New identified (3H)4d–(3H)4f transitions of Fe II from UVES spectra of HR 6000 and 46 Aquilae

F. Castelli; R. L. Kurucz; S. Hubrig

doi:10.1051/0004-6361/200912518

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Volume 508 / No 1 (December II 2009)

A&A, 508 1 (2009) 401-408

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Issue		A&A Volume 508, Number 1, December II 2009


Page(s)		401 - 408
Section		Stellar atmospheres
DOI		https://doi.org/10.1051/0004-6361/200912518
Published online		15 October 2009

A&A 508, 401-408 (2009)

New identified (³H)4d-(³H)4f transitions of Fe II from UVES spectra of HR 6000 and 46 Aquilae^,

F. Castelli¹ - R. L. Kurucz² - S. Hubrig³

1 - Istituto Nazionale di Astrofisica- Osservatorio Astronomico di Trieste, via Tiepolo 11, 34131 Trieste, Italy
2 - Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
3 - Astrophysical Institute Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany

Received 18 May 2009 / Accepted 4 September 2009

Abstract
Aims. The analysis of the high-resolution UVES spectra of the CP stars HR 6000 and 46 Aql has revealed the presence of an impressive number of unidentified lines, in particular in the 5000-5400 Å region. Because numerous 4d-4f transitions of Fe II lie in this spectral range, and because both stars are iron overabundant, we investigate whether the unidentified lines are Fe II.
Methods. ATLAS12 model atmospheres with parameters $T_{\rm eff}$ = 13 450 K, $\log~g$ = 4.3 and $T_{\rm eff}$ = 12 560 K, $\log~g$ = 3.8 were computed for the individual abundances of the stars HR 6000 and 46 Aql, respectively, to use them as spectroscopic sources to identify Fe II lines and determine Fe II gf-values. After identifying several unknown lines in the stellar spectra as (³H)4d-(³H)4f transitions of Fe II, we derived astrophysical $\log~gf$ -values for them. The energies of the upper levels were assigned on the basis of both laboratory iron spectra and predicted energy levels.
Results. We determined 21 new levels of Fe II with energies between 122 910.9 cm^-1 and 123 441.1 cm^-1. They allowed us to add 1700 new lines to the Fe II linelist in the wavelength range 810-15 011 Å. Many of these lines are sufficiently strong to contribute to the spectra of Population I late B-type stars, even when their iron abundance is subsolar. In the 5000-6000 Å region discussed in this paper, the astrophysical and computed $\log~gf$ -values show good general agreement and greatly improve the synthetic spectrum of both HR 6000 and 46 Aql. However, many features remain unidentified indicating that further work to classify Fe II high energy levels has still to be done

Key words: line: identification - atomic data - stars: atmospheres - stars: chemically peculiar - stars: individual: HR6000 - stars: individual: 46 Aquilae

1 Introduction

The analysis of the UVES spectrum of the chemically peculiar star HR 6000 performed by Castelli & Hubrig (2007) identified a large number of unidentified lines across the entire observed range from 3050 Å to 9460 Å. Most impressive regions were those at 4404-4411 Å and 5000-5400 Å. An attempt to identify unknown lines in the 5130-5136 Å interval using the available lists of predicted Fe II lines (version 2003) was laborious and unsuccessful.

An analysis of both the list of unidentified lines and of the plot of the observed and computed spectra available at the Castelli web-site led Johansson to identify about half of them as transitions between high excitation levels of Fe II. These identifications were made using unpublished line lists that he had obtained from laboratory spectra. Johansson (2009) was able to identify a group of 13 lines concentrated in the 4404-4411 Å interval as belonging to the multiplet 4s(⁷S)4d ⁸D-4s(⁷S)4f ⁸F. The upper terms have energies of between 132 145 cm^-1 and 132 158 cm^-1, and are therefore well above the Fe II ionization limit of 130 563 cm^-1. Another example of new identifications can be found in Castelli et al. (2008), where some unknown lines in the 5175-5180 Å interval of HR 6000 were identified with (³H)4d-(³H)4f transitions of Fe II. In this case, the energy of the upper levels is of the order of 123 000 cm^-1, and therefore just below the ionization limit.

Laboratory spectroscopic sources produce emission lines and must populate upper energy levels to produce such a spectrum. Most stars have spectra with lines in absorption, so that the line strength is determined from the lower energy level populations; for this reason, stellar lines are stronger than laboratory lines. HR 6000 and 46 Aql are bright and can be observed at high resolution and high signal-to-noise ratio. They have low projected rotation velocity, 1.5 km s^-1 for HR 6000, and 1.0 km s^-1for 46 Aql. Thus, blending is minimal and wavelengths and line strengths can be determined well by fitting the spectrum.

It is likely that most of the unidentified lines in these stars are those of Fe II. Some could be due to other overabundant elements, in particular P II, Mn II, and Xe II. However, as far as Mn II is concerned, the unidentified lines are either weaker or do not appear at all in the HgMn star HD 175640, which is iron weak ([Fe/H] = -0.25) and manganese overabundant ([Mn/H] = +2.4) (Castelli & Hubrig 2004; Castelli et al. 2008). It is also improbable that such a large number of unidentified lines, mostly concentrated in the 5000-6000 Å region, are not also due to Fe II. Since these lines are present at subsolar iron abundances, they must be present in all Population I late B-type stars, or in any object with strong Fe II lines, but they are normally smeared out by rotation and difficult to see.

