongly improve the agreement between model and the observed EUV flux (EUVE J0503−28.8, Werner et al. 2001). A more precise determination of T_eff and log g of RE 0503−289 based on additional high-signal-to-noise ratio (S/N) optical spectra and more ionization equilibria of different species is highly desirable. Our test calculations have shown that our Ge line identifications and abundance determination are affected only marginally by this uncertainty in atmosphere parameters.

6. Results and conclusions

Successful reproduction of the identified Ge lines in high-resolution UV spectra of RE 0503−289 by our synthetic spectra calculated from NLTE model atmospheres using newly calculated oscillator strengths of Ge V and Ge VI shows that – when done with sufficient care – theory works.

We derive a photospheric abundance of log Ge = −3.8 ± 0.3 (mass fraction) in RE 0503−289. This is about 650 times the solar abundance. This high value is similar to the results of Werner et al. (2012) for Kr (450 times solar) and Xe (3800 times solar).

The identifications of trans-iron elements in the FUSE spectrum of RE 0503−289 and the abundance determinations of Ge, Kr, and Xe show that RE 0503−289 is important for our understanding of the non-DA white dwarf evolutionary channel. Further abundance determinations of the identified species is highly desirable. This is a challenge for atomic physicists.

It is worthwhile mentioning here the two HST observations of RE 0503−289 taken with STIS¹⁶ (1999-03-23, ObsIds O56401010, O56401020) that missed the star because the prior target acquisition apparently failed. Unfortunately, they were not repeated. The available GHRS¹⁷ observations cover only small wavelength sections of the NUV, and the IUE high-resolution

spectra (e.g. SWP52803HL) have too-low an S/N. Obtaining high-resolution, high S/N spectra with HST/STIS should not be missed because the NUV spectrum probably offers important, additional spectral information.

The Ge model ions that were used in this analysis were developed in the framework of the Virtual Observatory (VO¹⁸) in a German Astrophysical Virtual Observatory (GAVO¹⁹) project and are provided within TMAD (Sect. 4). The spectral energy distribution of our final model can be retrieved in VO-compliant form via the registered VO service TheoSSA²⁰.

Online material

Fig. 4 He I / He II, C III / C IV, and O IV / O V ionization equilibria in our Teff = 70   kK model compared with FUSE, GHRS (smoothed with a low-pass filter (m = 15, n = 4) for clarity, Savitzky & Golay 1964), and UVES observations. Wavelength and flux scales are indicated by bars. The model spectrum is convolved with a Gaussian to match the respective instrument’s resolution. Unidentified lines in the model stem from Ca-Ni.

Fig. 5 Same as Fig. 4 for Teff = 65   kK.

Fig. 6 Same as Fig. 3 for Teff = 65   kK.

Acknowledgments

T.R. is supported by the German Aerospace Center (DLR, grant 05 OR 0806). Financial support from the Belgian FRS-FNRS is also acknowledged. E.B. and P.Q. are Research Director and Senior Research Associate, respectively, of this organization. This research has made use of the SIMBAD database, operated at the CDS, Strasbourg, France. We thank Ralf Napiwotzki for providing us the SPY spectrum of RE 0503−289. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts.

References

All Tables

All Figures

	Fig. 1 Ionization fractions of Ge iii–vii. The formation depths of the Ge V and Ge VI line cores are marked at the top.
In the text

	Fig. 2 Grotrian diagram of our Ge IV (top), Ge V (middle), and Ge VI (bottom) model ions. Thick black and thin gray lines represent radiative transitions with known and unknown f values, respectively. The identified lines (red) are labeled with their respective wavelengths in Å.
In the text

Fig. 3 Ge IV (top), Ge V, and Ge VI (bottom) lines in FUSE, ORFEUS/BEFS (Ge IV λ   1189 Å), and IUE (Ge V λ   1222 Å, Ge IV λ   1229 Å) observations compared with a Teff = 70   kK/log g = 7.5 TMAP model. The abundances (top right) are logarithmic mass fractions. IG denotes a generic model atom (Rauch & Deetjen 2003), which comprises Ca, Sc, Ti, V, Cr, Mn, and Co. The synthetic spectra a convolved with a Gaussian of 0.05 Å (FWHM, 0.1 Å for the IUE comparison) to match the instrument resolution. A radial-velocity shift of vrad = 23   km   s-1 is applied to the observation.

In the text

Fig. 4 He I / He II, C III / C IV, and O IV / O V ionization equilibria in our Teff = 70   kK model compared with FUSE, GHRS (smoothed with a low-pass filter (m = 15, n = 4) for clarity, Savitzky & Golay 1964), and UVES observations. Wavelength and flux scales are indicated by bars. The model spectrum is convolved with a Gaussian to match the respective instrument’s resolution. Unidentified lines in the model stem from Ca-Ni.

In the text

	Fig. 5 Same as Fig. 4 for Teff = 65   kK.
In the text

	Fig. 6 Same as Fig. 3 for Teff = 65   kK.
In the text