Issue 
A&A
Volume 606, October 2017



Article Number  A105  
Number of page(s)  27  
Section  Atomic, molecular, and nuclear data  
DOI  https://doi.org/10.1051/00046361/201730383  
Published online  20 October 2017 
Stellar laboratories
IX. New Se v, Sr iv–vii, Te vi, and I vi oscillator strengths and the Se, Sr, Te, and I abundances in the hot white dwarfs G191−B2B and RE 0503−289^{⋆,}^{⋆⋆,}^{⋆⋆⋆}
^{1} Institute for Astronomy and Astrophysics, Kepler Center for Astro and Particle Physics, Eberhard Karls University, Sand 1, 72076 Tübingen, Germany
email: rauch@astro.unituebingen.de
^{2} Physique Atomique et Astrophysique, Université de Mons, UMONS, 7000 Mons, Belgium
^{3} IPNAS, Université de Liège, Sart Tilman, 4000 Liège, Belgium
^{4} NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
^{5} Astronomisches RechenInstitut (ARI), Centre for Astronomy of Heidelberg University, Mönchhofstraße 1214, 69120 Heidelberg, Germany
Received: 2 January 2017
Accepted: 17 June 2017
Context. To analyze spectra of hot stars, advanced nonlocal thermodynamic equilibrium (NLTE) modelatmosphere techniques are mandatory. Reliable atomic data is crucial for the calculation of such model atmospheres.
Aims. We aim to calculate new Sr iv–vii oscillator strengths to identify for the first time Sr spectral lines in hot white dwarf (WD) stars and to determine the photospheric Sr abundances. To measure the abundances of Se, Te, and I in hot WDs, we aim to compute new Se v, Te vi, and I vi oscillator strengths.
Methods. To consider radiative and collisional boundbound transitions of Se v, Sr iv  vii, Te vi, and I vi in our NLTE atmosphere models, we calculated oscillator strengths for these ions.
Results. We newly identified four Se v, 23 Sr v, 1 Te vi, and three I vi lines in the ultraviolet (UV) spectrum of RE 0503−289. We measured a photospheric Sr abundance of 6.5^{+ 3.8}_{2.4}× 10^{4} (mass fraction, 9500–23 800 times solar). We determined the abundances of Se (1.6^{+ 0.9}_{0.6}× 10^{3}, 8000–20 000), Te (2.5^{+ 1.5}_{0.9}× 10^{4}, 11 000–28 000), and I (1.4^{+ 0.8}_{0.5}× 10^{5}, 2700–6700). No Se, Sr, Te, and I line was found in the UV spectra of G191−B2B and we could determine only upper abundance limits of approximately 100 times solar.
Conclusions. All identified Se v, Sr v, Te vi, and I vi lines in the UV spectrum of RE 0503−289 were simultaneously well reproduced with our newly calculated oscillator strengths.
Key words: atomic data / line: identification / stars: abundances / stars: individual: G191B2B / stars: individual: RE 0503289 / virtual observatory tools
Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS526666.
Full Tables A.15 to A.21 are only available via the German Astrophysical Virtual Observatory (GAVO) service TOSS (http://dc.gvo.org/TOSS).
© ESO, 2017
1. Introduction
Recent spectral analyses (cf., Rauch et al. 2017) of highresolution UV spectra of the heliumrich (DOtype) white dwarf (WD) RE 0503−289 (RX J0503.9−2854, WD 0501+527, McCook & Sion 1999a,b) revealed strongly enriched transiron elements (atomic numbers Z ≥ 30) in its photosphere (Fig. 1). Efficient radiative levitation (Rauch et al. 2016a) in this hot WD (effective temperature T_{eff} = 70 000 ± 2000 K, surface gravity log (g/ cm s^{2}) = 7.5 ± 0.1, Rauch et al. 2016b) can increase abundances by more than 4 dex compared with solar values. In the cooler (T_{eff} = 60 000 ± 2000 K, log g = 7.6 ± 0.05, Rauch et al. 2013), hydrogenrich (DAtype) WD G191−B2B (WD 0501+527, McCook & Sion 1999a,b), the radiative levitation is able to retain only a factor of ≈100 fewer transiron elements in the photosphere than in RE 0503−289 (Fig. 1).