Because every new energy level accounts for hundreds of new lines throughout the spectrum from the UV through to the IR wavelength regions, we extended to a wider range previous work for the 5175-5181 Å interval with the aim of increasing the number of the classified Fe II levels. We used identifications both based on laboratory spectra and derived from predicted energy levels. Furthermore, because numerous high-excitation lines from the 3d⁶(⁵D)4d-3d⁶(⁵D)4f transitions are observed in the 5000-5400 Å interval, we examined the computed $\log~gf$ -values used in the synthetic spectra computations. We compared them with both experimental (Johansson 2002) and astrophysical values, which we derived from the lines of both HR 6000 and 46 Aql. We used two stars to check the consistency and estimate the reliability of the astrophysical oscillator strengths. We then derived astrophysical $\log~gf$ -values for the new identified (³H)4d-(³H)4f lines. Finally, we show an example of synthetic spectrum computed both with old and new line lists.

To use HR 6000 and 46 Aql as spectroscopic sources for identifying Fe II lines, to determine Fe II $\log~gf$ -values, and to compute synthetic spectra, we fixed at first the model atmosphere and the abundances for each star. Special care was devoted to deriving the iron abundance.

2 The stars HR 6000 and 46 Aql

Both HR 6000 (HD 144667) and 46 Aql (HD 186122) are B-type CP stars. HR 6000 was extensively studied by Castelli & Hubrig (2007) in the 3050-9460 Å region, and 46 Aql, by Sadakane et al. (2001) in the 5100-6400 Å interval. Because model atmospheres are needed to determine astrophysical $\log~gf$ -values, we revised the model atmosphere and the abundances of HR 6000 and determined the model atmosphere and the abundances for 46 Aql on the basis of our observations.

2.1 Observations

The observations of HR 6000 are described in Castelli & Hubrig (2007). Those for 46 Aql were obtained in the framework of the same observational program (ESO prg. 076.D-0169(A)). They are of the same quality and were reduced with the same procedures used for HR 6000.

For this paper, we revised our previous analysis of HR 6000 (Castelli & Hubrig 2007) because further investigation indicated that the Balmer profiles used by us to derive the model parameters are too affected in the UVES spectra by imperfections related to the echelle orders. As we show in Appendix A, the spectral distortions for H $_{\delta}$ , H $_{\gamma}$ , and, to a less extent, for H $_{\beta}$ are so significant that it is impossible to determine a reliable continuum level for the observed profiles. Only H $_{\alpha}$ does not appear to be affected by these problems, so it could be used for the analysis with some confidence.

2.2 Model parameters and abundances

In Castelli & Hubrig (2007), the model parameters of HR 6000 ( $T_{\rm eff}$ = 12 850 K, $\log~g$ = 4.10, $\xi=0.0$ km s^-1) were derived from both Balmer profiles and Fe I and Fe II ionization equilibrium. In this paper, the model parameters for both HR 6000 and 46 Aql were obtained from the Strömgren photometry, from the requirement that there was no correlation between the Fe II abundances derived from high and low excitation lines, and from the constraint of Fe I-Fe II ionization equilibrium. This type of determination led to a revision of the model parameters for HR 6000.

Table 1: Observed and dereddened Strömgren indices for HR 6000 and 46 Aql.

The parameters of the two stars obtained from the Strömgren photometry are given in Table 1. They were derived with the method described in Castelli & Hubrig (2007), where the reddening for HR 6000 is also discussed. The observed indices were taken from the Hauck & Mermilliod (1998) catalogue. ATLAS9 models with parameters [13 800 K, 4.3] for HR 6000 and [12 750 K, 3.8] for 46 Aql were computed for solar abundances and zero microturbulent velocity. The iron abundance was derived from the equivalent widths of a selected sample of high-excitation Fe II lines with experimental $\log~gf$ -values available from Johansson (2002). They are due to (⁵D)4d-(⁵D)4f transitions and are listed in Table 2. The equivalent widths of these lines, as well as of the other lines discussed in this paper, were measured by integrating the residual fluxes over the profiles. Abundances were obtained with a Linux version (Castelli 2005) of the WIDTH code (Kurucz 1993). We note that there are no measured equivalent widths for the line at 5100.734 Å because it is part of a strong blend formed by four Fe II lines. The line was included in Table 2 to show the whole set of (⁵D)4d-(⁵D)4f transitions for which experimental $\log~gf$ -values are available. The lines from Table 2 are particularly well suited to providing the iron abundance because they are rather insensitive to the model parameters. In fact, for differences in $T_{\rm eff}$ of 500 K, the abundance difference is less than 0.05 dex; for differences in $\log~g$ of 0.2 dex, the abundance difference is of the order of 0.01 dex. For example, for HR 6000, the Fe II abundance from ATLAS9 models computed for $\log~g$ = 4.3, and $T_{\rm eff}$ = 13 300 K, 13 800 K, and 14 300 K, is -3.66 dex , -3.65 dex (Table 2), and -3.61 dex, respectively. For models computed for $T_{\rm eff}$ = 13 800 K, and $\log~g$ = 4.1, 4.3, and 4.5, the iron abundance is -3.65 dex, -3.65 dex (Table 2), and -3.64 dex. Similar results were obtained for 46 Aql.

Table 2: Iron abundance derived from a selected sample of high excitation (4d-4f) Fe II lines with experimental $\log~gf$ -values and ATLAS9 models.

After having determined the iron abundance, we checked the model parameters by inquiring whether the adopted model gives the same abundance for Fe I lines and for a large sample of Fe II lines including low-excitation transitions. To this purpose, we measured the equivalent widths of the Fe I and Fe II lines listed in Table B.1 and derived the corresponding abundances. They are -3.68 $\pm$ 0.06 dex and -3.68 $\pm$ 0.15 dex, respectively, for HR 6000 and -3.93 $\pm$ 0.06 dex and -3.91 $\pm$ 0.11 dex, respectively, for 46 Aql. For both stars, the ionization equilibrium condition is fulfilled within the error limits, and the Fe II abundance derived from the large sample of lines listed in Appendix B agrees, within the error limits, with the abundance yielded by the small sample of high-excitation Fe II lines listed in Table 2. We conclude that the [13 800, 4.3] ATLAS9 model for HR 6000 and the [12 750 K, 3.8] ATLAS9 model for 46 Aql not only reproduce the respective Strömgren colors, but also satisfy the constraints of both the Fe I-Fe II ionization equilibria and Fe II abundance, independent of the excitation potential. The H $_{\alpha}$ profile is also fairly well reproduced by the models in both stars.

