Free Access
Issue
A&A
Volume 564, April 2014
Article Number A41
Number of page(s) 8
Section Atomic, molecular, and nuclear data
DOI https://doi.org/10.1051/0004-6361/201423491
Published online 03 April 2014

© ESO, 2014

1. Introduction

In a recent spectral analysis of the hydrogen-rich DA-type white dwarf G191−B2B, Rauch et al. (2013) identified and reproduced stellar lines of C, N, O, Al, Si, O, P, S, Fe, Ni, Ge, and Sn. In addition, they identified 21 Zn iv lines. The determined Zn abundance (logarithmic mass fraction of −4.89, 7.5 × solar) was uncertain because the unknown Zn iv oscillator strengths were approximated by values of the isoelectronic Ge vi taken from Rauch et al. (2012).

In this paper, we introduce new oscillator strengths for Zn iv and Zn v (Sect. 2). Then, we describe briefly our observations (Sect. 3), our analysis strategy (Sect. 4), and revisit G191−B2B to perform a precise determination of its Zn abundance (Sect. 5). The white dwarf RE 0503−289 is hotter than G191−B2B and its trans-iron element abundances are strongly oversolar (Werner et al. 2012; Rauch et al. 2013) and, thus, it appears promising to identify Zn lines. In Sect. 6, we describe our search for these and the determination of its Zn abundance. We summarize our results and conclude in Sect. 7.

2. Transition probabilities in Zn iv and Zn v

Radiative decay rates (oscillator strengths and transition probabilities) have been computed using the pseudo-relativistic Hartree-Fock (HFR) method as described by Cowan (1981). For Zn iv, configuration interaction has been considered among the configurations 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. Using experimental energy levels published by Sugar & Musgrove (1995), the average energies (Eav), the Slater integrals (Fk, Gk), the spin-orbit parameters (ζnl), and the effective interaction parameters (α, β) corresponding to 3d9, 3d84s, 3d84p configurations were optimized using a well-established least-squares fitting process minimizing the differences between calculated and experimental energy levels within both configurations. In the case of Zn v, the configurations included in the HFR model were 3d8, 3d74s, 3d75s, 3d74d, 3d75d, 3d64s2, 3d64p2, 3d64d2, 3d64s5s, 3d64s4d, 3d64s5d for the even parity and 3d74p, 3d75p, 3d74f, 3d75f, 3d64s4p, 3d64s5p, 3d64s4f and 3d64p4d for the odd parity. For this ion, the semi-empirical fitting process was performed to optimize the radial integrals corresponding to 3d8, 3d74s, and 3d74p configurations using the experimental energy levels compiled by Sugar & Musgrove (1995). The HFR oscillator strengths (log gf) and transition probabilities (gA, in s-1) for Zn iv and Zn v spectral lines are reported in Tables 1 and 2, respectively, alongside with the numerical values (in cm-1) of lower and upper energy levels and the corresponding wavelengths (in Å). In the last column of each table, we also give the cancellation factor CF as defined by Cowan (1981). We note that very small values of this factor (typically <0.05) indicate strong cancellation effects in the calculation of line strengths. In these cases, the corresponding gf and gA values could be very inaccurate and so need to be considered with some care. However, very few transitions appearing in Tables 1 and 2 are affected by these effects. Figure 1 shows Grotrian diagrams of Zn iv and Zn v including all levels and transitions from Tables 1 and 2.

thumbnail Fig. 1

Grotrian diagrams of our Zn iv (top) and Zn v (bottom) model ions. Horizontal bars indicate levels, gray lines represent radiative transitions with known f values, respectively. The dashed lines show the ionization energies.

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3. Observations

In this analysis, we use the FUSE1 spectrum of RE 0503−289 and the FUSE and HST/STIS2 spectra G191−B2B that are described in detail by Werner et al. (2012) and Rauch et al. (2013), respectively.

Both FUSE spectra are co-added from all available observations of RE 0503−289 and G191−B2B. They cover the wavelength range 910 Å < λ < 1188  Å. Their resolving power is R = λλ ≈ 20 000. The HST/STIS spectrum of G191−B2B is co-added from 105 observation with the highest resolution (grating E140H, R ≈ 118 000, 1145 Å < λ < 1700  Å) available via MAST.

thumbnail Fig. 2

Ionization fractions of Zn ii vi in our G191−B2B model atmosphere. m is the column mass, measured from the outer boundary of our model atmosphere. The formation depths (i.e., τ = 1) of the Zn iv v line cores are marked.

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Table 3

Statistics of our N, O, and Zn model atoms for G191−B2B.

thumbnail Fig. 3

Zn iv lines (left panel, marked with their wavelengths in Å, blue in the online version) and Zn v lines (right panel, marked in green) in the FUSE (for lines at λ < 1150  Å) and HST/STIS (λ > 1150  Å) observations of G191−B2B compared with our theoretical line profiles. For the identification of other lines, see Rauch et al. (2013). The vertical bar shows 10% of the continuum flux.

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Table 4

Identified Zn lines in the UV spectrum of G191−B2B.