Fig. 1
Solar abundances (Asplund et al. 2009; Scott et al. 2015a,b; Grevesse et al. 2015, thick line; the dashed lines connect the elements with even and with odd atomic number) compared with the determined photospheric abundances of RE 0503−289 (red squares, Dreizler & Werner 1996; Rauch et al. 2012, 2014a,b, 2015, 2016a,b, 2017, and this work). The uncertainties of the WD abundances are about 0.2 dex in general. Arrows indicate upper limits. Top panel: abundances given as logarithmic mass fractions. Bottom panel: abundance ratios to respective solar values, [X] denotes log (fraction/solar fraction) of species X. The dashed, green line indicates solar abundances. 
The search for signatures of transiron elements in the spectra of RE 0503−289 and G191−B2B was initiated by the discovery of Ga, Ge, As, Se, Kr, Mo, Sn, Te, I, and Xe lines in RE 0503−289 (Werner et al. 2012b). Subsequent calculations of transition probabilities allowed reliable abundance determinations of Zn (atomic number Z = 30), Ga (31), Ge (32), Kr (36), Zr (40), Mo (42), Xe (54), and Ba (56) (e.g., Rauch et al. 2017, and references therein). Based on the wavelengths provided by the Atomic Spectra Database (ASD^{1}) of the National Institute of Standards and Technology (NIST), we have identified some strong lines of strontium (38), an element that was hitherto not detected in hot WDs. For an identification of other, weaker Sr lines and a subsequent abundance analysis, we decided to calculate new Sr ivvii transition probabilities.
The paper is organized as follows. We briefly introduce the UV spectra in Sect. 2. Our model atmospheres, the atomic data as well as the transitionprobability calculations are described in Sect. 3. Here, we have included the calculation of new transition probabilities for Se v, Te vi, and I vi because these are the last three elements (34, 52, and 53, respectively), that were previously identified by Werner et al. (2012b) in the spectrum of RE 0503−289. The line identification and abundance analysis then follows in Sect. 4.
2. Observations
Our analysis is based on UV spectroscopy that was performed with the Far Ultraviolet Spectroscopic Explorer (FUSE, 910 Å < λ < 1190 Å, resolving power R ≈ 20 000) and the Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS, 1144 Å < λ < 1709 Å, R ≈ 45 800). The spectra are described in detail in Hoyer et al. (2017). The observed spectra shown here were shifted to rest wavelengths, using v_{rad} = 24.56 km s^{1} for G191−B2B (Lemoine et al. 2002) and 25.8 km s^{1} for RE 0503−289 (Hoyer et al. 2017). To compare them with our synthetic spectra, the latter were convolved with Gaussians to model the respective instruments’ resolving power.
3. Model atmospheres and atomic data
To calculate model atmospheres for our analysis, we used the Tübingen ModelAtmosphere Package (TMAP^{2}, Werner et al. 2003, 2012a). These models are planeparallel, chemically homogeneous, and in hydrostatic and radiative equilibrium. TMAP considers nonlocal thermodynamic equilibrium (NLTE). More details are given by Rauch et al. (2016b). We include opacities of H^{G}, He, C, N, O, Al, Si, P, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Ga, Ge, As, Se, Kr^{R}, Sr, Zr, Mo, Sn, Te, I, Xe^{R}, and Ba (^{G}: only in G191−B2B models, ^{R}: only in RE 0503−289 models). Model atoms for all species with Z < 20 are compiled from the Tübingen Model Atom Database (TMAD). For the irongroup elements (Ca – Ni, 20 ≤ Z ≤ 28), model atoms were constructed with a statistical approach by calculating socalled super levels and super lines (IrOnIc code, Rauch & Deetjen 2003) with the Tübingen IronGroup Opacity – IrOnIc WWW Interface (MüllerRingat 2013). For transiron elements (Z ≥ 29), we transferred their atomic data into Kuruczformatted files (cf., Rauch et al. 2015), and followed the same statistical method. The Se, Sr, Te, and I modelatom statistics are given in Table 1.
New sets of oscillator strengths and transition probabilities for the Se v, Sr ivvii, Te vi, and I vi ions were computed using the pseudorelativistic HartreeFock (HFR) approach of Cowan (1981) modified for including corepolarization effects, giving rise to the HFR+ CPOL method, as described by Quinet et al. (1999, 2002). For each ion, this method was combined with a semiempirical leastsquares fit of radial energy parameters to minimize the differences between computed and available experimental energy levels.