The ATLAS9 models were used to obtain abundances for elements other than iron. For He I, we adopted the lines listed in Castelli & Hubrig (2004) and analyzed them as described in that paper. For the other elements, the lines listed in Table B.1 were used. For most lines, equivalent widths were measured. For weak lines or lines that are blends of transitions belonging to the same multiplet, such as Mg II 4481 Å, and most O I profiles, we derived the abundance from the line profiles with the synthetic spectrum method. Synthetic spectra were computed with a Linux version (Sbordone et al. 2004) of the SYNTHE code (Kurucz 2005). When no lines were observed for a given element an upper abundance limit was determined by reducing the intensity of the computed line at the noise level. To compute synthetic spectra, rotational velocities equal to 1.5 km s^-1 and 1.0 km s^-1 were adopted for HR 6000 and 46 Aql, respectively. They were derived by comparing the observed and computed Mg II profiles at 4481 Å.

Because the abundances found for most elements were far from solar, we computed ATLAS12 models (Kurucz 2005) for the individual abundances with the same parameters as determined for the ATLAS9 models. The structure of the ATLAS12 models is heavily affected by the large iron overabundance, while the helium underabundance, although large, has a negligible effect, in contrast to what was wrongly stated in Castelli & Hubrig (2007). As a consequence, the Fe I-Fe II ionization equilibrium is no longer achieved by the ATLAS12 models unless the parameters are changed. Because the gravity affects the wings of the Balmer profile more than the temperature does, we kept fixed the gravity which reproduces the H $_{\alpha}$ profile rather well and modified $T_{\rm eff}$ until the Fe I abundance from the lines listed in Appendix B agrees with the Fe II abundance obtained from the lines shown in Table 2. The final ATLAS12 parameters are $T_{\rm eff}$ = 13 450 K, $\log~g$ = 4.3, and $\xi$ = 0.0 km s^-1for HR 6000 and $T_{\rm eff}$ = 12 560, $\log~g$ = 3.8, and $\xi=0.0$ km s^-1 for 46 Aql. The computed indices (b-y), m, and c for HR 6000 are -0.064, 0.126, and 0.535, respectively. For 46 Aql, they are -0.052, 0.116, and 0.662. For both stars, the observed (b-y) is reproduced by the models within the observational uncertainties, while the c index is not. This means that the models are able to predict the optical spectrum but not the spectrum shortward of the Balmer discontinuity.

We note that we could simply have used the ATLAS9 models computed for solar abundances with the parameters given in Table 2, which reproduce both the Strömgren colors and the criteria for Fe I-Fe II ionization equilibrium. However in this case, the number densities of the input model are different from those computed by the final synthetic spectrum on the basis of non solar abundances for several elements, in particular for helium which heavily affects the state equation results. We preferred to use consistent computations in model and synthetic spectra rather than use different sets of abundances in the two cases, even though predictions more close to obsevations may be achievable when different abundances are indeed used for model atmosphere and synthetic spectrum.

Table 3 summarizes the final stellar abundances used to compute ATLAS12 models and synthetic spectra. For HR 6000, abundances that differ from previous determinations (Castelli & Hubrig 2007) by 0.2 dex or more are those for He I (+0.20), Ca II (+0.2), Ti II (+0.30), Cr II (+0.27), Mn II (+0.42), Fe I and Fe II (+0.21), and Y II (+0.2). For 46 Aql, abundances differing by more than 0.2 dex from those derived by Sadakane et al. (2001) are those for C II (-0.33), S II ( $\ge$ +0.77), Ti II (-0.44), and Fe I (-0.32). The number in parenthesis is the difference between the abundance determined in this paper and that from the other analyses. Sadakane et al. (2001) adopted an ATLAS9 model atmosphere with parameters $T_{\rm eff}$ = 13 000 K, $\log~g$ = 3.65, and $v_{\rm turb}=0.3$ km s^-1.

The abundances of 46 Aql have approximately the same pattern as in HR 6000, but the deviations from solar values are generally lower. The most remarkable differences between the two stars are the overabundance of copper, zinc, and arsenic in 46 Aql, while no lines of these elements were observed in HR 6000. The arsenic overabundance cannot be quantified owing to the lack of $\log~gf$ data for As II. Lines of As II observed in the spectrum are listed in Table B.1. To each line, we assigned the corresponding transition on the basis of the two separate lists of lines and energy levels taken from the NIST database^,. Furthermore, Cr II is slightly overabundant in HR 6000 ([0.3]) and underabundant in 46 Aql [-1.1], Ca II is solar in HR 6000 and slightly underabundant in 46 Aql [-0.3], and Y II and Hg II are less overabundant in HR 6000 than in 46 Aql.

Table 3: Abundances $\log$ (N(elem)/N_tot) for HR 6000 and 46 Aql from ATLAS12 models.

In both HR 6000 and 46 Aql, the He I profiles cannot be reproduced by the same abundance. We adopted the abundance that reproduced the wings of the lines at $\lambda\lambda$ 3867, 4026, and 4471 Å the most closely. The cores of all He I lines would require a lower abundance than that reproducing the wings.