4. Model atmospheres and atomic data

To determine the Zn abundance of G191−B2B, it would be straightforward to use the final model of Rauch et al. (2013) as well as their model atoms with the only exception that the Zn iv and Zn v model ions were replaced by the extended versions that consider the newly calculated transition probabilities (Sect. 2). Unfortunately, the employed Tübingen non-local thermodynamic equilibrium (NLTE) model-atmosphere package (Werner et al. 2003; Rauch & Deetjen 2003, TMAP3), which is used to calculate plane-parallel, chemically homogeneous, metal-line blanketed NLTE model atmospheres, overcharged our FORTRAN compilers. The program would not compile if the array sizes were increased further according to the much higher number of atomic levels treated in NLTE and the respective higher number of radiative and collisional transitions.

thumbnail Fig. 4

Theoretical line profiles of the strongest Zn iv lines (left) and Zn v lines (right) (marked with their wavelengths from Tables 1 and 2) calculated from our model of G191−B2B with a Zn abundance of 3.0 × 10-6 (mass fraction) located in the STIS wavelength range compared with the observation. The lines are shifted to the observation, see Table 4.

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thumbnail Fig. 5

Theoretical line profiles of the strongest Zn v lines calculated from our model of RE 0503−289 with a Zn abundance of 2.7 × 10-4 (mass fraction) located in the FUSE wavelength range compared with the observation. The lines are shifted to the observation, see Table 5.

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thumbnail Fig. 6

Zn v lines in the FUSE observation of RE 0503−289 compared with our theoretical line profiles.

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Table 5

Like Table 4, for RE 0503−289.

Thus, we decided to reduce the number of N and O levels treated in NLTE (Table 3) to create a TMAP executable. Test calculations have shown that the deviations in temperature and density structure between the final model of Rauch et al. (2013) and a model with reduced N and O model atoms are negligible. Then, the Zn occupation numbers are determined in a line-formation calculation, i.e., at fixed temperature and density structure. Since Zn opacities were already considered in our start model, the atmospheric structure and the background opacities are well modeled.

All model atoms (including Zn) are provided via the Tübingen Model-Atom Database (TMAD4, Rauch & Deetjen 2003), that has been set up within a project of the German Astrophysical Virtual Observatory (GAVO5). All SEDs that were calculated for this analysis are available via the registered Theoretical Stellar Spectra Access (TheoSSA6) VO service.

5. The photospheric Zn abundance in G191B2B

Zn iv and Zn v are the dominant ionization stages of Zn in the atmosphere of G191−B2B (Fig. 2). Therefore, we closely inspected the available spectra for lines of these ions.

In the FUSE and HST/STIS observations of G191−B2B (cf. Rauch et al. 2013) we identified 31 Zn iv (10 new identifications) and 16 Zn v (all new) lines. The observed wavelength positions (a radial velocity of vrad = 22.1 km s-1 was applied according to Holberg et al. 1994; Rauch et al. 2013) deviate partly from those given in Tables 1 and 2 by some hundredths of an Å. The good agreement of the strongest, unshifted lines in our model7 (Fig. 3) with the observations permits to shift the lines to observed absorption features in their closest vicinity. The reason for this uncertainty is most likely the limited accuracy of the Zn iv and Zn v energy levels from which the wavelengths of the line transitions were calculated. The identified lines are summarized in Table 4.

Our calculations have shown that the Zn iv / Zn v ionization equilibrium at and log g = 7.6 (cf. Rauch et al. 2013) is well reproduced (Figs. 3, 4). On the other hand, the Zn abundance given by Rauch et al. (2013, 1.3 × 10-5 ± 0.5 dex is too high. We reduced it to 3.0 × 10-6 ± 0.2 dex (about 1.7 times solar, following Asplund et al. 2009) to reproduce the observed Zn lines best. This agrees with the previous value within the error limits. Even a solar Zn abundance, however, is possible within the error limits.

6. The photospheric Zn abundance in RE 0503289

Our inspection of all UV spectra that were already used by Werner et al. (2012) has shown that only RE 0503−289 exhibits prominent Zn lines (Fig. 5). We find that in its FUSE spectrum (vrad = 26.3 km s-1), a rich Zn v spectrum of 128 lines (Fig. 6, Table 5) is present. The synthetic spectrum of our final model shows more, weak lines that do not have an unambiguous line identification due to the signal-to-noise ratio (S/N) of the observation. The model’s prediction of their relative line strengths facilitates to distinguish between noise and “real” lines in the observation and, hence, to identify even such weak lines. In general, all lines with oscillator strengths gf ≳ 0.01 can be detected.

thumbnail Fig. 7

Like Fig. 2, for our RE 0503−289 model atmosphere.