Se v:
the 4s^{2}, 4p^{2}, 4d^{2}, 4f^{2}, 4s4d, 4s5d, 4s6d, 4s5s, 4s6s, 4p4f, 4p5f, 4p6f, 4d5s, 4d6s, 4d5d, and 4d6d evenparity configurations and the 4s4p, 4s5p, 4s6p, 4s4f, 4s5f, 4s6f, 4p4d, 4p5d, 4p6d, 4p5s, 4p6s, 4d4f, and 4d5f oddparity configurations were explicitly included in the physical model. Corepolarization effects were estimated by assuming a Nilike Se vii ionic core with a corepolarizability α_{d} of 0.36 au, as reported by Johnson et al. (1983), and a cutoff radius, r_{c} equal to 0.62 au, corresponding to the HFR mean radius of the outermost core orbital (3d). Using the experimental energy levels published by Churilov & Joshi (1995), the radial integrals characterizing the 4s^{2}, 4p^{2}, 4s4d, 4s5d, 4s5s, 4s6s, 4s4p, 4s5p, 4s4f, 4p4d, and 4p5s configurations were fitted. This semiempirical adjustment allowed us to reduce the average deviations between calculated and measured energies to 8 cm^{1} and 219 cm^{1} for even and odd parities, respectively.
Fig. 2
Sr v lines in the observation (gray line) of RE 0503−289, labeled with their wavelengths from Table A.17. The thick, red spectrum is calculated from our best model with a Sr mass fraction of 6.5 × 10^{4}. The dashed, green line shows a synthetic spectrum calculated without Sr. In cases of Sr vλ 942.943 Å and Sr vλ 1412.959 Å, the red, dashed lines show two synthetic spectra calculated with Sr abundances that were increased and decreased by 0.3 dex. The vertical bar indicates 10% of the continuum flux. Identified lines are marked. “is” denotes interstellar. 
Sr iv:
we considered interaction among the configurations 4s^{2}4p^{5}, 4s^{2}4p^{4}5p, 4s^{2}4p^{4}6p, 4s^{2}4p^{4}4f, 4s^{2}4p^{4}5f, 4s^{2}4p^{4}6f, 4s^{2}4p^{4}6h, 4s4p^{5}4d, 4s4p^{5}5d, 4s4p^{5}6d, 4s4p^{5}5s, 4s4p^{5}6s, 4s4p^{5}5g, 4s4p^{5}6g, 4s^{2}4p^{3}4d^{2}, 4s^{2}4p^{3}4f^{2}, and 4p^{6}4f for the odd parity, and 4s4p^{6}, 4s^{2}4p^{4}4d, 4s^{2}4p^{4}5d, 4s^{2}4p^{4}6d, 4s^{2}4p^{4}5s, 4s^{2}4p^{4}6s, 4s^{2}4p^{4}7s, 4s^{2}4p^{4}5g, 4s^{2}4p^{4}6g, 4s4p^{5}4f, 4s4p^{5}5f, 4s4p^{5}6f, 4s4p^{5}5p, 4s4p^{5}6p, 4s4p^{5}6h, 4p^{6}4d, and 4p^{6}5s for the even parity. The corepolarization parameters were the dipole polarizability of a Nilike Sr ix ionic core as reported by Johnson et al. (1983), that is, α_{d} = 0.13 au, and the cutoff radius corresponding to the HFR mean value ⟨ r ⟩ of the outermost core orbital (3d), i.e., r_{c} = 0.49 au. Using experimental energy levels compiled by Sansonetti (2012), the radial integrals (average energy, Slater, spinorbit and effective interaction parameters) of 4p^{5}, 4p^{4}5p, 4p^{4}6p, 4p^{4}4f, 4p^{4}5f, 4p^{4}6h, 4s4p^{5}4d, 4s4p^{6}, 4p^{4}4d, 4p^{4}5d, 4p^{4}6d, 4p^{4}5s, 4p^{4}6s, 4p^{4}7s, 4p^{4}5g, and 4p^{4}6g configurations were optimized by a leastsquares fitting procedure in which the mean deviations with experimental data were found to be equal to 145 cm^{1} for the odd parity and 150 cm^{1} for the even parity.