In both stars, the average abundances of phosphorous and manganese have deviations larger than 0.2 dex. For phosphorous, these are caused by a difference of the order of 0.5 dex between the abundance from lines with $\lambda$ < 5000 Å and the abundance from lines with $\lambda > 5000$ Å. For manganese, the large deviation is due to a difference of 0.6 dex in HR 6000 and 0.4 dex in 46 Aql between the abundances from lines lying shortward and longward of the Balmer discontinuity. The Mn II abundance was derived from both equivalent widths and line profiles. In the first case, no hyperfine structure was considered in the computations, while in the second case hyperfine components were taken into account for all the lines except for 3917.318 Å, for which no hyperfine constants are available for its upper energy level. The hyperfine components were taken from Kurucz. The differences between the average abundances obtained by the two methods are of the order of 0.01 dex.

A plausible explanation of the discrepancy in the Mn II abundance is that the model structure is inadequate to reproduce the ultraviolet spectrum, as already deduced by comparing the computed and observed c indices. Vertical abundance stratification, which is a consequence of radiative diffusion acting in CP stars (Michaud 1970), can be invoked to explain the anomalous He I line profiles as well as the phosphorus and manganese inhomogeneous abundances. A comprehensive discussion of observational evidence for the abundance stratification in CP stars is given by Ryabchikova et al. (2003). It describes both the impossibility of fitting the wings and the core of strong spectral lines with the same abundance, and the differences in the abundances measured from the lines of the same ion that form at different optical depths, as, for instance, in the case of lines lying longward or shortward of the Balmer discontinuity. Finally, for a reliable discussion on phosphorus, more oscillator strengths data of P II and P III lines observed in the optical region are needed.

In both HR 6000 and 46 Aql, the Hg II line at 3983.890 Å is due mostly to the heaviest isotope of Hg. The lines of the Ca II infrared triplet at 8498, 8542, and 8662 Å are red-shifted by 0.14 Å in HR 6000 and by 0.13 Å in 46 Aql, so indicating a non solar Ca isotopic composition. In HR 6000, emission lines of Cr II, Mn II, and Fe II were observed. In the spectrum of 46 Aql, instead, there are emission lines of Ti II and Mn II.

3 The (⁵D)4f and (³H)4f states of Fe II

Energy levels of a given atom are described most often by the LS coupling in which the total orbital angular momentum L of the atom is coupled with the total spin angular momentum S to produce the total angular momentum J = L + S. Some high levels, such as the (⁵D)4f and (³H)4f states of Fe II, tend to appear in pairs, so they are more accurately described by the jK coupling with the notation $j_{\rm c}$ [K]_J, where j $_{\rm c}$ is the total angular momentum of the core and K = j $_{\rm c}$ + l is the coupling of j $_{\rm c}$ with the orbital angular momentum l of the active electron. The level pairs correspond to the two separate values of the total angular momentum J obtained when the spin s = $\pm$ 1/2 of the active electron is added to K.

While the energy levels of the 3d⁶(⁵D)4f states are known and available for instance in the NIST database, this is not the case for the levels with the higher parent term 3d⁶(³H)4f. Most of these levels have not been observed in the laboratory and remain unclassified.

4 The 3d⁶(⁵D)4d-3d⁶(⁵D)4f transitions of Fe II

The 4d-4f transitions discussed in this paper appear in the optical region, mostly between 4800 and 6000 Å. Their presence in stellar spectra was found a long time ago by Johansson & Cowley (1984). They are also present in the spectra of the iron-rich peculiar stars HR 6000 and 46 Aql. We used UVES spectra of these stars to derive values of astrophysical $\log~gf$ that we compared with experimental and computed values.

4.1 Experimental log gf-values

All the experimental data described in this section were made available to Castelli by Johansson and are briefly described in Johansson (2002). Radiative lifetime measurements of five 3d⁶(⁵D)4f levels, i.e., 4[6]_13/2, 4[7]_13/2, 4[7]_15/2, 3[6]_13/2, 3[5]_11/2, and branching fraction measurements for 13 transitions 4d-4f with wavelengths in the 4800-5800 Å region were performed at Lund. Einstein coefficients A, derived by combining the measured branching fractions with the lifetime measurements, were converted into experimental oscillator strengths. The 4d-4f transitions together with the experimental $\log~gf$ -values are given in Tables 2 and 4. While the 4f levels with J > 11/2 decay only to 4d levels, the 4f 3[5]_11/2 level may decay to 3d levels as well. As a consequence, the $\log~gf$ -value for the transitions involving the 3[5]_11/2 level may be less accurate than those related to levels with J>11/2, which have an estimated error of 0.05 dex.

4.2 Computed log gf-values

The computed $\log~gf$ -values were taken from both Kurucz's line lists (K09, January, 2009 version) and Raassen & Uylings (1998) (RU98) data. We note that Fuhr & Wiese (2006) (FW06) adopted the RU98 data for the few (⁵D)4d-(⁵D)4f transitions that they listed in their critical compilation.

Both K09 and RU98 results were obtained with semi-empirical methods, although different ones. The K09 results were obtained with the use of the Cowan (1981) atomic structure code, while the RU98 results were obtained by the orthogonal operators method. The computed $\log~gf$ -values are listed in Table 4.

4.3 Astrophysical log gf-values

To derive astrophysical $\log~gf$ -values we computed synthetic profiles for the Fe II lines listed in Table 4. We used the ATLAS12 models discussed in Sect. 2, the SYNTHE code (Kurucz 2005), and line lists based on the Kurucz database that we continually update with new data when available (Castelli & Hubrig 2004). By fixing the iron abundance to -3.65 dex for HR 6000 and to -3.91 dex for 46 Aql (Table 3), we adjusted the $\log~gf$ -values in the calculated spectrum, for the lines listed in Table 4, until observed and computed profiles were in optimal agreement. All the lines can be fitted well except for the very strong ones with $\log~gf$ higher than 0.9. Their observed cores are stronger than those computed and can never be reproduced by the computed spectrum because increasing the $\log~gf$ -value broadens the wings instead of increasing the core. An example is the line at 5260.254 Å, which we decided to exclude from our comparisons. The strongest Fe II lines are possibly affected by iron abundance vertical stratification, which does not affect the medium-strong and weak lines.