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Dreizler & Werner (1996) determined and log g = 7.50 ± 0.25 for RE 0503−289. This was recently verified by well-matched ionization equilibria of Kr and Xe (Werner et al. 2012, Kr vi / Kr vii, Xe vi / Xe vii) and Ge (Rauch et al. 2012, Ge v / Ge vi). We adopt these values and start our calculation based on the final model of Werner et al. (2012) that considers opacities of He, C, N, O, Ge, Kr, Xe, and of the iron-group elements (Ca - Ni). We follow the same strategy described in Sect. 4, but this time, we reduced the size of the Ge model atom in the line-formation calculations.

The higher Teff compared to that of G191−B2B shifts the Zn ionization equilibrium strongly towards higher ionization (Fig. 7). Zn v remains dominant while Zn iv is less occupied by a factor of about 100 at all depths. The ionization fraction of Zn vi is also much below that of Zn v and we only expect weak lines. The strongest Zn vi lines8 are located in the soft X-ray to EUV9 wavelength range where we do not have high-quality observations to evaluate.

We determine a Zn abundance of 2.7 × 10-4 ± 0.2 dex (about 155 × solar) to reproduce the observed Zn v line profiles best (Fig. 5).

7. Results and conclusions

The identified Zn iv and Zn v lines in the high-resolution UV spectra of G191−B2B and RE 0503−289 are well reproduced with our newly calculated oscillator strengths by our NLTE model-atmosphere calculations.

We determined photospheric abundances of log Zn = −5.52 ± 0.2 (mass fraction, 1.9−4.8 × 10-6, 1.1–2.8 times the solar abundance) and log Zn = −3.57 ± 0.2 (1.7−4.3 × 10-4, 98–248 times solar) for the DA-type white dwarf G191−B2B and the DO-type white dwarf RE 0503−289, respectively. The highly supersolar Zn abundance is in line with the high abundances of trans-iron elements Ge (650 × solar, Rauch et al. 2012), Kr (450 × solar), Xe (3800 × solar, Werner et al. 2012) in RE 0503−289.

The identification of new lines due to trans-iron elements, e.g., Ga, Ge, As, Se, Kr, Mo, Sn, Te, I, and Xe (Werner et al. 2012) and Zn (Rauch et al. 2013, and in this paper) in G191−B2B and RE 0503−289 promises to help enhance the understanding of extremely metal-rich white dwarf photospheres and their relation to AGB and post-AGB stellar evolution. Their reproduction, i.e., the precise abundance determination, e.g., of Kr and Xe (Werner et al. 2012), Ge and Sn (Rauch et al. 2012), and Zn (this paper) is strongly dependent on the available atomic data. This remains a challenge for atomic and theoretical physicists.


1

Far Ultraviolet Spectroscopic Explorer.

2

Hubble Space Telescope/Space Telescope Imaging Spectrograph, for our high-resolution spectrum of G191−B2B, see http://www.stsci.edu/hst/observatory/crds/calspec.html

7

All synthetic spectra shown in this paper are convolved with Gaussians to match the spectral resolution (FUSE: FWHM = 0.06 Å, STIS: FWHM = 0.01 Å).

9

Extreme ultraviolet.

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. PQ is research director of this organization. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. 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

Table 3

Statistics of our N, O, and Zn model atoms for G191−B2B.

Table 4

Identified Zn lines in the UV spectrum of G191−B2B.

All Figures

thumbnail Fig. 1

Grotrian diagrams of our Zn iv (top) and Zn v (bottom) model ions. Horizontal bars indicate levels, gray lines represent radiative transitions with known f values, respectively. The dashed lines show the ionization energies.

Open with DEXTER
In the text
thumbnail Fig. 2

Ionization fractions of Zn ii vi in our G191−B2B model atmosphere. m is the column mass, measured from the outer boundary of our model atmosphere. The formation depths (i.e., τ = 1) of the Zn iv v line cores are marked.

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In the text
thumbnail Fig. 3

Zn iv lines (left panel, marked with their wavelengths in Å, blue in the online version) and Zn v lines (right panel, marked in green) in the FUSE (for lines at λ < 1150  Å) and HST/STIS (λ > 1150  Å) observations of G191−B2B compared with our theoretical line profiles. For the identification of other lines, see Rauch et al. (2013). The vertical bar shows 10% of the continuum flux.

Open with DEXTER
In the text
thumbnail Fig. 4

Theoretical line profiles of the strongest Zn iv lines (left) and Zn v lines (right) (marked with their wavelengths from Tables 1 and 2) calculated from our model of G191−B2B with a Zn abundance of 3.0 × 10-6 (mass fraction) located in the STIS wavelength range compared with the observation. The lines are shifted to the observation, see Table 4.

Open with DEXTER
In the text
thumbnail Fig. 5

Theoretical line profiles of the strongest Zn v lines calculated from our model of RE 0503−289 with a Zn abundance of 2.7 × 10-4 (mass fraction) located in the FUSE wavelength range compared with the observation. The lines are shifted to the observation, see Table 5.

Open with DEXTER
In the text
thumbnail Fig. 6

Zn v lines in the FUSE observation of RE 0503−289 compared with our theoretical line profiles.

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In the text
thumbnail Fig. 7

Like Fig. 2, for our RE 0503−289 model atmosphere.

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In the text

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