Sr v:
the HFR method was used with, as interacting configurations, 4s^{2}4p^{4}, 4s^{2}4p^{3}5p, 4s^{2}4p^{3}6p, 4s^{2}4p^{3}4f, 4s^{2}4p^{3}5f, 4s^{2}4p^{3}6f, 4s^{2}4p^{3}6h, 4s4p^{4}4d, 4s4p^{4}5d, 4s4p^{4}6d, 4s4p^{4}5s, 4s4p^{4}6s, 4s4p^{4}5g, 4s4p^{4}6g, 4s^{2}4p^{2}4d^{2}, 4s^{2}4p^{2}4f^{2}, 4p^{6}, and 4p^{5}4f for the even parity, and 4s4p^{5}, 4s^{2}4p^{3}4d, 4s^{2}4p^{3}5d, 4s^{2}4p^{3}6d, 4s^{2}4p^{3}5s, 4s^{2}4p^{3}6s, 4s^{2}4p^{3}5g, 4s^{2}4p^{3}6g, 4s4p^{4}4f, 4s4p^{4}5f, 4s4p^{4}6f, 4s4p^{4}5p, 4s4p^{4}6p, 4s4p^{4}6h, 4p^{5}4d, and 4p^{5}5s for the odd parity. Corepolarization effects were estimated using the same α_{d} and r_{c} values as those considered in Sr iv. The radial integrals corresponding to 4p^{4}, 4p^{3}5p, 4s4p^{5}, 4p^{3}4d, 4p^{3}5d, 4p^{3}5s, and 4p^{3}6s were adjusted to reproduce at best the experimental energy levels tabulated by Sansonetti (2012). We note that the few levels reported by this author as belonging to the 4p^{3}4f and 4p^{3}5f configurations were not included in the fitting process because it was found that most of those levels were strongly mixed with states of experimentally unknown configurations, such as 4s4p^{4}4d, 4p^{3}6p, 4p^{2}4d^{2}, and 4s4p^{4}5s. It was then extremely difficult to establish an unambiguous correspondence between the calculated and experimental energies. For the levels considered in our semiempirical adjustment, we found mean deviations equal to 138 cm^{1} and 231 cm^{1} in even and odd parities, respectively.
Sr vi:
the configurations included in the HFR model were 4s^{2}4p^{3}, 4s^{2}4p^{2}5p, 4s^{2}4p^{2}6p, 4s^{2}4p^{2}4f, 4s^{2}4p^{2}5f, 4s^{2}4p^{2}6f, 4s^{2}4p^{2}6h, 4s4p^{3}4d, 4s4p^{3}5d, 4s4p^{3}6d, 4s4p^{3}5s, 4s4p^{3}6s, 4s4p^{3}5g, 4s4p^{3}6g, 4s^{2}4p4d^{2}, 4s^{2}4p4f^{2}, 4p^{5}, and 4p^{4}4f for the odd parity, and 4s4p^{4}, 4s^{2}4p^{2}4d, 4s^{2}4p^{2}5d, 4s^{2}4p^{2}6d, 4s^{2}4p^{2}5s, 4s^{2}4p^{2}6s, 4s^{2}4p^{2}5g, 4s^{2}4p^{2}6g, 4s4p^{3}4f, 4s4p^{3}5f, 4s4p^{3}6f, 4s4p^{3}5p, 4s4p^{3}6p, 4s4p^{3}6h, 4p^{4}4d, and 4p^{4}5s for the even parity. The same corepolarization parameters as those used for Sr iv were considered while the fitting process was performed with the few experimental energy levels listed in the compilation of Sansonetti (2012) for optimizing the radial parameters of 4p^{3}, 4s4p^{4}, and 4p^{2}5s configurations, leading to mean deviations equal to 13 cm^{1} (odd parity) and 32 cm^{1} (even parity).
Sr vii:
a model similar to that of Sr vi was used, for which the 4s^{2}4p^{2}, 4s^{2}4p5p, 4s^{2}4p6p, 4s^{2}4p4f, 4s^{2}4p5f, 4s^{2}4p6f, 4s^{2}4p6h, 4s4p^{2}4d, 4s4p^{2}5d, 4s4p^{2}6d, 4s4p^{2}5s, 4s4p^{2}6s, 4s4p^{2}5g, 4s4p^{2}6g, 4s^{2}4d^{2}, 4s^{2}4f^{2}, 4p^{4}, and 4p^{3}4f evenparity configurations and the 4s4p^{3}, 4s^{2}4p4d, 4s^{2}4p5d, 4s^{2}4p6d, 4s^{2}4p5s, 4s^{2}4p6s, 4s^{2}4p5g, 4s^{2}4p6g, 4s4p^{2}4f, 4s4p^{2}5f, 4s4p^{2}6f, 4s4p^{2}5p, 4s4p^{2}6p, 4s4p^{2}6h, 4p^{3}4d, and 4p^{3}5s oddparity configurations were explicitly included in the HFR model. Here also, we used the same corepolarization parameters as those considered for Sr iv. The semiempirical optimization process was carried out to adjust the radial parameters in 4p^{2}, 4s4p^{3}, and 4p5s with the experimental energy levels taken from Sansonetti (2012) giving rise to average deviations of 0 cm^{1} and 247 cm^{1} for even and odd parities, respectively.