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f1.eps} \end{figure}$	Figure 1: Comparison of astrophysical $\log~gf$ -values from HR 6000 and 46 Aql for (⁵D)4d-(⁵D)4f transitions of Fe II. The horizontal dashed line indicates the average difference.
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$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f2.eps} \end{figure}$	Figure 2: Calculated $\log~gf$ -values (K09) for (⁵D)4d-(⁵D)4f transitions of Fe II are compared with experimental $\log~gf$ -values. The horizontal dashed line indicates the average difference.
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Figure 1 shows the difference between the astrophysical $\log~gf$ -values from both HR 6000 and 46 Aql as function of the astrophysical $\log~gf$ of HR 6000. The average difference, shown by the dashed line, is -0.019 $\pm~$ 0.042 dex, but for single lines the difference increases with increasing $\log~gf$ from 0.00 to 0.15 dex, in the sense that the values from 46 Aql become larger than those from HR 6000. The largest difference of -0.15 dex occurs for $\lambda$ 5961.705 Å. Because each astrophysical value reproduces the observed line in each star well we do not have an explanation of this discrepancy.

As astrophysical $\log~gf$ -values we assumed the average of the values obtained from HR 6000 and 46 Aql. Astrophysical $\log~gf$ -values for both the two stars and the average are listed in Table 4.

4.4 Comparison of values of log gf

The difference between experimental and computed $\log~gf$ -values versus the experimental $\log~gf$ is shown Figs. 2 and 3, where the computed data are those from K09 and RU98, respectively. The average difference of 0.028 $\pm$ 0.061 dex yielded by the RU98 values is lower than the average difference of 0.043 $\pm$ 0.071 dex given by the K09 values, but they agree within the error limits. The largest difference of +0.130 in Fig. 2 is due to the transition at 4883.292 Å. However, the J value of the 4f upper level of this line is 11/2, which is not high enough to ensure that there are no additional decays to 3d levels (Johansson 2002). This fact could affect the experimental $\log~gf$ -value and the closer agreement with the RU98 data may be fortuitous. In fact, Table 4 shows that the astrophysical $\log~gf$ -value agrees more closely with the K09 than the RU98 value.

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f3.eps} \end{figure}$	Figure 3: Calculated $\log~gf$ -values (RU98) for (⁵D)4d-(⁵D)4f transitions of Fe II are compared with experimental $\log gf$ -values. The horizontal dashed line indicates the average difference
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$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f4.eps} \end{figure}$	Figure 4: Calculated $\log~gf$ -values (K09) for (⁵D)4d-(⁵D)4f transitions of Fe II are compared with astrophysical $\log~gf$ -values. The horizontal dashed line indicates the average difference.
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Astrophysical $\log~gf$ -values are compared with $\log~gf$ -values from K09 and RU98 in Figs. 4 and 5, respectively. The mean difference of 0.006 $\pm$ 0.116 dex given by the K09 data is fully comparable with the average difference of -0.007 $\pm$ 0.144 dex yielded by the RU98 $\log~gf$ -values. In both cases, the dispersion around the mean value is rather large. The lines giving the largest discrepancies are different for K09 and RU98. In K09, the lines are those at wavelengths of $\lambda\lambda$ 5257.119 (-0.47), 5359.237 (-0.314), 5358.872 (+0.286), 5355.421 (+0.285), 5366.210 (-0.267), 5062.927 (-0.260) Å. In RU98 they are those with wavelength $\lambda\lambda$ 5070.583 (-0.760), 5140.689 (-0.543), 5093.783 (-0.399), 5200.798 (+0.287), 5081.898 (-0.279) Å. The values in parentheses are the difference $\log~gf$ (computed) - $\log~gf$ (astrophysical). For all of these transitions, the difference between the astrophysical $\log~gf$ -values from HR 6000 and 46 Aql is less than 0.06 dex, so that the cause of the disagreements is probably due to the computed values.

We note that Kurucz updates his calculation whenever new Fe II levels become available. The January 2009 version of the Fe II linelist used for the (⁵D)4d-(⁵D)4f transitions discussed in this paper includes only a few of the new (³H)4d-(³H)4f levels presented in Sect. 5. In the near future, a new Fe II linelist with all the new levels given in Tables 5 and 6 will be made available at the Kurucz web-site.

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f5.eps} \end{figure}$	Figure 5: Calculated $\log~gf$ -values (RU98) for (⁵D)4d-(⁵D)4f transitions of Fe II are compared with astrophysical $\log~gf$ -values. The horizontal dashed line indicates the average difference.
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5 The new identifications in HR 6000 and 46 Aql

The spectrum of HR 6000 contains an enormous number of unidentified lines mostly concentrated in the 5000-5400 Å region (Castelli & Hubrig 2007). The same unidentified lines can also be observed in the spectrum of 46 Aql. Johansson (2006) remarked that a great number of unidentified lines in the plots of HR 6000 available at the Castelli web-site (see footnote 2), are also present in laboratory iron spectra. He therefore identified several unknown features in the 4000-5500 Å interval of HR 6000 as beign produced by iron. These identifications are at different levels of completeness. In a few cases, the transition is identified only as Fe , in most cases, as Fe II, and in some cases, as Fe II with both levels of the transition being classified.

5.1 The 3d⁶(³H)4d-3d⁶(³H)4f transitions of Fe II

Most of the Fe II lines classified by Johansson are due to the (³H)4d-(³H)4f transitions. Their lower excitation potential is higher than 103 800 cm^-1 (12.87 eV) and their upper excitation potential is of the order of 123 000 cm^-1 (15.25 eV), and therefore close to the ionization limit of 130 563 cm^-1(16.19 eV).

In preliminary work, Castelli et al. (2008) provide an example in both HR 6000 and 46 Aql of four lines at 5176.711, 5177.3896, 5177.7762, and 5179.536 Å identified for the first time with Fe II (³H)4d-(³H)4f transitions. Only for two lines (at 5177.3896 and 5179.539 Å) were energies and terms known for both levels, while for the other two lines (at 5176.711 and 5179.536 Å) the term of the upper level was unknown, except for the J quantum number. Further lines and energies indicated by Johansson are those marked with a ``J'' in Table 5.

To complete and extend the number of the identifications, we proceeded as follows. We started from the ``J'' lines. Knowing the term, the energy of the lower level of a ``J'' line was determined using either the NIST database (see footnote 4) or the Kurucz linelists (see footnote 1). A given (³H)4d-(³H)4f transition was then searched for among the Fe II predicted lines available in the Kurucz database (version 2007). For this search, both the lower energy level and the J quantum number of the upper level were used as key parameters. Once the predicted line corresponding to the new identified transition was fixed, the predicted energy was replaced by the energy assigned by Johansson to the level. This substitution was made not only for the given line but also for all lines with that predicted level as their upper level. We then compared the pattern of the computed $\log~gf$ -values with the pattern of astrophysical $\log~gf$ -values for those lines. If they were similar, we accepted the identification. If not, we tried another match. In this way, because of the J lines, we fixed 11 new energy levels and all the transitions with a new level as an upper level. In addition, we determined another 10 new levels from predicted lines. For a given predicted upper level, we searched in the spectrum for unidentified lines with similar intensity and the same wavelength difference as the predicted lines. We selected the lines with positive $\log~gf$ -values, or even negative, but close to zero. The observed wavelength and the known lower energy level were then used to fix the upper level of the transitions.

Table 5 lists both the (³H)4d-(³H)4f transitions originally identified by S. Johansson and those that we derived from the above described procedure. The letter ``J'' is associated with the first group of lines, the letter ``K'' with the second group. Not all the lines listed in Table 5 are observable in the spectra, so that values of astrophysical $\log~gf$ cannot be assigned to all lines. The last column of Table 5 lists lines observed in HR 6000 that were listed as unidentified lines by Castelli & Hubrig (2007).

Figure 6 compares astrophysical $\log~gf$ -values from HR 6000 and 46 Aql. It is the analogous to Fig. 1, but for the (³H)4d-(³H)4f transitions. The average difference, shown by the dashed line, is negligible, but the scatter is larger than that obtained for the (⁵D)4d-(⁵D)4f transitions. The reason is the very low intensity of some of the (³H)4d-(³H)4f transitions, which makes the fitting of the profile problematic. As for the (⁵D)4d-(⁵D)4f transitions, we assumed astrophysical $\log~gf$ -values to be the average of values obtained for HR 6000 and 46 Aql, but we excluded the lines for which astrophysical $\log~gf$ -values differed by more than 0.1 dex. Astrophysical $\log~gf$ -values for the two stars and the average values are listed in Table 5.

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f6.eps} \end{figure}$	Figure 6: Comparison of astrophysical $\log~gf$ -values from HR 6000 and 46 Aql for (³H)4d-(³H)4f transitions of Fe II. The horizontal dashed line indicates the average difference.
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The astrophysical $\log~gf$ -values are compared with the calculated $\log~gf$ -values in Fig. 7. From this comparison, we excluded the lines at $\lambda\lambda$ 5177.777 (-1.45), 5250.632 (-2.61), 5346.098 (-1.21), and 5420.234 (-1.76) Å, for which the $\log~gf$ difference between computed and astrophysical $\log~gf$ -values, given in parenthesis, is larger than 1.0 dex. The upper energies of the lines are 122 952.73, 123 026.35, 123 015.40, and 123 251.47 cm^-1, respectively. The most probable explanation of these large discrepancies is the presence of some additional unidentified component contributing to the absorption, so that the astrophysical $\log~gf$ -value is largely overestimated. The mean difference between the two sets of data is -0.07 $\pm$ 0.22 dex, indicating that the astrophysical $\log~gf$ -values are, on average, higher than the computed $\log~gf$ -values. The differences for the individual lines increase with decreasing $\log~gf$ , namely with decreasing line intensity. Weak lines are more difficult to be fitted by the synthetic spectrum owing to the contribution of the noise and the non-negligible effect of the position for the continuum.

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f7.eps} \end{figure}$	Figure 7: The calculated $\log~gf$ -values (calc.) for (³H)4d-(³H)4f transitions of Fe II are compared with astrophysical $\log~gf$ -values obtained averaging $\log~gf$ -values from HR 6000 and 46 Aql. The horizontal dashed line indicates the average difference.
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$\begin{figure} \includegraphics[angle=90,width=14.3cm,clip]{12518f8.eps} \end{figure}$

Figure 8:

Comparison of the UVES spectrum of HR 6000 with a synthetic spectrum computed after this study (upper plot) and before this study (lower plot). The black line is the observed spectrum, and the red line is the synthetic spectrum. Nine Fe II lines corresponding to (³H)4d-(³H)4f newly identified transitions are marked in the upper plot. Their calculated $\log~gf$ -values were used to compute the synthetic spectrum.

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5.2 More new Fe II identified lines

There are a few other lines that do not belong to the (³H)4d-(³H)4f transitions, that were identified by S. Johansson in HR 6000. They are indicated with a ``J'' in Table 6. The lines marked with a ``K'' were then obtained from predicted lines^, because of the coincidence of the term of the upper predicted level with the term of a ``J'' line. Table 6 shows that we fixed two new (⁵D)6d levels. Some computed $\log~gf$ -values are much weaker than the astrophysical $\log~gf$ -values. Some other unknown transition is probably the main component of the observed line so that the astrophysical $\log~gf$ -value is unreliable.