Te vi:
the configuration interaction was considered among the following configurations: 4d^{10}5s, 4d^{10}6s, 4d^{10}7s, 4d^{10}5d, 4d^{10}6d, 4d^{10}7d, 4d^{9}5s^{2}, 4d^{9}5p^{2}, 4d^{9}5d^{2}, 4d^{9}4f^{2}, 4d^{9}5s5d, 4d^{9}5s6d, 4d^{9}5s6s, 4d^{9}4f5p, and 4d^{9}4f6p (even parity) and 4d^{10}5p, 4d^{10}6p, 4d^{10}7p, 4d^{10}4f, 4d^{10}5f, 4d^{10}6f, 4d^{10}7f, 4d^{9}5s5p, 4d^{9}5s6p, 4d^{9}5s5f, 4d^{9}5s6f, 4d^{9}4f5s, 4d^{9}4f6s, 4d^{9}4f5d, 4d^{9}4f6d (odd parity). The corepolarization parameters were those corresponding to a Rhlike Te viii ionic core, that is, α_{d} = 1.15 au (Fraga et al. 1976) and r_{c} ≡ ⟨ r ⟩ _{4d} = 0.95 au. The radial parameters of 4d^{10}5s, 4d^{10}6s, 4d^{10}5d, 4d^{9}5p^{2}, 4d^{10}5p, 4d^{10}6p, and 4d^{9}5s5p configurations were optimized to minimize the differences between the computed Hamiltonian eigenvalues and the experimental energy levels published by Crooker & Joshi (1964), Dunne & O’Sullivan (1992), and Ryabtsev et al. (2007) giving rise to mean deviations of 89 m^{1} (even parity) and 13 cm^{1} (odd parity).
I vi:
thirtytwo configurations were included in the HFR model used to compute the atomic structure, i.e., 5s^{2}, 5p^{2}, 5d^{2}, 4f^{2}, 5f^{2}, 5s5d, 5s6d, 5s7d, 5s6s, 5s7s, 5p4f, 5p5f, 5p6f, 5d6s, 5d7s, 5d6d, and 5d7d for the even parity and 5s5p, 5s6p, 5s7p, 5s4f, 5s5f, 5s6f, 5s7f, 5p5d, 5p6d, 5p7d, 5p6s, 5p7s, 5d4f, 5d5f, and 5d6f for the odd parity. An ionic core of the type Pdlike I viii was considered to estimate the corepolarization effects with the parameters α_{d} = 1.03 a.u. (Johnson et al. 1983) and r_{c}≡⟨ r ⟩_{4d} = 0.90 au. The semiempirical optimization process was carried out to adjust the radial parameters in 5s^{2}, 5p^{2}, 5s5d, 5s6s, 5s7s, 5s5p, 5s6p, 5p5d, and 5p6s with the experimental energy levels taken from Tauheed et al. (1997) giving rise to average deviations of 72 cm^{1} and 175 cm^{1} for even and odd parities, respectively.
Fig. 3
STIS observation of G191−B2B (gray) compared with synthetic line profiles of Se vλ 1433.466 Å, Sr vλ 1413.882 Å, Te viλ 1313.874 Å, and I viλ 1219.395 Å. The models were calculated with four abundances of the respective elements, without (thin, blue), with 100 times (thick, red), 1000 times (short dashed, violet) and 10 000 times solar abundance (long dashed, green). 