6 Conclusions

Figure 8 compares the synthetic spectra for HR 6000 computed before and after the study presented in this paper. The interval plotted is an example of the quality of the improvement that we obtained for the whole 5100-5400 Å region. It shows that as many as nine new Fe II lines have been identified within this 10 Å range. Nevertheless, several absorption lines remain unidentified. They are probably Fe II lines whose levels have still to be fixed. A very similar plot was obtained for 46 Aql. We can infer that a large part of the unidentified lines observed in the spectra of B-type stars are due to unknown high-excitation Fe II transitions.

The new lines identified in this paper correspond to high excitation transitions of Fe II with an upper level just below the ionization limit. We fixed 21 new levels of Fe II whose energies range from 122 910.9 cm^-1 to 123 441.1 cm^-1, and added 1700 lines to the Fe II linelist for the range 810-15011 Å. Furthermore, Johansson (2009) identified in the spectrum of HR 6000 the Fe II lines of the multiplet 4s4d⁸D-4s4f⁸F at 4410 Å. Their lower energy level is near the ionization limit and their upper energy level is above it.

Among the newly identified high-excitation Fe II lines, several have residual flux in HR 6000 and 46 Aql of the order of 0.7 and numerous others are observable as weak absorption lines or parts of blends. The two stars are iron-overabundant stars, but these lines are also present with lower intensity in the UVES spectrum of HD 175640, a B-type peculiar star with an iron underabundance of -0.25 dex with respect to the Sun (Castelli & Hubrig 2004). This implies that Fe II lines from the new high excitation levels contribute to the spectrum of all Population I late B-type stars, even when their abundance is less than solar. The lines are clearly observable in high resolution, high signal-to-noise spectra of slowly rotating stars, while they contribute to the broad observed features in B-type stars with high rotational velocities. In general, they would appear in any object with strong Fe II lines.

We conclude that we have clarified the nature of several unidentified lines observed in the optical spectra of B-type stars and concentrated mostly in the 5000-5400 Å region (see also Wahlgren et al. 2000), but that a large amount of work remains to be done to reproduce stellar observations well. More than 1000 energy levels of Fe II are known, but we have seen that they are not enough. Ignorance of them and of the transitions involved still remain an outstanding shortcoming affecting the model atmosphere and synthetic spectra computations.

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Online Material

Appendix A: The Balmer lines of HR 6000 observed on the UVES spectra

Figure A.1 shows the UVES spectra of HR 6000 reduced by the UVES pipeline Data Reduction Software (version 2.5, Ballester et al. 2000) that were used by Castelli & Hubrig (2007) and also in this paper. All spectra are FLUXCAL_-SCIENCE products. Those at $\lambda\lambda$ 3290-4520 Å and 4780-5650 Å are flux-calibrated spectra in 10^-16 erg s^-1 cm^-2 A^-1 corrected for terrestrial extinction. The red spectrum at 5730-7560 Å is in non-physical units ``quasi-ADU'' because the flux calibration procedure is not implemented in the reduction software for the REDL and REDU data taken with the red mosaic CCD's. The sizable distortions in UVES spectra make the difficulty in drawing a true continuum over H $_{\gamma}$ and H $_{\delta}$ evident. The use of H $_{\beta}$ also causes problems because of the position of this line at the left end of the spectrum order. Only H $_{\alpha}$ does not have significant problems.

Computed spectra from the final ATLAS12 model ([13450, 4.3], Sect. 2.2) are also plotted in Fig. A.1 to show the different slopes of the observed and computed continua. The computed fluxes were scaled by a given arbitrary quantity to be roughly overimposed on the UVES spectra.

$\begin{figure} \par\resizebox{3.in}{!}{\rotatebox{90}{\includegraphics[30,100][6... ...}{\includegraphics[30,100][600,700] {12518fAc.eps}}}\vspace*{5mm} \end{figure}$

Figure A.1:

The observed UVES spectra of HR 6000 (black line) are plotted together the computed spectra (red line) in order to show the different slopes of the observed and computed continua. The computed fluxes are scaled by a given arbitrary quantity to be roughly overimposed on the UVES spectra. The ATLAS12 final model with parameters $T_{\rm eff}$ = 13450 K, $\log~g$ = 4.3 was used for the computations.

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Appendix B: Lines used for the abundance analysis

Table B.1 lists the lines examined in the spectra of HR 6000 and 46 Aql to derive the stellar abundances. The wording ``not obs'' is given for lines not present in the spectra, while the wordings ``profile'' and ``blend'' are given for lines well observed in the spectra that do not have measurable equivalent widths either because they are too weak to be measurable or because other components affects the line. These wordings also indicate lines for which adequate equivalent widths cannot be computed, as in the cases of Mg II at 4481 Å and most O I lines, which are blends of transitions belonging to the same multiplet. The abundances from the final ATLAS12 models derived from the equivalent widths or from the profiles are given in the table, as well as upper abundance limits for lines not observed, but predicted at solar abundance by the synthetic spectrum. For Fe I and Fe II, $\log~gf$ -values were taken from Fuhr & Wiese (2006) (FW06) when available. Otherwise Kurucz's last determination was adopted (Kurucz 2009), except for Fe II at 5257.119 Å. In this case, the previous values (Kurucz 2007) produce synthetic profiles in closer agreement with the observations.

Table B.1: Analyzed lines in the stellar spectra, measured equivalent widths in mÅ, and relative abundances.He I is not included.