The parameters adopted in our computations are summarized in Tables A.1–A.7 while calculated and available experimental energies are compared in Tables A.8–A.14, for Se v, Sr ivvii,Te vi, and I vi, respectively. Tables A.15–A.21 give the newly computed weighted oscillator strengths (log g_{i}f_{ik}, i and k are the indexes of the lower and upper energy level, respectively) and transition probabilities (g_{k}A_{ki}, in s^{1}) together with the numerical values (in cm^{1}) of the lower and upper energy levels and the corresponding wavelengths (in Å). In the final column of each table, we also give the cancellation factor, CF, as defined by Cowan (1981). We note that very low values of this factor (typically <0.05) indicate strong cancellation effects in the calculation of line strengths. In these cases, the corresponding log g_{i}f_{ik} and g_{k}A_{ki} values could be very inaccurate and therefore need to be considered with some care. Figure B.1 shows the newly calculated log g_{i}f_{ik} values from the Xray to the far infrared wavelength range.
Radiative decay rates for some transitions in the same ions as those considered in the present work were reported in previous papers. More precisely, for Se v, largescale calculations for the 4s^{2}–4s4p transitions were performed by Liu et al. (2006) using the multiconfiguration DiracFock (MCDF) method and by Chen & Cheng (2010) using Bspline basis functions while the Relativistic Many Body Perturbation Theory (RMBPT), including the Breit interaction was used by Safronova & Safronova (2010) to compute oscillator strengths for transitions between evenparity 4s^{2}, 4p^{2}, 4s4d, 4d^{2}, 4p4f, 4f^{2} and oddparity 4s4p, 4s4f, 4p4d, 4d4f states. In Sr iv, transition probabilities and oscillator strengths for the electric dipole transitions involving the 4s^{2}4p^{5}, 4s^{2}4p^{4}4d and 4s4p^{6} configurations were obtained using the multiconfiguration DiracFock approach by Singh et al. (2013) and by Aggarwal & Keenan (2014). These works were subsequently extended by Aggarwal & Keenan (2015) to transitions involving the 4s^{2}4p^{5}, 4s^{2}4p^{4}4ℓ, 4s4p^{6}, 4s^{2}4p^{4}5ℓ, 4s^{2}4p^{3}4d^{2}, 4s4p^{5}4ℓ, and 4s4p^{5}5ℓ configurations. For Sr vi, relativistic quantum defect orbital (RQDO) and MCDF calculations of oscillator strengths were carried out by Charro & Martín (1998, 2005) for the 4p^{3}–4p^{2}5s transition array while the same methods were used by Charro & Martín (2002, 2005) for investigating the 4p^{2}–4p5s transitions in Sr vii. In the case of Te vi, Chou & Johnson (1997) performed thirdorder relativistic manybody perturbation theory (MBPT) calculations to evaluate the rates for 5s–5p transitions while Migdalek & Garmulewicz (2000) used a relativistic ab initio model potential approach with explicit local exchange to produce oscillator strengths. In the same ion, the 5s–5p transition rates were also computed by Głowacki & Migdałek (2009) who employed a configurationinteraction method with numerical DiracFock wave functions generated with noninteger outermost core shell occupation number while transition probabilities for 5s–5p, 5p–5d, 4f–5d, and 5d–5f transitions were calculated by Ivanova (2011). Finally, for I vi, the oscillator strengths of the allowed and spinforbidden 5s^{2}^{1}S_{0}–5s5p ^{1,3}P_{1} transitions were evaluated by Biémont et al. (2000) using the relativistic HartreeFock approach, including a corepolarization potential, and the MCDF method, as well as by Glowacki & Migdalek (2003) who used a relativistic configurationinteraction method with numerical DiracFock wavefunctions generated with an ab initio model potential allowing for corevalence correlation.
In order to estimate the overall reliability of the new atomic data obtained in the present work, we have compared them with some of the most recent and the most extensive calculations available in literature, selected among those listed hereabove. More particularly, in Se v, we noticed that our oscillator strengths were in excellent agreement (within a few percent) with the RMBPT values published by Safronova & Safronova (2010). In the case of Sr iv, we found a general agreement of about 20−30% between our results and the oscillator strengths published by Aggarwal & Keenan (2015), this agreement reaching even 10% for the most intense lines. For Te vi, the mean ratio between our transition probabilities and the few values reported by Ivanova (2011) was found to be equal to 1.18 while, for I vi, a very good agreement (within 10%) was observed when comparing the gfvalues obtained in the present work with those computed by Biémont et al. (2000) using either a relativistic HartreeFock or an MCDF model, taking corevalence correlation effects into account. All these comparisons allowed us to conclude that the accuracy of the new atomic data listed in the present paper should be about 20%, at least for the strongest lines.
Identified Se v, Sr v, Te vi, and I vi lines in the UV spectrum of RE 0503−289.
Fig. 4
As Fig. 2, for Se v (top, mass fraction of 1.6 ± 1.0 × 10^{3} in the model), Te vi (middle, 2.5 × 10^{4}), and I vi (bottom, 1.4 × 10^{5}) lines. Abundance dependencies (±0.3 dex, red, dashed lines) are demonstrated for Se vλ 1454.292 Å, Te viλ 951.021 Å, and I viλ 1057.530 Å. 
4. Results
In the FUSE and HST/STIS observations of RE 0503−289, we newly identified 23 Sr v lines, listed in Table 2 which complements Table A.1 of Hoyer et al. (2017). Many more weak Sr v lines are visible in our model spectra that are not detectable in the noise of the available observations. The models show that the strongest Sr vi lines are located in the extreme ultraviolet (EUV) and Xray wavelength range while Sr iv lines are too weak in general and fade within the noise of the available observations. The observed Sr v lines are well reproduced by our model calculated with a mass fraction of 6.5 × 10^{4} (Fig. 2). To estimate the abundance uncertainty from the error propagation of T_{eff} and log g, we evaluated models at the error limits (T_{eff} = 70 000 ± 2000 K, log g = 7.5 ± 0.1) and found that it is smaller than 0.1 dex. To consider the abundance uncertainties of other metals and the impact of their background opacities, we finally adopted a Sr mass fraction of 6.5 × 10^{4} with an uncertainty of 0.2 dex (Fig. 2 shows exemplarily the abundance dependence of two lines in a [−0.3 dex, +0.3 dex] abundance interval). The determined Sr abundance matches well the abundance pattern of transiron elements in RE 0503−289 (Fig. 1). Their extreme overabundances are the result of efficient radiative levitation (Rauch et al. 2016a).
Five Se v, three Te vi, and four I vi lines are used for the abundance determination of these elements (Fig. 4). We measured mass fractions of 1.6 × 10^{3}, 2.5 × 10^{4}, and 1.4 × 10^{5} for Se, Te, and I, respectively. These agree well with the expectations from the abundance pattern of transiron elements in RE 0503−289 (Fig. 1).
A very weak impact of Se, Sr, Te, and I lines is noticeable in the EUV wavelength range. The socalled EUV problem, that is, the flux discrepancy between model and observation in this wavelength range (cf., Hoyer et al. 2017) is, however, not significantly reduced. We note that Preval et al. (2017) showed recently that improved, larger photoionization crosssection of Ni can reduce this discrepancy.
The search for Se, Sr, Te, and I lines in the FUSE and HST/STIS observations of G191−B2B was entirely negative. Figure 3 shows the most prominent lines that are predicted by our models, namely Se vλ 1433.466 Å (log g_{i}f_{ik} value of 0.16), Sr vλ 1413.882 Å (0.82), Te viλ 1313.874 Å (−0.05), and I viλ 1219.395 Å (−0.63). For all these elements, the upper abundance limit is ≈100 times the solar abundance.
Acknowledgments
T.R. and D.H. are supported by the German Aerospace Center (DLR, grants 05 OR 1507 and 50 OR 1501, respectively). The GAVO project had been supported by the Federal Ministry of Education and Research (BMBF) at Tübingen (05 AC 6 VTB, 05 AC 11 VTB) and is funded at Heidelberg (05 AC 11 VH3). Financial support from the Belgian FRSFNRS is also acknowledged. P.Q. is research director of this organization. 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 NAS526555. Support for MAST for nonHST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. The TIRO (http://astro.unituebingen.de/~TIRO), TMAD (http://astro.unituebingen.de/~TMAD), and TOSS (http://astro.unituebingen.de/~TOSS) services were constructed as part of the Tübingen project of the German Astrophysical Virtual Observatory (GAVO, http://www.gvo.org). This research has made use of NASA’s Astrophysics Data System and the SIMBAD database, operated at CDS, Strasbourg, France.
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Appendix A: Additional tables
Radial parameters (in cm^{1}) adopted for the calculations in Se v.
Radial parameters (in cm^{1}) adopted for the calculations in Sr iv.
Radial parameters (in cm^{1}) adopted for the calculations in Sr v.
Radial parameters (in cm^{1}) adopted for the calculations in Sr vi.
Radial parameters (in cm^{1}) adopted for the calculations in Sr vii.