Table 4: Astrophysical $\log~gf$ -values for a sample of (⁵D)4d-(⁵D)4f lines of Fe II observed in HR 6000 and 46 Aql. The values of $\log~gf$ from the two stars are averaged and compared with experimental $\log~gf$ -values from Johansson (2002) and calculated $\log~gf$ -values from Kurucz (2009) (K09) (footnote 7) and from Raassen & Uylings (1998) (RU98).

Table 5: Lines due to (³H)4d-(³H)4f transitions of Fe II.

Table 6: More new Fe II identified lines.

Footnotes

... 46 Aquilae: This study is the result of a collaboration with Sveneric Johansson, who unfortunately died before this paper started to be written.
...: Tables 4-6, and Appendices A and B are only available in electronic form at http://www.aanda.org
... II lines: http://kurucz.harvard.edu/atoms/2601/gf2601.lines0600
... web-site: http://wwwuser.oat.ts.astro.it/castelli/hr6000/hr6000.html
... catalogue: http://obswww.unige.ch/gcpd/gcpd.html
... database: http://physics.nist.gov/PhysRefData/ADS/lines_form.html
...: http://physics.nist.gov/PhysRefData/ADS/levels_form.html
... Kurucz: http://kurucz.harvard.edu/atoms/2501/hyper250155.srt
... version): http://kurucz/harvard/edu/atoms/2601/gf2601kjan09.pos
... lines: http://kurucz.harvard.edu/atoms/2601/gf2601.lines0500
...: http://kurucz.harvard.edu/atoms/2601/gf2601.lines0600
... pipeline: http://www.eso.org/observing/dfo/quality/UVES/pipeline/pipe_reduc.html

All Tables

Table 1: Observed and dereddened Strömgren indices for HR 6000 and 46 Aql.

Table 2: Iron abundance derived from a selected sample of high excitation (4d-4f) Fe II lines with experimental $\log~gf$ -values and ATLAS9 models.

Table 3: Abundances $\log$ (N(elem)/N_tot) for HR 6000 and 46 Aql from ATLAS12 models.

Table B.1: Analyzed lines in the stellar spectra, measured equivalent widths in mÅ, and relative abundances.He I is not included.

Table 4: Astrophysical $\log~gf$ -values for a sample of (⁵D)4d-(⁵D)4f lines of Fe II observed in HR 6000 and 46 Aql. The values of $\log~gf$ from the two stars are averaged and compared with experimental $\log~gf$ -values from Johansson (2002) and calculated $\log~gf$ -values from Kurucz (2009) (K09) (footnote 7) and from Raassen & Uylings (1998) (RU98).

Table 5: Lines due to (³H)4d-(³H)4f transitions of Fe II.

Table 6: More new Fe II identified lines.

All Figures

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f1.eps} \end{figure}$	Figure 1: Comparison of astrophysical $\log~gf$ -values from HR 6000 and 46 Aql for (⁵D)4d-(⁵D)4f transitions of Fe II. The horizontal dashed line indicates the average difference.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f2.eps} \end{figure}$	Figure 2: Calculated $\log~gf$ -values (K09) for (⁵D)4d-(⁵D)4f transitions of Fe II are compared with experimental $\log~gf$ -values. The horizontal dashed line indicates the average difference.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f3.eps} \end{figure}$	Figure 3: Calculated $\log~gf$ -values (RU98) for (⁵D)4d-(⁵D)4f transitions of Fe II are compared with experimental $\log gf$ -values. The horizontal dashed line indicates the average difference
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f4.eps} \end{figure}$	Figure 4: Calculated $\log~gf$ -values (K09) for (⁵D)4d-(⁵D)4f transitions of Fe II are compared with astrophysical $\log~gf$ -values. The horizontal dashed line indicates the average difference.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f5.eps} \end{figure}$	Figure 5: Calculated $\log~gf$ -values (RU98) for (⁵D)4d-(⁵D)4f transitions of Fe II are compared with astrophysical $\log~gf$ -values. The horizontal dashed line indicates the average difference.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f6.eps} \end{figure}$	Figure 6: Comparison of astrophysical $\log~gf$ -values from HR 6000 and 46 Aql for (³H)4d-(³H)4f transitions of Fe II. The horizontal dashed line indicates the average difference.
Open with DEXTER
In the text

$\begin{figure} \par\includegraphics[angle=90,width=8cm,clip]{12518f7.eps} \end{figure}$	Figure 7: The calculated $\log~gf$ -values (calc.) for (³H)4d-(³H)4f transitions of Fe II are compared with astrophysical $\log~gf$ -values obtained averaging $\log~gf$ -values from HR 6000 and 46 Aql. The horizontal dashed line indicates the average difference.
Open with DEXTER
In the text

$\begin{figure} \includegraphics[angle=90,width=14.3cm,clip]{12518f8.eps} \end{figure}$	Figure 8: Comparison of the UVES spectrum of HR 6000 with a synthetic spectrum computed after this study (upper plot) and before this study (lower plot). The black line is the observed spectrum, and the red line is the synthetic spectrum. Nine Fe II lines corresponding to (³H)4d-(³H)4f newly identified transitions are marked in the upper plot. Their calculated $\log~gf$ -values were used to compute the synthetic spectrum.
Open with DEXTER
In the text

$\begin{figure} \par\resizebox{3.in}{!}{\rotatebox{90}{\includegraphics[30,100][6... ...}{\includegraphics[30,100][600,700] {12518fAc.eps}}}\vspace*{5mm} \end{figure}$	Figure A.1: The observed UVES spectra of HR 6000 (black line) are plotted together the computed spectra (red line) in order to show the different slopes of the observed and computed continua. The computed fluxes are scaled by a given arbitrary quantity to be roughly overimposed on the UVES spectra. The ATLAS12 final model with parameters $T_{\rm eff}$ = 13450 K, $\log~g$ = 4.3 was used for the computations.
Open with DEXTER
In the text

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