Radial parameters (in cm^{1}) adopted for the calculations in Te vi.
Radial parameters (in cm^{1}) adopted for the calculations in I vi.
Comparison between available experimental and calculated energy levels in Se v.
Comparison between available experimental and calculated energy levels in Sr iv.
Comparison between available experimental and calculated energy levels in Sr v.
Comparison between available experimental and calculated energy levels in Sr vi.
Comparison between available experimental and calculated energy levels in Sr vii.
Comparison between available experimental and calculated energy levels in Te vi.
Comparison between available experimental and calculated energy levels in I vi.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Se v.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Sr iv.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Sr v.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Sr vi.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Sr vii.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Te vi. CF is the absolute value of the cancellation factor as defined by Cowan (1981).
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in I vi.
Appendix B: Additional figure
Fig. B.1
Newly calculated log g_{i}f_{ik} values of Se v, Sr iv–vii, Te vi, and I vi (from top to bottom). The log g_{i}f_{ik} values are normalized to the strongest line, matching 95% of the panels’ heights. The wavelength ranges of EUVE and of our FUSE and STIS spectra are indicated at the top. 
All Tables
Comparison between available experimental and calculated energy levels in Se v.
Comparison between available experimental and calculated energy levels in Sr iv.
Comparison between available experimental and calculated energy levels in Sr v.
Comparison between available experimental and calculated energy levels in Sr vi.
Comparison between available experimental and calculated energy levels in Sr vii.
Comparison between available experimental and calculated energy levels in Te vi.
Comparison between available experimental and calculated energy levels in I vi.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Se v.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Sr iv.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Sr v.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Sr vi.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Sr vii.
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in Te vi. CF is the absolute value of the cancellation factor as defined by Cowan (1981).
Calculated HFR oscillator strengths (log g_{i}f_{ik}) and transition probabilities (g_{k}A_{ki}) in I vi.
All Figures
Fig. 1
Solar abundances (Asplund et al. 2009; Scott et al. 2015a,b; Grevesse et al. 2015, thick line; the dashed lines connect the elements with even and with odd atomic number) compared with the determined photospheric abundances of RE 0503−289 (red squares, Dreizler & Werner 1996; Rauch et al. 2012, 2014a,b, 2015, 2016a,b, 2017, and this work). The uncertainties of the WD abundances are about 0.2 dex in general. Arrows indicate upper limits. Top panel: abundances given as logarithmic mass fractions. Bottom panel: abundance ratios to respective solar values, [X] denotes log (fraction/solar fraction) of species X. The dashed, green line indicates solar abundances. 

In the text 
Fig. 2
Sr v lines in the observation (gray line) of RE 0503−289, labeled with their wavelengths from Table A.17. The thick, red spectrum is calculated from our best model with a Sr mass fraction of 6.5 × 10^{4}. The dashed, green line shows a synthetic spectrum calculated without Sr. In cases of Sr vλ 942.943 Å and Sr vλ 1412.959 Å, the red, dashed lines show two synthetic spectra calculated with Sr abundances that were increased and decreased by 0.3 dex. The vertical bar indicates 10% of the continuum flux. Identified lines are marked. “is” denotes interstellar. 

In the text 
Fig. 3
STIS observation of G191−B2B (gray) compared with synthetic line profiles of Se vλ 1433.466 Å, Sr vλ 1413.882 Å, Te viλ 1313.874 Å, and I viλ 1219.395 Å. The models were calculated with four abundances of the respective elements, without (thin, blue), with 100 times (thick, red), 1000 times (short dashed, violet) and 10 000 times solar abundance (long dashed, green). 

In the text 
Fig. 4
As Fig. 2, for Se v (top, mass fraction of 1.6 ± 1.0 × 10^{3} in the model), Te vi (middle, 2.5 × 10^{4}), and I vi (bottom, 1.4 × 10^{5}) lines. Abundance dependencies (±0.3 dex, red, dashed lines) are demonstrated for Se vλ 1454.292 Å, Te viλ 951.021 Å, and I viλ 1057.530 Å. 

In the text 
Fig. B.1
Newly calculated log g_{i}f_{ik} values of Se v, Sr iv–vii, Te vi, and I vi (from top to bottom). The log g_{i}f_{ik} values are normalized to the strongest line, matching 95% of the panels’ heights. The wavelength ranges of EUVE and of our FUSE and STIS spectra are indicated at the top. 

In the text 
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